Decision support system for project monitoring portfolio
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Rafael A. Vallejo Antich Decision Support System for Project Monitoring Portfolio Diploma Thesis for the degree computer engineering Athens, July 2010 National and Technical University of Athens School of Electrical and Computer Engineering Laboratory of Decision Support Systems
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 2 NTUA National and Technical University of Athens Thesis for the degree computer engineering School of Electrical and Computer Engineering Laboratory of Decision Support Systems © Rafael Alberto Vallejo Antich Diploma theses at NTUA, 2010
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 3 Preface This thesis is the result of a diploma project at the Decision Support Systems laboratory at the National and Technical University of Athens (NTUA). The work has been carried out from March 2010 to July 2010. The topic of this thesis is decision support system for project monitoring portfolio. The two concepts were italicised to emphasise some essential delimitations of the thesis. • ‘Decision support system’ means a system which is developed in order to provide a satisfactory solution in a decision problem. Usually, like occurs in the problem that this thesis is focused on, decision problems are characterized by multiple conflicting criteria that must be taken into consideration. These specific decision problems are called multicriteria decision problems. • ‘Project monitoring portfolio’ means that the focus of this thesis will be on the planning of a large number of projects, funded by the European Commission, in order to decide which ones of the whole set of projects are the most appropriate to monitor. The thesis is focused on supporting the Decision Support Systems laboratory in order to solve the multi-criteria decision problem provided to them by the European Commission. As the Commission provides to the DSS’s laboratory a set of projects in order to monitor the most appropriate ones, the goal of this thesis is to support the DSS’s laboratory by selecting those projects that are considered the most important ones to be monitored. When reading the thesis, it is important to realize that this work and the accompanying modellisation of a multi-criteria decision analysis (MCDA) have been carried out by a student of computer engineering, and not by experts in decision analysis. This thesis is divided in two main parts. First, this thesis focuses in the study of the different MCDA methods that have been published in the last years by different expert authors in the decision analysis. The purpose here is to determine which one, from all the different MCDA methods, is the methodology that will fit better to the decision problem that this thesis
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 4 faces. In order to carry out this task, several MCDA methods belonging to different MCDA methodology families will be exposed, by explaining their main features and analysing their procedures. After this, a comparison between all the methods will be made according to the methodology families these methods belong to, and also between the methods belonging to the same family. Once the comparison between the methods has been analysed, the proper method for the decision problem that this thesis wants to solve will be selected. In the second part of this thesis, once the method is selected, the modellisation of the problem according to the chosen method will be carried out. The needed parameters for the method in order to allow it to provide the solution for the described problem will be calculated. Finally, some suggestions for further research will be described in the thesis, as well as the discussion of some conclusions that have been reached during the elaboration of this thesis. Athens, July 2010 Rafael A. Vallejo Antich
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 5 Definitions and Abbreviations MCDA: Multi-Criteria Decision Analysis. The use of methods that support people make decisions according to their preferences in the cases characterized by multiple conflicting criteria. See Section 2.2 for more details. Decision-maker (DM): The person or entity that is responsible of making a decision. The DM can be an individual, a small and homogeneous group with common goals, a big group that represents the different elements of an organisation, or a number of groups of very diverse interests. Stakeholder: Everybody who has a legitimate interest on the system, or “those ones who have the right to impose requisites on a solution”. An alternative definition is those ones who “have demonstrated their need or willingness to participate in the searching of a solution”. See Section 1.7 for more details. Analyst: The person who models the studied situation, helps the DM to reach a satisfactory decision, and formulates recommendations for the final election. The analysts must not express their personal preferences, but must facilitate the obtaining of the DM’s preferences, which should be dealt as objectively as possible. Alternative. Projects, candidates and investment plans, among which a choice has to be made. The term is often used for actions that exclude between them in terms of execution. There can either be a finite number of explicitly defined discrete alternatives or implicitly defined continuous alternatives. Optimal alternative: An alternative that results in the maximum performance value for each of the objective functions simultaneously. An ideal alternative will quite rarely be found in the real-world. Dominance: If – in a pairwise comparison of two alternatives – an alternative A scores higher than alternative B on at least one criterion and does not score lower on any of the other criteria, then A dominates B, while B is dominated by A. Objective: An objective is a statement of something that somebody wants to get and is characterized by a decision context, an object and a direction of preference.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 6 Criterion: A tool constructed for the evaluation and comparison of alternatives and the degree to which they achieve objectives. Criteria offer integral and measurable representations of the DM’s preferences. Quantitative criterion: A criterion that can be measured on a clear, concrete defined scale. Qualitative criterion: A criterion for which evaluations cannot be made on a numerical basis. Instead, a verbal scale or an ordinal ranking can be used. Attribute: A quantitative measure of performance, used to evaluate directly or indirectly the degree to which the objectives are achieved. A good attribute both defines precisely what the associated objective means and serves as a scale to describe the consequences of the alternative. Criteria weight: Assessment of the relative importance of a given criterion. The weight of a criterion can reflect both the range of difference of the options and how much that difference matters.
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National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 8 Table of Contents 1. Description of the problem ....................................................................... 13 1.1 The EuropeAid program ......................................................................... 14 1.2 The ROM system ....................................................................................... 15 1.2.1 What is the ROM system? ................................................................. 15 1.2.2 Why is the ROM system important? ................................................ 15 1.2.3 The ROM system in practice ............................................................ 16 1.3 Monitoring ................................................................................................. 17 1.4 Which projects should be monitored? ................................................. 18 1.5 Available input parameters ................................................................... 19 1.6 Required outputs ..................................................................................... 21 1.7 Stakeholder Analysis ................................................................................ 22 1.7.1 The European Commission and Internal Stakeholders ................ 22 1.7.2 Development companies ................................................................ 23 1.7.3 The end-users/customers ................................................................. 24 1.7.4 Other companies .............................................................................. 25 1.7.5 Third party ........................................................................................... 25 2. Bibliographical Review .............................................................................. 27 2.1 Decision Support Systems ....................................................................... 30 2.1.1 Definitions ........................................................................................... 30 2.1.2 Brief history .......................................................................................... 31 2.1.3 Function and features ...................................................................... 32 2.1.4 Taxonomies ........................................................................................ 33 2.1.5 Architectures ...................................................................................... 34 2.1.6 Development environments ............................................................ 35 2.2 Description of the Multi-Criteria Decision Support Systems ............... 37 2.2.1 Multi-Objective Decision Making (MODM) and Multi-Attribute Decision Making (MADM) ......................................................................... 38
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 9 2.2.1.1 Alternatives .................................................................................. 38 2.2.1.2 Multiple Attributes ....................................................................... 39 2.2.1.3 Conflict among Criteria ............................................................. 39 2.2.1.4 Incommensurable Units ............................................................. 39 2.2.1.5 Decision Weights ......................................................................... 39 2.2.1.6 Decision Matrix ............................................................................ 40 2.2.2 Classification of MCDM Methods ................................................ 40 2.3 Multi-Criterial Methodologies ................................................................. 42 2.3.1 The Weighted Sum Model (WSM) method.................................... 42 2.3.1.1 Explanation of the WSM method ............................................. 42 2.3.1.2 Applying the WSM Method ....................................................... 43 2.3.2 The Weighted Product Model (WPM) method ............................. 44 2.3.2.1 Explanation of the WPM method ............................................. 44 2.3.2.2 Applying the WPM Method ....................................................... 46 2.3.3 The AHP (Analytic Hierarchy Process) method............................. 47 2.3.3.1 Explanation of the AHP method ............................................... 47 2.3.3.2 Applying the AHP Method ........................................................ 47 2.3.4 The Analytic Network Process (ANP) method .............................. 50 2.3.4.1 Explanation of the ANP method .............................................. 50 2.3.4.2 Applying the ANP Method ........................................................ 52 2.3.5 The ELECTRE method ........................................................................ 55 2.3.5.1 Explanation of the ELECTRE method ........................................ 55 2.3.5.1.1 Brief History............................................................................. 55 2.3.5.1.2 ELECTRE’s versions ................................................................ 55 2.3.5.2 Applying the ELECTRE Method ................................................. 56 2.3.5.2.1. Example of the ELECTRE Method ...................................... 56 2.3.5.2.2. Study of the different versions of the ELECTRE Method . 62 2.3.5.2.2.1 ELECTRE I .......................................................................... 63 2.3.5.2.2.2 ELECTRE III ........................................................................ 66 2.3.5.2.2.3 ELECTRE IV ....................................................................... 68 2.3.5.2.2.4 ELECTRE IS ........................................................................ 69 2.3.6 The Promethee method ................................................................... 70
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 16 information allocated there is available to all the members contracted by the EC in order to get the necessary data for the efficient evaluation and monitoring of projects. Furthermore, this information is also useful for the EC, as these data provide an overview of the performance of its aid portfolio. In addition, ROM also provides benefits at the level of programming and learning. Quantitative and qualitative studies based on ROM data contribute lessons learned and best practices to the programming and planning of new projects (Clauss & Hall, 2009). 1.2.3 The ROM system in practice The ROM system is executed by the external organisations (in this case the Decision Support Systems laboratory of the National and Technical University of Athens), contracted by the European Commission, that are responsible for the monitoring of the projects in different geographical zones. ROM monitors carry out onsite visits to projects and programmes in all countries, reviews of the most important documents of the project and, interviews with the main stakeholders, which are the beneficiaries of the project. Based on empirical data, they produce and deliver objective, impartial and concise reports.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 17 1.3 Monitoring The ROM system, as its name says, is a kind of monitoring system. This means that its task is to perform regular reviews in order to keep track of the progress of a project in terms of use of resources, execution, delivery of results and risk management. Monitoring is the systematic and continuous collection of data, analysis and use of management information in order to provide decision support especially at the level of operational management. Monitoring often focuses only on inputs, activities and outputs. This means that the monitoring process evaluates the results obtained according to the outputs of the project and also, informs about how these outputs came to be according to the inputs and the activities that took place. However, the ROM system also focuses on the results (which are the benefits obtained from these outputs) and on the impact (contribution of the project to the solution of a problem). Therefore, the European Commission expects that the organisations contracted by them (included the National and Technical University of Athens) will carry out the tasks of monitoring of the projects provided to each one of them.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 18 1.4 Which projects should be monitored? The Decision Support Systems laboratory, as mentioned above is a contracted member of the European Commission with the task to carry out the ROM process for a number of projects funded by the Commission. The laboratory is provided with a list of projects to be monitored from EuropeAid. This list isn’t limited to one thematic area or geographical region, unless the contract refers to a specific one. The EC expects that the DSS laboratory will select a group of projects to monitor due to the high financial and human resources’ cost that would be inflicted if all projects were to be monitored. The selection of the projects that will be monitored is a central organizational task for the laboratory, which is carried out using both qualitative and quantitative criteria.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 19 1.5 Available input parameters In order to decide which projects will be monitored it will be necessary to make use of all the information available for the projects. This information can be found in the CRIS database, which contains all the information related to all the projects funded by the European Commission. Information collected in this database can be accessed only by people authorised by the EC. The DSS laboratory, as a member organization contracted by the European Commission, has access to the CRIS database. For each project there are 63 attributes that contains information on various aspects. The problem is that not all these attributes are given for all the projects, so for some projects this information has to be excluded from the decision process. Moreover, not all of these attributes are represented in the same data types. Therefore, there are attributes whose value is just a name (sometimes one name selected from a list of defaults) and other attributes whose value is just a date or even a number. The list of all the attributes that are available for each project is shown in the Table 1.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 20 1. Domain 2. Step number 3. Contract 4. Planned amount 5. Former system reference 6. Paid 7. Contract 8. Balance 9. Status 10. Payment currency 11. Title 12. Decision No 13. Delegation 14. Commitment type 15. Entity 16. Commitment ID 17. Contract type 18. Budget line 19. Nature 20. DAC Code 21. Sub-nature 22. Sector code 23. Type of services 24. Budget Management Type 25. Contractor’s signature date 26. Legal justification 27. Expiry date 28. Payment class 29. EC signature date 30. Serial number 31. Closing date 32. Value date 33. Implementation starting date 34. Workflow type 35. Contracting party 36. Status 37. Payment currency 38. Mailing Entity Ref. 39. Geographical zone 40. Mailing Entity Ref. 41. Person in charge 42. Negotiated Procedure Type 43. DG 44. Signature refusal 45. Nationality 46. Action location 47. Call reference 48. Publication allowed 49. Procedure 50. Reason to restrict the publication 51. Negotiated procedure type 52. Final date for implementation (FDI) 53. Legal Entity (LEF) 54. Contractual currency 55. Geographical zone (LEF) 56. Specific payment currency 57. Bank Account Ref (BAF) 58. Previous amount in contractual currency 59. Report deadline 60. Paid amount in contractual currency 61. Document type 62. Balance amount in contractual currency 63. Received? Table 1: Set of the provided criteria
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 21 1.6 Required outputs The result that must be provided in the solution of this problem is the collection of all of these projects, the ones that the Commission provided to the DSS laboratory, separated into three different groups: 1) Projects that should be monitored 2) Projects that should be considered for monitoring 3) Projects that are not recommended for monitoring The separation of the projects into these groups must be done according to the importance of each one of the projects. Thus, the most important projects should be collected in the first group. The projects that are considered the less important should go to the third one. Finally, the second group will collect those projects whose level of importance is not so clear. Separation of all the projects into these groups must be made in order to help the decision maker about choosing the projects on which the ROM system must be applied. However, some degree of freedom must be provided to the decision maker about the selection of the project to be monitored. This is the reason for which the second group must also be considered.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 22 1.7 Stakeholder Analysis In a monitoring investment-planning project, there will be many stakeholders. There are many ways to define a stakeholder. For example, stakeholders can be defined like “everybody that has a just interest in the system”, “those who have a right to impose requirements on a solution”, or those that “have demonstrated their need or willingness to be involved in seeking a solution” (Sproles, 2000). It is essential that all parts are interested in the beginnings of the decision process. This makes to be more probable their disposition to cooperate, as they know that decision has not been made yet. (Keeney, 1988). It is common that several actors are directly involved in the planning process. However, in most of the planning problems, there are also many actors that have not been invited to take a direct roll in the decision process, but who would like to participate, because the decisions can affect to their own welfare or to the global stability of the environment (Diakoulaki, Antunes, & Martins, 2005). These actors can be called decision receivers, and it is essential to include some goals in the analysis process for these stakeholders. If it is not possible to involve all the interested ones personally, it could still be advantageous for the decision process asking somebody to play the position roll of the key stakeholders, ensuring in this way that their perspectives won’t be ignored (Dodgson, Spackman, Pearman, & Phillips, 2001). As the projects that are desired to be monitored can be destined to any kind of sector (education, sanitation, nutrition, etc.), the stakeholders that are involved in this problem are quite diverse. However, in the following lines, the most important stakeholders in monitoring-planning problems will be presented. 1.7.1 The European Commission and Internal Stakeholders The most important beneficiary in a monitoring-planning problem provided by the European Commission is, obviously, this very organisation which desires to carry out a monitoring tasks among the projects that the EC funds. However, this organisation cannot be considered as a homogeneous group. Inside the EC, there are groups that not necessary share the same functions, for example, the
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 23 leadership, the managers and the employees of the commission. Together, these groups are constituted as the internal stakeholders in the EC. The EC’s leadership will make decisions according to the strategies, plans and budget limits of the commission. For the managers, the most essential goal is usually to get the maximum benefits according to the tasks on which they are assigned to. The EC, as a part of the European Union carries out a large number of projects. The monitoring-planning of projects is just one of the big amounts of tasks realized by the EC. The proper managers are the ones that try to get as much benefits as possible for the monitoring-planning project, while the leaderships try to get the maximum benefit from the whole set of tasks carried out by the EC. The employees, on the other hand, desire the commission to make decisions which will protect their jobs and/or provide them interesting and challenging responsibilities and professional development. Consequently, is important for the EC to care about the wills and values of the employees, although it is possible that there are many different opinions between employees about how diverse actions will affect to the criteria. The employees are not the less value asset in an organisation, but the most valuable one (Bogetoft & Pruzan, 1997). It is also fundamentally to take into account that in the EuropeAid program, the program funded by the EC and hence, which belongs to it, may have numerous divisions and subsidiaries that work in different sectors. Different divisions don’t need to agree about the main goals of the organisation, and it is essential the DMs to be conscious about such a powerful differences. Finally, as the funds that the EC and, hence, the European Union receive are from all the countries that constitute the EU, the set of these countries can be also considered stakeholders. Also, as the funds that each member country of the EU come from their population, the whole population among these country can be also considered stakeholders, because the economic resources that will be spend by the EC come from each country and, then, from the budgets of each person that lives in a member country of the EU. 1.7.2 Development companies The main development companies are those ones which are involved in the realization of the projects funded by the EC (through the EuropeAid program). Development companies are often important interested parts in the monitoring-
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 24 planning process because the monitoring of the projects that these companies carry out will de done (or not) according to the decisions made by the DSS’s laboratory. Moreover, these companies are in contact with the EC, and in many cases evaluations made to their development process can be a useful tool for them to know how can them to improve their development process. Different development companies, obviously, have different criteria, but probably the objectives of a development company include the ending on time of the project that they carry out, without exceeding the funds invested by the EC. 1.7.3 The end-users/customers The end-users of the monitoring-planning process are the customers of the different projects funded by the EC and which are provided to the DSS’s laboratory in order to monitor the appropriate ones. The end-users are key actors in the system, because they will be the customers of the services delivered through the EuropeAid program. However, customers are in some measure neglected in the development projects process, because they usually don’t know when the investment decisions are carried out. In some measure, it would be useful to include the opinions of the customers in the decision analysis by contacting the associations or groups related to each one of the projects that is wanted to carry out. However, as the task carried out by the DSS’s laboratory is provided by the EC, this commission is which should care about the customer’s opinions. Also it can be necessary to distinguish between users and owners of the companies that will carry out the different projects. Users are the persons that will get any benefit in the implementation of each project. Owners of the companies can be the organisations or companies that will be selected by the EC through the EuropeAid program in order to develop the projects for which the EC makes investments on them. Therefore, the owners and leaderships of these organisations are also stakeholders in the monitoring-planning process. Different end-users groups have not necessary the same interests or the same influence power for the important decisions. For example, the benefits of the end-users are not the same as the owner of the companies. End-users only will get the benefits related to the purposes on which different projects are focused on. On the other hand, the owners of companies will try to maximize the economical benefits of developing of the projects that they were assigned to implement by the EC.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 25 1.7.4 Other companies Many other companies will also be affected by the investment decisions carried out by the EC. Even the task developed by the DSS’s laboratory is just to choose the set of projects that are better to monitor, this decision will make the EC to monitor and to analyze the selected projects. Because it has been proved that this monitoring of projects can help managers to get a better performance on them, it can be said that this decision will affect the develop process of several projects. As mentioned above, companies selected by the EC to carry out specific projects are important stakeholders. However, these companies or organisations may also hire the services of another companies or organisations to realize specific tasks of the proper project. These new companies are also considered to be stakeholders of this monitoring-planning process. Nevertheless, these companies are unlikely to be between the main stakeholders. Moreover, there will be also many rival companies that will try to be selected by the EC to develop each one of the different projects. However, they cannot be considered as stakeholders, because –obviouslythe decisions of an organisation must not be based on the goals of other companies. 1.7.5 Third party Third parties can include different kind of groups, like public in general, press, diverse non-governmental organisations (environmental, trade, etc.), and future generation. Some of these groups could be important actors for some projects. Public opinion will be important in many cases; the opinions of potential customers are especially important. This includes persons who live in areas specially affected by the decided projects. If some projects are developed with a bad reputation, some companies could refuse to carry on other projects. Also it will be essential to establish good communication with the people of the affected are. Maybe it will be difficult to carry out major projects if the affected people are against their development.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 32 intelligence, human-machine interaction, simulation methods, software engineering and telecommunications. The DSS’s also have a weak connection with the paradigm of hypertext user interface. Both the PROMIS system (for medical decision making) at the University of Vermont, as the system ZOG / KMS (for military decision-making and business) at Carnegie Mellon were two systems of decision support that constituted great advances in user interface research. Moreover, although the hypertext researches, in general, have entered the information overload, some researchers, notably Douglas Engelbart, have focused on decision making in particular. 2.1.3 Function and features The DSS’s are very useful tools in Business Intelligence (Business Intelligence); allow the analysis of different variables to support business decision making process of managers: § It can extract and manipulate information in a flexible manner. § Help unstructured decisions. § Allows the user to interactively define information needs and how to combine. § It usually includes simulation tools, modelling, etc. § It can combine information from transactional systems inside the company with another foreign company. Its main feature is the capability of the multidimensional analysis (OLAP) that allows in-depth information to reach a high level of detail, analyzing data from different perspectives, make projections of information in order to predict what should happening in the future, trend analysis, prospective analysis, etc. A DSS supports people who have to make decisions at any level of management, whether individuals or groups, semi-structured situations and in informal, through the combination of human judgment and objective information: § Supports multiple interdependent or sequential decisions. § Offers assistance in all phases of decision-making process-intelligence, design, selection, and implementation, as well as a variety of processes and decision-making styles. § It is adaptable by the user at the time to deal with changing conditions.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 33 § Generates learning, resulting in new demands and refinement of the application, which in turn results in further learning. § Generally uses quantitative models (standard or custom made). § DSS are equipped with an advanced knowledge management component that enables effective and efficient solution of complex problems. § Can be implemented for use in web or desktop environments on mobile devices (PDA). § Allows easy implementation of sensitivity analysis. 2.1.4 Taxonomies As with the definition, there is no universally accepted taxonomy for DSS. Different authors propose different classifications. Using the relationship with the user as a criterion, Haettenschwiler (Haettenschwiler, 1999) distinguishes between: § Passive DSS: Is a support system for decision-making process, but can not carry out decision suggestions or solutions. § Active DSS: Can bring out such decision suggestions or solutions. § Cooperative DSS: Allows the charge of making decisions (or their advisers), alter, expand or improve decision suggestions provided by the system before shipping back to the system for validation. The new system improves, complete and accurate the suggestions of the decision maker and sends them back to her for validation. Then, the whole process begins again, until it generates a consolidated solution. Using the method of assistance as a criterion, Power (Power D. J., 2002) distinguishes between: § Model-driven DSS’s: Emphasis is placed on the access and manipulation of a statistical model, financial, optimization or simulation. Use data and parameters provided by users to assist decision makers in the analysis of a situation, which are not necessary intensive data. Dicodess is an example of a DSS based on open source models. (Gachet, 2004) § Communication-driven DSS’s: They have support for multiple people working on the same shared task.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 34 § Data-driven DSS’s: Also called data-oriented, emphasize access and manipulation of time series of internal company data and sometimes also external data. § Documents-driven DSS’s: Manage, retrieve and manipulate unstructured information in a variety of electronic formats. § Knowledge-driven DSS’s: They provide experience in the form of facts, rules, procedures, or similar structures specialized for solving problems (Power D. J., 2002) 2.1.5 Architectures Again, different authors identify different components of a DSS. Sprague and Carlson, (Sprague & Carlson, 1982) identify three basic components which are explained in more detail by Haag and others (Haag, Cummings, McCubbrey, Pinsonneault, & Donovan, 2000): § The management system of the data base: Stores information from various sources, may come from data repositories of a traditional organization, from external sources (such as Internet), or staff (of ideas and experiences of individual users). § The model management system: It deals with representations of events, facts or situations by using various types of models (two examples are models of search optimization and target models). § The management system and the dialogs generator: It consists on a user interface; is, of course, the component that allows to a user to interact with the system. For Power (Power D. J., 2002) a DSS has four basic components: § The user’s interface. § The data base. § The analytic and modelling tools. § The DSS’s architecture and net. Hättenschwiler (Haettenschwiler, 1999) identifies five components in a DSS: § Users: With different roles or functions in the decision making process (decision maker, consultants, domain experts, system experts, data collectors). § Decision context: Must be specific and definable.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 35 § Target system: This describes most of the preferences. § Knowledge basis: Composed of external data sources, knowledge databases, working databases, data warehouses and meta-databases, mathematical models and methods, procedures, inference and search engines, administrative programs, and systems reports. § Work environment: For the preparation, analysis and documentation of decision alternatives. Marakas (Marakas, 1999) proposes a general architecture consisting of five distinct parts: § The management data system. § The management models system. § The engine of knowledge. § The user interface. § The users. 2.1.6 Development environments The DSS systems are not totally different from other systems and require a structured approach. Sprague and Watson (Sprague & Watson, 1993) provided an environment of three main levels: 1Technology levels: Is proposed a division in 3 hardware and software levels for DSSs: a. Specific DSS: Real application that will be used by the user. This is the part of the application that allows the decisions making in a concrete problem. User will be able to act over this concrete problem. b. DSS generator: This level contains environmental hardware and software that allows to persons be able to develop easily DSS specific applications. This level uses case tools. Also includes special programming languages, functions libraries and linked schedules. c. DSS’s tools: Contains low level hardware and software.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 36 2People involved: For the DSS’s development cycle, 5 types of users are suggested: a. Final user b. Intermediary c. Developer d. Technical support e. Systems expert 3The development approach: The approach based on the development of a DSS should be very iterative. That will allow the application to be changed and redesigned at different intervals. The initial problem is used to design the system and then it is tested and revised to ensure that it achieves the desired result.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 37 2.2 Description of the Multi-Criteria Decision Support Systems Nowadays, there exist several mathematical tools appropriate in order to support the decision makings with multiple criteria. In the multi-criteria decision making the attribute term makes refer to the features that describe each one of the alternatives available in a decision situation. This concept refers to values related to an objective reality. However, criteria constitute attributes, objective or goals that are considered relevant for a certain decision problem. In a general point of view, (Zeleny, 1982) defines criteria as measures, rules and standards that lead the decision. Therefore, the multi-criteria decision theory constitutes a general frame or decisional paradigm on which different attributes, objectives or goals underlie. Several authors have described, in a general way, a multi-criteria decision problem, highlighting the different parts and phases of it. Between these authors are (Zeleny, 1982), (Chankong & Haimes, 1983) and (Goicoechea, Hansen, Duckstein, & Goicochea, 1982), which have constituted an obligated reference source in the elaboration of the algorithm for the steps of the multiple criteria decision problem. The discrete multi-criteria methods suit to the problems on which the number of alternatives that must be considered by the decision centre is finite and normally not very elevated. Practical interest of the discrete multi-criteria problems (multi-attribute) is evident. In effect, there are so many decisional contexts on which a reduced number of alternatives and possible choices must be evaluated based on various attributes or criteria. In order to take decisions is important to realize a set of actions that allow deciding acceptably between the possible choices. First of all, it must be determined the necessity of a decision that is generated by a problem or gap between a desire and the real condition of the moment. After, it will be required to identify the decision criteria and to assign weight to these criteria in order to give priority to the most important ones in the decision. Then, it must be developed all alternatives or possible solutions to the problem and, if it’s not possible, to know all the ways that can be taken in order to solve the problem. The more alternatives are available, the more probably to find a satisfactory one. Evaluating each one of the alternatives would be the other action in this
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 38 process. This means, to realise a detailed study of each one of the possible solutions in an individual way respect on the decision criteria. There exist tools, in order to evaluate different alternatives. Finally, must be selected the best alternative (decision making): When the best alternative is selected the decision making process has arrived to the end of the process. From this, is necessary to implement the decision in order to evaluate if the decision was or not successful and to evaluate the results. 2.2.1 Multi-Objective Decision Making (MODM) and Multi-Attribute Decision Making (MADM) Multi-Criteria Decision Making (MCDM) is one of the most common methods of decision making. MCDM is divided into multi-objective decision making (MODM) and multi-attribute decision making (MADM) according to many authors (Zimmermann, 1996). Nevertheless, usually MADM and MCDM are used to refer the same class of models. The MODM studies decision problems where the decision space is continuous. The typical examples are mathematical problems with several objective functions. Kuhn and Tucker (Kuhn & Tucker, 1951) wrote the first reference to this problem, also known as “vector-maximum” problem. However, MCDM/MADM concentrates on problems with discrete decision spaces. Problems with discrete decision spaces are the ones on which the set of alternatives has been predetermined. In spite of MCDM methods can be really diverse, most of them have some common aspects. These are the notions of alternatives and attributes (that can also be called goals or decision criteria) as described below. 2.2.1.1 Alternatives Usually they represent the different options of action that are available to the decision maker. Often, set of alternatives is assumed to be finite, ranging from several to hundreds. They are supposed to be screened, sorted and, sometimes, also ranked.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 39 2.2.1.2 Multiple Attributes The MCDM problems are associated with many attributes. The attributes are also referred as “goals” or “decision criteria”, because are the criteria on which the decision must be taken. They represent the different dimensions which the alternatives can have information on. In the cases on which the number of criteria is large (i.e. more than a dozen), criteria may be collected in a hierarchical way. That means, some criteria may be major ones. In this case, each major criterion should be associated with several sub-criteria. Then, each sub-criterion should be associated with several sub-sub-criteria and so on. 2.2.1.3 Conflict among Criteria Because different criteria represent different dimensions of alternatives, they can conflict with others. For example, cost can conflict with benefits etc. 2.2.1.4 Incommensurable Units Often, different criteria are associated with different units of measure. For example, in the case of calculate the profit of a company, the criteria “costs” and “benefits” can be measured in different units; in this case, dollar and euros for example. 2.2.1.5 Decision Weights Many of the MCDM methods require assigning weights of importance to the criteria. This is because not all the available criteria provide the same information, so one criterion can be much more important than another one(s) in terms to decide which alternative must be taken.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 40 2.2.1.6 Decision Matrix Any MCDM problem can be expressed in a matrix format. The decision matrix A is an (m x n) matrix in which element aij indicates the performance of alternative Ai when is evaluated in terms of decision criterion Cj (for i = 1, 2, 3, ..., m, and j = 1, 2, 3, ..., n). It is also assumed that the decision maker has determinate the weights of relative performance of the decision criteria (denoted as wj, for j = 1, 2, 3, ..., n). This information is best explained in the definition given by Zimmermann (Zimmermann, 1996). But there, instead of the term “criteria”, the author uses the term “goals”. Let A = {Ai, for i = 1, 2, 3, ..., n} be a (finite) set of decision alternatives and G = {gj, for j = 1, 2, 3, ..., m} a (finite) set of goals according to which the desirability of an action is judged. Determine the optimal alternative A* with the highest degree of desirability with respect to all relevant goals gj. Figure 1 A Typical decision matrix 2.2.2 Classification of MCDM Methods There are a lot of MCDM available methods in the literature. Each one of them has its own features. There are a lot of ways to classify MCDM methods. One of them is by classifying them according to the data type they use. This means, that it can be deterministic, stochastic, or fuzzy MCDM methods [for an overview of fuzzy MCDM methods see (Chen & Hwang, 1999)]. The deterministic approach considers that the decision making problem (i.e. the alternatives, criteria, etc.) are perfectly described before applying the decision method. The stochastic (also known as probabilistic) corresponds to a type of modelling in
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 41 which the criteria are viewed as random variables. Finally, fuzzy methods consider different types of uncertainty and imprecision in some of the elements of the decision making problem. However, there can be situations which involve combinations of all the above (such as stochastic and fuzzy) data types. Another form to classify the MCDM methods is according to the number of decision makers that are involved in the decision process. Therefore, there exist single decision maker MCDM methods and group decision makers MCDM methods. In this thesis we will only focus our attention to single decision maker MCDM methods. In conclusion, it must be stated that there are a lot of other alternative ways in order to classify MCDM methods (Chen & Hwang, 1999). But, these previous ones are the most common schemes.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 48 Figure 3 Diagram of the Levels in the AHP method PAIR-BY-PAIR COMPARISON MATRIX FOR HIERARCHY LEVEL 2: Attributes Attributes A1 A2 A3 A1: Cost 1 2 5 A2: Environmental Impact 1/2 1 3 A3: Execution Time 1/5 1/3 1 Then, the values of the weights Wi must be calculated: Min n1 + p1 + n2 + p2 + n3 + p3 W1 – 2W2 + n1 – p1 = 0 W1 - 5W3 + n2 – p2 = 0 W2 – 3W3 + n3 – p3 = 0 W1 + W2 + W3 = 1 Therefore, the relative weights of level 2 are W = (0.588, 0.294, 0.118)
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 49 PAIR-BY-PAIR COMPARISON MATRIX FOR HIERARCHY LEVEL 3: Cost: Alternatives A B C A 1 6 3 B 1/6 1 ½ C 1/3 2 1 Environmental Impact: Alternatives A B C A 1 1/9 1/5 B 9 1 2 C 5 1/2 1 Execution Time: Alternatives A B C A 1 1/2 1/4 B 2 1 1/2 C 4 2 1 Therefore, the relative weights for the level 3 are: Cost: W = (0.667, 0.111, 0.222) Environmental impact: W = (0.069, 0.621, 0.31) Execution time: W = (0.143, 0.286, 0.571)
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 50 So, the determination of the global weights is: Figure 4 Diagram of the Levels in AHP after calculating the weights Therefore: A: 0.667*0.588 + 0.069*0.294 + 0.143*0.118 = 0.429 B: 0.111*0.588 + 0.621*0.294 + 0.286*0.118 = 0.282 C: 0.222*0.588 + 0.31*0.294 + 0.571*0.118 = 0.289 So, the route A of the highway’s tram is the best solution 2.3.4 The Analytic Network Process (ANP) method 2.3.4.1 Explanation of the ANP method The Analytic Network Process (ANP) is a more general way that the Analytic Hierarchy Process (AHP) used in multi-criteria decision analysis.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 51 AHP structures a decision problem in a hierarchy with a goal, the decision criteria and the alternatives, while the ANP structures it like a network. Both then use a system of pairwise comparisons in order to measure the weights of the structure’s weights and, finally, to classify the alternatives of the decision. In the AHP, each element of the hierarchy is considered independent of all of the rest, the decision criteria are considered independents between them, and alternatives are considered independents of the decision criteria and of each other. But in many cases of the real world, there exist interdependence between the items and alternatives. ANP doesn’t require the independence among the elements, so it can be used as an efficient tool in these cases. In order to illustrate this, consider a simple decision about the buying of an automobile. The decision maker desires it, can choose among several sedans of complete size with more moderate prices. Decision maker could choose to base his decision in just three factors: buying price, security and comfort. Both the AHP and ANP provide useful frames to use in the decision making. The AHP may suppose that the buying price, security and comfort are independents among them, and would evaluate each one of the sedans in a independent way in those criteria. The ANP will allow the consideration of the interdependence of prices, security and comfort. If one person wants to get more safety or comfort features by paying more for the automobile (or less by paying less), the ANP could take this into account. Similarly, the ANP could allow the decision criteria to be affected by the traits of the cars under consideration. If, for example, all cars are very, very safety, the importance of security as an appropriate decision criterion could be reduced. Academic articles about the ANP appear on the journals and take care about the decision sciences, and several books have been written about the subject (Saaty T. , 1996) (Saaty T. L., 2005) (Saaty & Vargas, 2006) (Saaty & Cillo, 2009). There are a big number of practical applications of the ANP, many of them relative to the complex decisions about the benefits (B), opportunities (O), costs (C) and risks (R). The study of these applications can be very useful to understand complexities of the ANP. Literature has hundreds of elaborated process examples, developed by executives, managers, engineers, MBA and Ph.D. students and other persons from many countries. A hundred of those uses are illustrated and discussed in the Encyclicon, a dictionary of the decisions with the dependence and the feedback (Saaty & Cillo, 2009).
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 52 Academics and practitioners meet biennially at the International Symposium on the Analytic Hierarchy Process (ISAHP), which, despite its name, devotes considerable attention to the ANP. 2.3.4.2 Applying the ANP Method Understanding of the ANP is better obtained by using the software of the ANP in order to work with the completed decisions. One of the field normative texts provides the steps that must be followed (Saaty T. L., 2005): 1Make sure that the decision problem in detail is understood, including its objectives, criteria and sub-criteria, actors and their objectives and the possible outcomes of that decision. Give details of influences that determine how that decision may come out. 2Determine the control criteria and sub-criteria in the four control hierarchies’ one each for the benefits, opportunities, costs and risks of that decision and obtain their priorities from paired comparison matrices. You may use the same control criteria and perhaps sub-criteria for all of the four merits. If a control criterion or sub-criterion has a global priority of 3% or less, you may consider carefully eliminating it from further consideration. The software automatically deals only with those criteria or sub-criteria that have subnets under them. For benefits and opportunities, ask what gives the most benefits or presents the greatest opportunity to influence fulfilment of that control criterion. For costs and risks, ask what incurs the most cost or faces the greatest risk. Sometimes (very rarely), the comparisons are made simply in terms of benefits, opportunities, costs, and risks by aggregating all the criteria of each BOCR into their merit. 3Determine a complete set of network clusters (components) and their elements that are relevant to each and every control criterion. To better organize the development of the model as well as you can, number and arrange the clusters and their elements in a convenient way (perhaps in a column). Use the identical label to represent the same cluster and the same elements for all the control criteria. 4For each control criterion or sub criterion, determine the appropriate subset of clusters of the comprehensive set with their elements and
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 53 connect them according to their outer and inner dependence influences. An arrow is drawn from a cluster to any cluster whose elements influence it. 5Determine the approach you want to follow in the analysis of each cluster or element, influencing (the suggested approach) other clusters and elements with respect to a criterion, or being influenced by other clusters and elements. The sense (being influenced or influencing) must apply to all the criteria for the four control hierarchies for the entire decision. 6For each control criterion, construct the super-matrix by laying out the clusters in the order they are numbered and all the elements in each cluster both vertically on the left and horizontally at the top. Enter in the appropriate position the priorities derived from the paired comparisons as sub-columns of the corresponding column of the super-matrix. 7Perform paired comparisons on the elements within the clusters themselves according to their influence on each element in another cluster they are connected to (outer dependence) or on elements in their own cluster (inner dependence). In making comparisons, you must always have a criterion in mind. Comparisons of elements according to which element influences a third element more and how strongly more than another element it is compared with are made with a control criterion or sub-criterion of the control hierarchy in mind. 8Perform paired comparisons on the clusters as they influence each cluster to which they are connected with respect to the given control criterion. The derived weights are used to weight the elements of the corresponding column blocks of the super-matrix. Assign a zero when there is no influence. Thus obtain the weighted column stochastic supermatrix. 9Compute the limit priorities of the stochastic super-matrix according to whether it is irreducible (primitive or imprimitive [cyclic]) or it is reducible with one being a simple or a multiple root and whether the system is cyclic or not. Two kinds of outcomes are possible. In the first, all the columns of the matrix are identical and each gives the relative priorities of the elements from which the priorities of the elements in each cluster are normalized to one. In the second, the limit cycles in blocks and the different limits are summed and averaged and again
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 54 normalized to one for each cluster. Although the priority vectors are entered in the super-matrix in normalized form, the limit priorities are put in idealized form because the control criteria do not depend on the alternatives. 10Synthesize the limiting priorities by weighting each idealized limit vector by the weight of its control criterion and adding the resulting vectors for each of the four merits: Benefits (B), Opportunities (O), Costs (C) and Risks (R). There are now four vectors, one for each of the four merits. An answer involving ratio values of the merits is obtained by forming the ratio BiOi / CiRi for alternative i from each of the four vectors. The synthesized ideals for all the control criteria under each merit may result in an ideal whose priority is less than one for that merit. Only an alternative that is ideal for all the control criteria under a merit receives the value one after synthesis for that merit. The alternative with the largest ratio is chosen for some decisions. Companies and individuals with limited resources often prefer this type of synthesis. 11Determine strategic criteria and their priorities to rate the top ranked (ideal) alternative for each of the four merits one at a time. Normalize the four ratings thus obtained and use them to calculate the overall synthesis of the four vectors. For each alternative, subtract the sum of the weighted costs and risks from the sum of the weighted benefits and opportunities. 12Perform sensitivity analysis on the final outcome. Sensitivity analysis is concerned with “what if” kinds of questions to see if the final answer is stable to changes in the inputs, whether judgments or priorities. Of special interest is to see if these changes change the order of the alternatives. How significant the change is can be measured with the Compatibility Index of the original outcome and each new outcome.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 55 2.3.5 The ELECTRE method 2.3.5.1 Explanation of the ELECTRE method 2.3.5.1.1 Brief History The ELECTRE (Elimination Et Choix Traduisant la REalité) methods belong to multi-attribute methods that deal cardinal information. They have been developed from the LAMSADE of the Paris-Dauphine University (Paris IX) since year 1968, year on which Bernard Roy and his collaborators developed the first ELECTRE method. Since then, uses of ELECTRE methods have been extended all over Europe, as has been proved by the big amount of existent literature about these methods and its applications (Roy, 1985) . ELECTRE was conceived by Bernard Roy (Roy, 1985) in response to deficiencies of existing decision making solution methods. ELECTRE is more than just a solution method; it is a philosophy of decision aid - the philosophy is discussed at length by Roy (Roy, 1985). However, other versions of this method, like the ELECTRE III (the most popular of them and the most used) have been published by several authors since then. ELECTRE has evolved through a number of versions (I through IV); all are based on the same fundamental concepts but are operationally somewhat different. It is important to note that ELECTRE is not being presented as the "best" decision aid. It is one proven approach. Simpson (Simpson, 1996) has compared both AHP and ELECTRE and she concludes that, "There are obvious differences between the methods, but it is not obvious that one method is stronger than the other." 2.3.5.1.2 ELECTRE’s versions The first important parameter in the election of an ELECTRE method depends on the kind of problematic included in the project: § For the election of a sub-set with the alternatives “best ones”, or “satisfactory ones” (α problematic) the appropriate methods are ELECTRE I and ELECTRE IS. § For the distribution of the alternatives in categories predefined by reference alternatives (β problematic) the appropriate method is ELECTRE TRI.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 56 § For the sort of the alternatives (γ problematic) it can be applied the ELECTRE II, ELECTRE III and ELECTRE IV methods. Moreover, depending on the logic followed in the classification during the development the ELECTRE methods can be divided in two big groups: § ELECTRE I and ELECTRE II use clear classification (description of the criteria in a classical way) § ELECTRE III, ELECTRE IV, ELECTRE IS and ELECTRE TRI use logic with blurred classification (pseudo-criteria, quasi-criteria or pre-criteria). 2.3.5.2 Applying the ELECTRE Method Despite of the existence of several versions of the ELECTRE Method, the funds of all these versions are the same. New versions of ELECTRE just add some improvements, but the common way on which they work is very similar and will be shown in next section with an example studied by (Buchanan & Sheppard, 2001). 2.3.5.2.1. Example of the ELECTRE Method The example that will be explained in this section will show the way on which all the ELECTRE methods work. In this section will be only consider the common part of all of the different versions of ELECTRE. A set of some projects is given: • Project 1 • Project 2 • Project 3 • Project 4 • Project 5 For each project, there are a number of criteria that measure the impact of each alternative or project. The choice of appropriate criteria can be quite an art and is typically far more difficult than identifying alternatives. The five criteria eventually used to evaluate the projects are:
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 57 • Financial (F) • Solution delivery (SD) • Strategic contribution (SC) • Risk management (RM) • Environmental (E) These are then combined to produce a score for each project for each criterion. The scores for the last four criteria use a 0-100 scale. The financial criterion (Strategic contribution) uses net present value (NPV). This input, where each alternative is assessed using each criterion, produces a matrix of impacts - referred to as performances. Next table provides an example of such a performance matrix, using a subset of five projects. Figure 5 Performance Matrix The subjective inputs are provided by the decision makers and relate specifically to the criteria and their relative importance. There are some methods to establish appropriate weight to each one of the criteria, but this subject is not important in this section and will be explained in next sections. Two important concepts underscore the ELECTRE approach; thresholds and outranking. These will now be discussed. Assume that there exist defined criteria, gj, j=1, 2… r and a set of alternatives, A. Traditional preference modeling assumes the following three relations hold for two alternatives (a, b) 4A: aPb (a is preferred to b) | g(a) > g(b) aIb (a is indifferent to b) | g(a) = g(b) aJb (a cannot be compared to b).
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 64 6%7) V WH,%I)XH,%J) where V. - , and gj(a) is the evaluation of the alternative a for the criterion gj. Therefore, the concordance index takes values between 0 and 1, and also measures the strength of the assertion “the alternative ‘a’ overcomes the alternative ‘b’”. Nevertheless, any overcome of the alternative b by alternative a can be weakened or considered doubtful by the discordance index D(a, b), which is defined as D (a, b) = 0 if gj(a) ≥ gj(b), for j = 0, 1, 2, ..., n Y%7) Z[\]^_` a,%_)bH%J)O=%7)c=%)Pd=%)e=%7)CfA%7) where d is the maximum difference to any criterion and any pair of alternatives. In this way, D(a,b) is an index whose values are between 0 and 1, and increases if the preference of the b alternative over the a alternative is important in at least one criterion. This index can be used, only if the evaluations of the different criteria are comparable and are not of a qualitative nature. If the discordance index reaches a certain threshold value, the overcome of the b alternative by the a alternative that the concordance index could indicate, is rejected. Then, the outranking relation of the ELECTRE I is constructed by comparing the concordance and discordance indices, after the specification of their respective thresholds. If c* is the supposed threshold value specified to the concordance index (concordance threshold equal to 1 as maximum), and d* is the threshold value specified to the discordance index (discordance threshold equal to 0 as minimum), then the S outranking relation, can be defined in this way: g7h6%7)@9 and D (a, b) ≤ d*
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 65 Regarding to the second phase, the exploitation of the outranking relation, the ELECTRE method, by the use of the previous indices, tries to get a partition of the A set of alternatives, which as has been explained previously, is a finite set and contains all the considered feasible alternatives, in two sub sets N and A\N such that: 1Q b 4 A\N, exists a 4 N, such that a S b 2Q a, b 4 N, a notS b and b notS a 3N T A\N is the empty set 4N U A\N = A If a graphical representation of the S relation is made, the N set constitutes the nucleus or kernel of the resultant graph. If this graph does not have circuits, this kernel exists and also contains only one element. In any case, the number of alternatives of the kernel could be reduced, relaxing the values of c* (decreasing from one), and of d* (increasing from 0). Searching for the best compromise solution should be realised with a detailed analysis of the alternatives that share the kernel. Such analysis should be made by a sensitivity analysis, introducing variations in the different used parameters, and by a study of the hardiness of the obtained results, respecting to the mentioned variations. The sensitivity analysis is relatively a classic study in all aspects; software versions that are developed include it from the beginning. However, the hardiness analysis for the multi-criteria decision support is still in a discussion and studying phase. Not all authors are used to this kind of analysis, nor exists another methodology for this purpose yet. Is for this reason for which it must be remarked. Is very important, in order to provide a bigger reliability to the model that is considered, to effectuate the hardiness analysis of the obtained results, subjecting the values of weights and defined thresholds to possible variations and observing the effects on the final results. Normally, the rank of the parameter values on which the result does not change is indicated, and also must be indicated the variables that are crucial to change the chosen alternative. Therefore, with a hardiness study is possible to overcome some of the doubts appeared during the decision process, both by the decision maker, and the analyst, respecting to the original values of parameters. If, introducing variations in both extremes of the established interval for its initial values, results don’t suffer significant changes, then can be said that are robust.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 66 Generally, studying the hardiness of provided results by ELECTRE I, the following values can experiment some variations: • The rank of scales of the used values in the evaluation of the criteria • Weights of criteria (wj) • The concordance threshold c* • The discordance threshold d* 2.3.5.2.2.2 ELECTRE III To build the upper-classification relation, ELECTRE III inserts two criteria thresholds, called indifference and preference thresholds in order to study the concordance. Figure 9 Types of preference according to indifference and preference thresholds Also, a third threshold is included, the veto threshold, used to study the discordance. Agreement indexes Agreement index for each criterion It will be defined an alternative i better than an alternative k for criterion j since the index cj(ai, ak), which is defined as: i j k j l 9%m)"hAe=%m)c=%) "e9%m)eh?e=%m)c=%)5A 9%m)h=%m)c=%)5?E Global concordance index
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 67 The Cik index indicates when the alternative i over-classifies the alternative k, since the formula: 6m.An9%m o - ) .A o - Global indices make a matrix (i × k). Discordance indexes As new in ELECTRE III it includes the veto threshold (vj), which, by definition, is the value of the difference between gj(ak) – gj(ai) from which it is unwise to refuse the over-classification. When the veto threshold value is passed the over-classification must be rejected, independently of what can happen in the rest of the criteria. The construction of the discordance index is shown as follows: i j k j l p%m)"h=%m)c=%)5A "ep%m)ehAe=%m)c=%)5q p%m)hqe=%m)c=%)E Lineal interpolation Algorithm of the method The ELECTRE III method makes two possible partial sorts from the potential alternatives collection. First, a classification of the alternatives is made, from the best one to the less good (descending distillation), which consists on several stages. First, the Potency, Weakness and Qualification sets are defined in every stage of each distillation, which are: § Potency of an action is the set of alternatives that are over-classified by the alternative that is being studied. § Weakness of an action is the set of alternatives that over-classify the alternatives that is being studied.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 68 § Qualification of an action is the set got by the difference between the sets of potent weakness for an alternative. An alternative is better when the biggest (in positive number) the set of Qualification. From these sets several distillations are made until all alternatives have been selected. 2.3.5.2.2.3 ELECTRE IV According to (Figueira, Greco, & Ehrgott, 2005) the name ELECTRE IV was an unofficial name created for designating ELECTRE I with veto threshold. This method is equipped with a different but extremely useful tool. The new tool made possible for analysts and DMs to overcome the difficulties related to the heterogeneity of scales. Whichever the scales type, this method is always able to select the best compromise action or a subset of actions to be analyzed by DMs. The new tool introduced was the veto threshold, vj, that can be attributed to certain criteria gj belonging to the family of criteria F. The concept of veto thresholds is related in some way, to the definition of an upper bound beyond which the discordance about the assertion “a outranks b” can not surpass and allow an outranking. In practice, the idea of threshold is, however, quite different from the idea of discordance level like in ELECTRE I. Indeed, while discordance level is related to the scale of criterion gj in absolute terms for an action a from A, threshold veto is related to the preference differences between gj(a) and gj(b). In terms of structure and formulae, little changes occur when moving from ELECTRE I to ELECTRE IV. The only difference being the discordance condition, now called no veto condition, which may be stated as follows: =%)>qO=%)P@=%7)QR4r To validate the assertion “a outranks b” it is necessary that, among the minority of criteria that are opposed to this assertion, none of them puts it s veto. ELECTRE IV uses the same exploitation procedures as ELECTRE I. But, this method is by no means complete; the problem of imperfect knowledge remains.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 69 2.3.5.2.2.4 ELECTRE IS How general an ELECTRE method can be when applied to choice decisionmaking problems? Is it possible to take into account simultaneously the heterogeneity of criteria scales, and imperfect knowledge about real-world decision-making situations? Previous theoretical research done on thresholds and semi-orders may, however, illuminate the issue of inaccurate data and permit to build a more general procedure, the so-called ELECTRE IS method. The main novelty of ELECTRE IS is the use of pseudo-criteria instead of truecriteria. This method is an extension of the previous one aiming at taking into account a double objective: primarily the use of possible no nil indifference and preference thresholds for certain criteria belonging to F and, correlatively, a backing up (reinforcement) of the veto effect when the importance of the concordant coalition decreases. Both concordance and no veto conditions change. Now, the formulae for each one of theses conditions will be presented separately. Concordance condition: The following two indices sets are introduced: 1. Concerning the coalition of criteria in which aSb rsR4rt=%)>?u=%)v@=%7)w 2. Concerning the coalition of criteria in which bQa rxsR4rt=%)>?u=%)ve=%)5=%7)>A%=%7))w The concordance condition will be: 9%g7)>y@z 4{| 4{} where, yH,%I)GF,uH,%I)vH,%J) F,uH,%I)vK,%H,%I))
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 70 the coefficient φj decreases linearly from 1 to 0, when gj describes the range [gj(a) + qj(a)), gj(a) + pj(gj(a))]. No veto condition: The no veto condition can be stated as follows: =%)>qu=%)v@=%7)>?u=%7)v~ where, ~c9%g7)c czc In the exploitation procedure, actions belonging to a cycle are no longer considered as indifferent as in the previous versions of ELECTRE for choice problems. Now, the concept of degree of robustness of “a outranks b” will be taken into account. It is a reinforcement of veto effect and allows building true classes of ex aequo (ties) and thus defining an acycle graph over these classes. In such conditions there is always a single kernel. 2.3.6 The Promethee method 2.3.6.1 Explanation of the Promethee methods The PROMETHEE methods were purposed for first time in the year 1982 (Brans, 1982). Since then many developments and complementary adaptations to these methods have been carried out. The PROMETHEE methods support the decision maker both in election problems and in classification problems and are based in three stages: 1. Enrichment of the preference structure: This stage is essential. The generalised criterion notion, defined since a preference function, is introduced with the goal of keep in mind the wide of the existent
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 71 difference between the evaluations of two alternatives according to the different criteria. This notion is easily understandable for the decision maker because of all the parameters that are needed to define the criteria correctly have a physical or economical interpretation. 2. Enrichment of the dominance relationship: Takes into account the purposed criteria set. For each pair of actions, a global preference index of one action over another one is established. 3. Supports to the decision: the PROMETHEE I method allows to obtain a partial sort of the alternatives. Is possible to define in which way an alternative is more desired than another one by using the function Pj (a, b) called function on preference for the criterion j, which is based on the existent difference between two evaluations: dj(a,b) = fj(a) – fj(b). This preference function has these following four features: Pj(a, b) = 0 if dj(a, b) ≤ 0 No preference Pj(a, b) ≈ 0 if dj(a, b) > 0 Weak preference Pj(a, b) ≈ 1 if dj(a, b) >> 0 Strong preference Pj(a, b) = 1 if dj(a, b) >>> 0 Strict preference The pair {fj(.), Pj(a, b)} is called generalised criterion associated to the criterion fj(.). If dj (a, b) ≤ 0, Pj (a, b) is null, but Pj (b, a) can be positive. In order to consider all the real line, and not only the positive part, the preference function Hj (dj) is introduced: Hj(dj) = Pj(a, b) if dj(a, b) > 0 Hj(dj) = 0 if dj(a, b) = 0 Hj(dj) = Pj(b, a) if dj(a, b) < 0 2.3.6.2 Applying the Promethee method The PROMETHEE (Preference Ranking Organization METHod for Enrichment Evaluations) method, as a multicriteria decision technique, tries to establish, by
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 72 the evaluation in function of k criteria, f1, f2, ..., fk, a hierarchical sort in the A set of alternatives. The main idea of the PROMETHEE philosophy, consists on enrich the existent dominance relationship between the different alternatives. Because of this, it carries out these following stages: 1) Definition of the generalised criterion This stage requires that each criterion fj must be associated a generalised criterion, pj(x), that will value the preference of an alternative a by respect to another b alternative as a function of the difference between evaluations, fj(a) – fj(b). With the purpose to facilitate the election of a generalised criterion associated to each criterion, Brans et al. (Brans, Vincke, & Mareschal, 1986) propose six different types, for each one of them; the decision maker must fix, as maximum, the level of two parameters with economical meaning. These parameters are the next ones: q (threshold that defines the indifference area), p (threshold that defines the strict preference area) and s (parameter that relates the values of p and q). 2) Construction of the multi-criteria preference index The next step consists on defining a multi-criteria preference index, T(a, b), that measures the degree on which a is preferred instead of b in all the criteria: %7)2%7) m - where wj > 0 (j=1, ..., k) is the weight of importance associated to the j criterion, having . m - . 3) Adoption of the final decision Two sort flows will be considered, the outgoing and the ingoing, that reflect the grade on which i alternative dominates or is dominated by the other rest, and which are defined as follows:
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 73 yG Cc%) 4 y Cc%) 4 The outgoing flow represents the dominant feature of an alternative, its dominant power, because of that it will be better that alternative which has a bigger outgoing flow. The ingoing flow represents the weakness of an alternative, that is to say, how is dominated by the others; therefore, it will be better that alternative which has a little ingoing flow. Throughout these two flows it can be defined a partial order between the alternatives (PROMETHEE I Method). In order to get a total sort of the alternatives (PROMETHEE II Method) the order clear flow is defined: φa = φa+ - φaSo an alternative a will overcome to another alternative b if φa > φb and will be different if φa = φb. This clear order flow deletes the problem of the incomparabilities between alternatives; even part of the provided information by the previous flows gets loose. 2.3.6.2.1 PROMETHEE I and PROMETHEE II methods In the last section, the standard methodology carried out by the PROMETHEE method was exposed, but as many versions of the PROMETHEE were published after the first approach, several variations of this first PROMETHEE version (PROMETHEE I) appeared during the last years. Therefore, the purpose of next sections is to analyse the difference between the existent versions of PROMETHEE. In the following paragraphs, difference among PROMETHEE I and PROMETHEE II is exposed.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 80 Before determine concluded the decision process is recommended the decision maker to effect different sensibility analysis, by simulating diverse distributions of weights. In each case, situation can be seen directly in the GAIA map. For each weights vector the recommended alternatives will be the ones that are allocated in the direction of the decision axis in PROMETHEE. This sensitivity analysis results to be extremely useful for the decision makers, is very simple to perform and to interpret as the alternatives and criteria axes stay immovable while the decision “stick” moves. 2.3.6.2.3 PROMETHEE V As it could be seen in the previous sections, PROMETHEE I and II Methods are particularly appropriate for choosing one alternative. However, in many cases must be selected a subset of alternatives under a set of restrictions that must be verified between the different subsets and inside them. Boolean variables are especially appropriate to face such problems. Considering that {αi, i =1,2,...,n} is the set of feasible alternatives and that to each alternative the following Boolean variables are associated: sz9:z;C "D:;z; E The PROMETHEE V method is performed in two stages. First stage: Initially the multi-criteria problem is considered, without segmentation restrictions. Net outranking flows are calculated φ(αi), i=1,2,...,n and the complete order of the PROMETHEE II is obtained. This can be made by the basic procedure PROMETHEE-GAIA already explained. Second stage: Additional segmentation restrictions are incorporated to the problem by considering the following lineal program (0-1): L.y%) - FFCSA2 - KK?S$ 4 4"C where ~ remains for ≤, ≥ or =.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 81 The φ(αi) coefficients of the objective function are the net outranking flows. The goal of the maximization problem is to collect as much dominance flows as possible in favor to the sub set of alternatives that is going to be selected. Relations .F - and .K 4 express, respectively, the segmentation restrictions between sub sets and also inside each one of them. The P restrictions of the .F - type are restrictions that must accomplish all the sub sets. The different relations of the .K 4 type define restriction inside the sub sets. For each sub set, Qr restrictions must be considered. The formulated restrictions, for both types, can express limitations of cardinality, of budget, of investment, of financing, of marketing … Once the lineal program (0-1) is resolved by using classical tools (Branch and Bound Technique) is possible to obtain a sub set of alternatives that besides satisfying the formulated restrictions, also offers the highest net flow possible. The advantage that PROMETHEE V offers is that allows combining the analysis of the evaluation matrix with a lineal program (0-1) considering segmentation restrictions formulated over the set of alternatives. 2.3.6.2.4 PROMETHEE VI PROMETHEE VI is an extension of the PROMETHEE-GAIA Methodology that offers to the decision maker some information respect to his proper vision of the multi-criteria problem, allowing the decision maker to analyse according to his proper preference structure, depending if he faces to a “hard” or “soft” problem. “Hard” and “soft” terms are frequently used in the United Kingdom to describe Operative Researching Methods. Then, the “hard” term is used to describe analytic methods that generally look for offering optimal solutions. On the other hand, the “soft” term, describes those Operative Researching methods that face to complex difficulties to the obtaining of results. In the multi-criteria ambit on which this thesis is focused on, words “hard” and “soft” have a different connotation: “hard” problems make reference to difficult or complex problems, while “soft” ones refer to easy or simple problems. As it was seen in the previous sections of the PROMETHEE methods, distribution of weights has a relevant roll in all multi-criteria problems. As soon as weights are established, PROMETHEE recommends a final decision.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 82 But in many situations, the decision maker has doubts when he assigns concrete values to weights. This doubt is due to several factors: indeterminacy, imprecision, uncertainty, control deficiency in the real-world situation. However, the decision maker has, usually, in his mind a kind of magnitude for weights, therefore, despite his doubts, is able to formulate some intervals that include appropriate values for weights. Consider that those intervals have this form: 55GR8 where and G are the lower and upper limit, respectively, of the values interval that the weight of the gj(.) criterion can take. Considering the set of the whole extreme points of vectors associated to all the vectors of admissible weight vectors according to the last formula, it can be observed that such set defines a domain over unitary hyper sphere, centred in origin of the k-dimensional space. Projection of this domain onto the GAIA map is called Decision Maker Freedom Space (DMFS). Obviously, the (DMFS) is the geometrical place of the extreme points of the PROMETHEE decision axis (h) for each probable weights set. Two different situations respect to the (DMFS) can be indentified: 1) If (DMFS) does not include the origin of the GAIA map, the PROMETHEE decision axis will remain globally oriented in the same map area when modifications will be introduced in the weights inside the defined interval. In this case, each set of weights allows obtaining similar compromise solutions. Current values of weights are, moreover less relevant in the decision process. The multi-criteria problem is quite simple or easy to solve and therefore is called soft multi-criteria problem. 2) On the contrary, if (DMFS) includes the origin, the PROMETHEE decision axis can have any orientation, depending on the values of weights. In this case, it can be obtained quite different compromise solutions for different sets of probable weights. It results quite complex taking a final decision in this context. Therefore, according to his preferences and doubts, the decision maker faces to a hard multi-criteria problem. It is important to take in account that visually it can be seen which is the difficulty or complexity degree of a multi-criteria problem. It is only necessary
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 83 to analyse the position of the DMFS respect to the GAIA map origin. This process is called PROMETHEE VI. In most of the practical applications and real-world situations deal up to the present days, problems are simple and not too much complex. This means that in most of the multi-criteria problems there exist good and appropriate compromise solutions. This information is of great utility in the decision process. 2.3.7 The MURAME method 2.3.7.1 Explanation of the MURAME method This method is based in the construction of an outranking relation. Pair-wise comparison between alternatives results in the degree of dominance of the one over the other. Such methods, introduced by (Roy, 1968) require less information from the Decision Maker (DM) than methods that create only one score to each alternative, like the multi-attribute utility theory (Keeney & Raiffa, 1976), or the hierarchy analytic process (Saaty T. L., 1980). On the other hand, MURAME can work even there are some evaluation that don’t favour a project instead of another one. Finally, this method takes into account both qualitative and quantitative criteria. For a detailed description of the MURAME see (Goletsis, Askounis, & Psarras, 2001). MURAME is carried out in two main phases, by the combination of the two most popular outranking methods, ELECTRE III (Roy, 1968) (Roy, 1990) and Prométhée (Brans & Vincke, 1985): • In the first phase, the aggregation, the outranking relation is constructed. The DM’s value system is modelled by the criteria definition and its weights, as well as thresholds. The DM’s hesitations between preference and indifference are modelled in a fuzzy way. On the other hand, the use of the threshold is often considered necessary in some kinds of applications. • In the second phase, the exploitation phase, outranking relation is used to provide a recommendation. Calculation of the flows in a similar way
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 84 of the Prométhée method produces a total pre-order. A generalised presentation in the net flows scope can be found in (Bouyssou, 1992). 2.3.7.2 Applying the MURAME method The aggregation phase In the aggregation phase the outranking relation S is constructed. Having two alternatives ai and ak, ai S ak means that alternative ai is at least as good as ak. It will be consider having a set of m alternative proposals A = {a1, a2, . . . , ai, . . . , am} and a consistent family of n criteria F = {C1,C2, . . . ,Cj, . . . , Cn}. The criteria could be both, quantitative and qualitative. Inputs The evaluation matrix. The evaluation matrix (m×n) contains the score gij of each i alternative in each j criterion. There is no need for a common measurement unit. Each quantitative criterion is counted in its own unit while for qualitative criteria a constructed scale should be used. The thresholds qj, pj, vj. In order to reflect the DM’s preference in a realistic way the use of pseudo-criteria was adopted. The three zones scheme (strict preference, weak preference, indifference) was modelled by the use of two thresholds for each criterion j the indifference threshold qj and the preference threshold pj . The values of pj and qj could be constant or have a form α gij + b. In any case qj (gij ) - pj (gij ). There is also a veto threshold vj for each criterion i. This threshold is used for rejecting the hypothesis ai S ak , if in one criterion alternative ai is so much worse than ak, that gij + vj < gkj . Veto threshold vj cannot be less than pj. The weights. The weight vector W = {w1,w2, . . . , wj, . . . , wn} provides the relative importance of each criterion. The weights in an outranking relation should be considered as votes in a voting procedure. We believe that direct weighting usually cannot reflect the DM’s preferences in an effective way. A number of special methods have been developed. There are several methods for the calculation of the weights of each criterion. One of the most common of these methods is the use of personal construct theory, proposed by Rogers and Bruen (Rogers & Bruen, 1998). The calculation of criterion weights with the use of personal construct theory is based on the Personal Construct Theory – PCT (Kelly, 1955) and on its bipolar modelling of the human preferences system. Without analyzing the Kelly’s
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 85 hypothesis, a bipolar construction (extreme) of the two possible cases is associated to each criterion, for example, by the cost: low cost / high cost. For each construct, one of the two cases is the most preferable (for example, the low cost). In a pair-wise comparison between constructors and assuming that the current state is the most preferable for each construct, the DM defines which one of the two constructions he is more willing to see changed to the non preferable situation (or vice versa, which one resists to change). By calculating this resistance-to-change the criterion weights are produced. A symmetrical matrix where the rows and columns represent the constructions can then be created. In a given cell within this resistance grid the following notation signifies the result obtained: (1) a X indicates that the column of the construction “resists to change”, (2) a blank indicates that the row of the construction “resists to change”, (3) an I indicates that the two modifications are equally undesirable, (4) an e indicates that the two constructs change at the same time. The resistance to change is the result of adding the amount of “blanks” in the rows and the X corresponding to each construct. This resistance to change is considered like a measure to know the importance of each criterion. Criterion wj is then , . where RtC means Resistance-to-Change. Calculation of indices The concordance–discordance indices. Local concordance cj (ai, ak), concordance Cik and discordance dj (ai, ak) indices are calculated according to the ELECTRE III model. The outranking index O aggregates the concordance and discordance indices in order to indicate how much ai outranks ak. The exploitation phase In order to rank the preferences, the outranking index O is used to calculate entering and leaving flows for each alternative: leaving flow: yG%).%m) m
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 86 entering flow: y%).%mm ) Leaving flow +(ai) indicates the strength of alternative ai over all remaining alternatives. Vice versa, entering flow -(ai) indicates the weakness of alternative ai (by indicating the strength of all other alternatives over it). The net flow is defined as follows: y%)yG%)cy%)L The alternatives can be then ranked according the net flow (in a descending order). In this way a total preorder is produced. Missing evaluations It is common, especially when the list of alternatives is long, that some evaluation have disappeared. MURAME ensures that missed evaluations do not affect to the pair-wise comparisons. In case a grade gij is missing when alternative ai is compared to ak, under criterion j, it is assumed that gij = gkj, which means that the missing grade is replaced by the one that it is compared to. In this way, there is cj (ai, ak)=cj (ak, ai ) = 1, Q b 4 A, dj (ai, ak)=dj (ak, ai ) = 0, Q b 4 A, and it will be ensured that any alternative will not be favored. Alternative solutions could include the removal of the criteria which corresponds with the missed value or the substitution of this missed value for another one (for example, the average or the most frequent value). However, first solution would alter the criteria weights giving too much importance to other criterion or criteria (especially if the deleted criterion is essential). In terms of the second solution, the missed values could not statistically been produced with the use of a statistical method or a more advanced data mining technique because there is no reason justifying such a replacement.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 87 2.3.7.3 Group support techniques for the MURAME method 2.3.7.3.1 The aggregation of individual preferences The aggregation of individual preferences does not get by the aggregation of the individual classification, as is suggested in some methods like (Cook & Seiford, 1982). On the contrary, with the purpose to take the preference intensities into account, the individual preference flows are used. This is achieved with the technique suggested by Macharis et al. (Macharis, Brans, & Mareschal, 1998). Figure 10 Aggregation of preferences The main idea is the weighted addition of the individual preferences of each member gm of the group G (Ramathanan & Ganesh, 1994). Flow φgm indicates that the individual net flow for alternative ai, as produced by MURAME. Because of the fact that not all the members of the group cannot carry the same weight in the decision making process, a value βgm indicates the weight (importance) of DM gm in the decision outcome. This can differ due to
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 88 differences in decisional skills, problem knowledge and expertise, or hierarchical power in organizations (Bui, 1987). There is no general formal rule how βgm values are decided. Often all group members are considered by the MoE of equal importance. As it can be seen, for each alternative a group leaving flow y G%)HoyHo G%) Ho4 a group entering flow y %)HoyHo %) Ho4 And a net group flow y%)y G%)cy %) can be defined. Following the flow philosophy, y G%) indicates the degree that ai outranks the other alternatives and y %) the degree ai is outranked, for the group of DMs. By using the net flow, the total group pre order is produced. 2.3.7.3.2 Consensus check Following the common proposal, consensus reaching is examined while, if not, its achievement is supported. This is done with the use of four new specific indexes. The Personal Satisfaction Index (PSI): PSI can be defined as the correlation coefficient between the individual and the preorders group. Taking in account that the decision problem belongs to problematic γ (ranking) and the fact that the above describes techniques that usually produce only a few cases of indifference, the Spearman Rank Correlation Coefficient (SRCC) can be applied. For a presentation of the Spearman Rank Correlation Coefficient (SRCC) see, for example (Lehmann & D'Abrera, 1998).
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 89 As a result, for each group member gm, having the individual order Rgm and the group order RG: 2grHoc.Z oo where di is distance of the ranks between Rgm and RG, m is the number of alternatives. PSI values are between -1 and +1. Since the SRCC is mainly sensitive to great differences between orders (differences of many positions) than to small differences (for example, on position differences), • PSI close to 1 means that there are not big differences between two orders and, then, the agreement/satisfaction is big. • PSI close to 0 means that there are many significant differences between the two orders. As a result, there is no agreement at all, any satisfaction by the group order. • PSI close to -1 means that the group order is almost the personal order reversed. The discomfort/disagreement is then maximized. The Group Satisfaction Index (GSI): GSI is the weighted addition of the PSI providing in this way an index of group’s satisfaction by the proposed as common proposal grHo2grHo Ho4 The Rest Group Satisfaction Index (RGSI): RGSIgm measures the satisfaction of the remaining members of the group, for example G – {gm}, $grHo.2gr4, G* = G – {gm}, βr* = the weight value of group member r of the group G* (normalized).
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 96 • Selection of university professors (Bloomsburg University of Pennsylvania). • Evaluation of risks in the operating cross-country petroleum pipelines (American Society of Civil Engineers). • Deciding the best way to manage the U.S. watersheds (U.S. Department of Agriculture). AHP is sometimes used in the very specific procedures design for particular situations, like the classification of buildings according to their historic importance. It was recently applied to a project that uses video sequences, in order to evaluate the state of the Virginia’s highroads. Highroad engineers used this method first to determine the optimum scope of the project, and then, to justify their budget to legislators. The AHP is included nowadays in most of the operations research and science textbooks management, and is taught in many universities. Moreover, is used so much in the organizations that have carried out detailed researches on its theoretical funds. The general consensus is technically valid and useful in practice, but this method has its critics. In the beginning of 1990 a series of debates between critics and defenders of the AHP was published in Management Science and The Journal of the Operational Research Society. These debates seem to have resolved in favor of the AHP: • An in-depth paper discussing and rebutting the academic criticisms of AHP was published in Operations Research in 2001. • A 2008 Management Science paper reviewing 15 years of progress in all areas of Multi-criteria Decision Making showed that AHP publications have overcome in number to any other methodologies, qualifying its grow as “enormous”. • Also in 2008, the international society in the area of operations research and sciences management recognized the wide impact of the AHP method at its fields. Occasional criticisms are still appearing. A document in 1997 examined possible flaws in the verbal scale often used in AHP pairwise comparisons. Another, in the same year affirmed that inoffensive changes to the AHP model can introduce order where no order exists. A 2006 paper found that the addition of new criteria can alter the priorities of the alternatives. The decisions making implies classification of alternatives in terms of criteria or attributes of those criteria. An axiom of some decision theories (including AHP)
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 97 is that when new alternatives are aggregated to a decision problem, the ranking of the old alternatives must not change – that “rank reversal” must not occur. Validity of this hypothesis is discussed by some people. Addition of new alternatives can change the rank of the old ones. These rank reversals do not occur frequently, but the possibility this can occur has important logic implications of the used methodology to the decisions making, the underlying assumptions of several decision theories, etc. The presidential elections of the U.S. in 2000 are an example of a decision that can be understood like a case of rank reverse. Ralph Nader was an ‘irrelevant’ alternative, in that he was dominated both democrat and republic candidates. However, since he engaged more votes from those ones that voted to the democrats instead of republicans, his presence caused the ranks to reverse. In another way, if Nader wouldn’t have been in the race, it is widely accepted that Al Gore would have won. There are two schools of thoughts about the rank reverse. One of them establishes that new introduced alternatives without additional attributes must not cause the rank reverse at all. The other one establish that there are two situations on which the rank reverse is not reasonable; also there are situations on which rank reverse is possible. Current version of the AHP can accommodate these two schools – its Ideal Mode preserves rank, while it’s Distributive Model allows the ranks to change. Either mode is selected according to the proper problem. Rank reversal and ideal alternative was widely debated in the document mentioned above, Operational Research. Also, was debated in a chapter entitled Rank Preservation and Reversal, in the basic book in AHP. This last one published examples of rank reverses due to the copies of an alternative, due to the intransitivity of decision rules, due to addition of phantom and decoy alternatives, and due to the changing phenomenon in the utility functions. Also, the Distributive and Ideal Modes of the AHP is discussed. 2.4.5 Analysis of the ANP method The Analytic Network Process (ANP) is a more general form that the Analytic Hierarchy Process (AHP) used in the multi-criteria decision analysis.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 98 AHP structures a decision problem in a hierarchy with one goal, the decision criteria, and the alternatives, while the ANP structures the decision problem like a net. Both then use a system of pairwise comparisons to measure the weights of the components of the structure, and finally to rank the alternatives in the decision. In the AHP, each element of the hierarchy is considered to be independent of all of the rest, the decision criteria are considered to be independent between them, and alternatives are considered to be independent on the decision criteria and on the other alternatives. But in many cases of the real world, there exist interdependence between the items and the alternatives. ANP does not require interdependence between elements, so it can be used as an efficient tool in these cases. In order to illustrate this, a simple decision about the buy of an automobile can be considered. The decision maker can decide between some sedans full-sized with moderate prices. The decision maker could base his decision in only three factors: buying price, the security and comfort. Both the AHP and the ANP provide useful frames to use in the decision making. The AHP could suppose that the buying price, security and comfort are independent among them, and to evaluate each one of the sedans in an independent way in these criteria. The ANP will let consider the interdependence of prices, security and comfort. If it would be possible to get more security or comfort by paying more for the automobile (or less, by paying less), the ANP would take this into account. In the same way, the ANP could let the decision criteria to be affected by the features of the different cars. If, for example, all cars are very, very secure, the importance of the security as an adequate decision criterion could be reduced. 2.4.6 Analysis of the ELECTRE methods Despite of the fact that there are several versions of the ELECTRE method (in the previous section [Chapter 2.3.5.1] the ELECTRE I, ELECTRE II, ELECTRE III, ELECTRE IV, ELECTRE TRI and ELECTRE IS methods were introduced) all of them have many characteristics in common. Different versions of the first ELECTRE method add to this one some improvements in the exploitation of data phase.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 99 Therefore, in spite of the existence of several versions of the ELECTRE method, all of them have almost the same properties and are suitable to work in projects with the same particular properties. Many authors have discussed about the kind of projects on which the ELECTRE methods (independent of the version that will be used) are more suitable to work with. According to José Ruiz Figueira et al. (Figueira, Greco, & Ehrgott, 2005), ELECTRE methods are relevant when facing decision situations with the following characteristics: 1The Decision Maker (DM) wants to include it the model at least three criteria. However, aggregation procedures are more appropriate in those models on which more than five criteria are wanted to be included (up to twelve or thirteen). And, at least one of the following situations must be verified: 2Actions are evaluated (for at least one criterion) on an ordinal scale or on a weakly interval scale. These scales are not suitable for the comparison of differences. Hence, it is difficult and/or artificial to define a coding that makes sense in terms of preference differences of the ratios H,%I)H,%J) H,%)H,%Z), where gj(x) is the evaluation of action x on criterion gj. 3A strong heterogeneity related with the nature of evaluations exists among criteria (for example, duration, noise, distance, security, cultural sites, monuments …). This makes it difficult to aggregate all the criteria in a unique and common scale. 4Compensation of the loss on a given criterion by a gain on another one may not be acceptable for the DM. Therefore, such situations require the use of non-compensatory aggregation procedures. 5For at least one criterion the following holds true: small differences of evaluations are not significant in terms of preferences, while the accumulation of several small differences may become significant. This requires the introduction of discrimination thresholds (indifference, preference and veto, which where mentioned in the previous section of this thesis) which leads to a preference structure with a comprehensive intransitive indifference binary relation.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 100 2.4.7 Analysis of the PROMETHEE methods Last decade has experienced a growing number of publications referred to the Multi-Criteria Decision Support Systems on which new and interesting methods are proposed. This researching field is getting enriched with the pass of the years and is getting more the improvements on this field. All these methods solve the very basic problem but they differ according to the additional information that they require. Advantage of the PROMETHEE Methods against the rest of its competitors is that the additional information that it requires is very clear and concise, this information can be easily gotten by the decision maker with the constant and active help of the analyst. PROMETHEE Methods were developed and carried out in practice in order to resolve multi-criteria problems where the set of alternatives, A, is a finite set of feasible alternatives. In this case, the decision maker has to deal with a decision matrix. Is important to remark that the matrix must always be ready for possible evolutions, this means that additional alternatives must be considered as a bigger amount of information are gotten during the decision process progress, new evaluation criteria or the temporal elimination of others. Structuring of the matrix is making in a progressive way and because of that, normative, constructive, descriptive and prescriptive arguments must be considered. The additional information required by the PROMETHEE Methods consists on: • Information between the different criteria (inter-criteria) • Proper information of each criterion (intra-criterion) Information between different criteria consists on the establishment of weights that will reflect the relative importance of each one of them. Therefore, a criterion will be more important than another one when the value of its weight will be bigger. Weights are supposed to be always positive. The work of the determination of weights is not trivial or simple. Because of the strength of the existent subjective component, it can be assert that the selection of weights is the “freedom space” of the decision maker, that is to say, that scope on which the decision maker can freely express his preferences according to the structure of the criteria he has in mind.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 101 The proper information of each criterion refers to the way on which the decision maker perceives the specific scale that each criterion is expressed in. For each criterion a particular preference function Pj(. , .) is defined. This function indicates the preference degree associated to the best alternative in the case of binary comparisons, according with the deviation between the evaluations of the alternatives to that particular criterion. Therefore, for small deviations the decision maker will assign a reduced preference to the best alternative, while for big deviations the preference will be bigger. In this way, in the PROMETHEE Methods is suggested to modify the modelling of the decision preferences, by considering for each criterion, some possible extensions. These extensions receive the name of generalized criteria. The preference functions allow converting the deviations observed in the scale for a specific criterion into preference degrees that are independent to the scales. In order to support the decision maker in the selection of these preference functions six basic types have been purposed (Brans, 1982) (Brans & Vincke, 1985) (Brans, Vincke, & Mareschal, 1986). Is the decision maker who decides which one of the different types is going to be used and which one is going to be the value of the correspondent thresholds. In general, is considered that both the nature of criteria and the value of the thresholds can be established according to the economic significance associated to them in each particular case. Also is considered that the six types published in the literature are enough to solve most of the real practice cases. More sophisticated functions could be considered, but in any case, is the analyst the one who must help the decision maker in order to evaluate the associated parameters in an economical meaning way. 2.4.8 Analysis of the MURAME method As was mentioned in previous sections, MURAME method is a hybrid of the ELECTRE III and the PROMETHEE methods. MURAME carries out its methodology for the decision problems by combining the advantages of each one of these two methods. Therefore, in the first phase, the aggregation phase, the MURAME constructs the outranking relation following, that is, the defining of the criteria, their
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 102 weights and the value of the thresholds (concretely, the indifference, preference and veto thresholds). The way on which the Decision Maker defines these values in the MURAME method is by following the ELECTRE III technique. In the second phase, the exploitation phase, all the calculations made to the outranking relation constructed in the first phase are made. Calculations of flows are then made in MURAME by following the PROMETHEE method. As both ELECTRE III and PROMETHEE methods are outranking methods inside the family of the MCDA families of methodologies, the MURAME method can also be considered a method of the family of the MCDA outranking methodologies. Outranking methods are seemed to be very popular for most kind of problems. For example, outranking has been used in many evaluations of alternative strategies. In fact, the most popular outranking methods on these evaluations have been the different versions of PROMETHEE (Diakoulaki & Karangelis, 2007) (Tzeng, Shiau, & Lin, 1992) (Georgopoulou, Sarafidis, & Diakoulaki, 1998) and ELECTRE (Siskos & Hubert, 1983) (Beccali, Cellura, & Ardente, 1998) (Beccali, Cellura, & Mistretta, 2003) (Georgopoulou, Lalas, & Papagiannakis, 1997) (Capros, Papathanassiou, & Samoulidis, 1988) (Assimakopoulos, Charalambopoulos, & Samoulidis, 1991). The use of the MURAME method, as hybrid of the ELECTRE III and PROMETHEE, has been significantly more reduced that such these methods. One may reason is that the MURAME method is not as widely known by analysts and other possible manager like different versions of the ELECTRE and PROMETHEE methods. However, the MURAME method has been applied successfully in some real-world decision problems. One example of its use was the ranking of projects in the Armenian Energy Sector (Goletsis, Psarras, & Samoulidis, 2003). Goletsis et al. (Goletsis, Psarras, & Samoulidis, 2003) think that one of the main advantages of the outranking focus is that these methods (on which the MURAME method is included) require less information from the Decision Maker than other MCDA methods. MURAME even works when some information or evaluations are missing. Other authors like Georgopoulo et al. (Georgopoulou, Sarafidis, & Diakoulaki, 1998) (Georgopoulou, Lalas, & Papagiannakis, 1997) and Haralambopoulos (Haralambopoulos & Polatidis, 2003) have focused on other advantages of the outranking methods. Moreover, authors think that the way on which results are represented in the outranking
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 103 methods like the MURAME is simpler and easier to understand than results provided by another MCDA methods, like AHP. A main difference between MURAME (and other outranking methods) and the rest of methodologies are the calculation procedure. PROMETHEE (and so MURAME method) provides a transparent calculation procedure, so then is easy to understand and accept by decision makers (Georgopoulou, Sarafidis, & Diakoulaki, 1998) (Haralambopoulos & Polatidis, 2003), while decision makers often find calculations in ELECTRE III too much complex and incomprehensible. Consequently, ELECTRE method is finally seen like a ‘black box’ by the decision makers, which see this method not very satisfactory. MURAME, as a hybrid between ELECTRE III and PROMETHEE methods does not constitute such a complex calculation procedure. The reason is that MURAME is a methodology implemented from the ELECTRE method, but in difference with ELECTRE, the calculation procedure (the exploitation phase) is implemented in MURAME from the PROMETHEE method, which, as mentioned before, provides a simple and understandable calculation procedure. Therefore, MURAME method includes the advantages of the outranking MCDA method ELECTRE III, but excludes the disadvantages underlying its calculation procedure, so it can be understood and accepted by decision makers. 2.4.9 Combination of methods The purpose of this section is to provide a brief analysis of the possible combinations between the methods mentioned in previous sections. As the MURAME method is a hybrid between the ELECTRE III and PROMETHEE methods, other hybrid methods can result by the combination of two other MCDA methods. In the last years, some authors proposed new MCDA methods by the combination of two popular methodologies, while others have carried out some publications on which they analyse the advantages and disadvantages of these new proposed methods. As it is being mentioned, some researchers have tried to combine the use of different MCDA methods. AHP has been a very popular choice in order to combine with other methods. Tzeng et al. (Tzeng, Shiau, & Lin, 1992) studied the combination of the AHP and the PROMETHEE II, while Yang and Chen (Yang & S.L., 1989) combined the AHP and the TOPSIS methods (TOPSIS
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 104 method was not explained in this thesis as it was not considered one of the main MCDA methods that have been published in the last years) in their evaluations of energetic strategies. Ramanathan and Ganesh (Ramanathan & Ganesh, 1995) combined the AHP and the GP methods (GP method was not explained in this thesis because of the same reasons than the TOPSIS method) into a one that they called weighted sum of deviations in order to solve an energy resources assignation problem in India. An appropriate combination of two (or more) methods could be a very good strategy. This kind of integration can make use of the strengths of both methods. On the other hand, in spite of both methods have some limitations, their limitations can be complementary. Ramanathan and Ganesh (Ramanathan & Ganesh, 1995) argue that the GP and the AHP are appropriate for a combination to solve a resources assignation problem. It is possible that adequate combinations of MCDA methods also can be found in other kind of problems in order to provide a satisfactory solution of the decision problem. Therefore, although there are a lot of possible combinations between two or more MCDA methods into one in order to eliminate the disadvantages of each one of them, there are not many publications or studies about the combination of methods. So, for the purpose of this thesis the only MCDA hybrid method that will be considered is the MURAME method, as some publications and examples carried out successfully are available in the literature. Taking in account hybrid methods on which there is not enough information is considered to be risky considering the purpose of this thesis.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 105 2.5 Comparison between each multi-criteria method Once the analysis of each MCDA method has been exposed in the previous sections, the purpose of this chapter is to compare the different methods that have been carefully explained in this thesis. The purpose is to simplify the task of deciding which one, from all the MCDA methods, is the most appropriate to use in the project on which this thesis is focused. 2.5.1 The WSM and the WPM methods According to the analysis of the Weighted Sum Model and the Weighted Product Model methodologies provided in the previous sections, and with the publications made in the last years by many authors, like Evangelos Triantaphyllou (Triantaphyllou, 2001), these methods are probably the most commonly used all over the world, especially in single dimensional problems. The most important property of these two approaches is the simplicity of their methodology, which basically consists on assign a concrete value to each alternative. So then, the ranking of alternatives is a quite easy task. The main, and the only one, difference between these two methods is that the WPM instead of addition in the model there is multiplication. So each alternative is compared with the others by multiplying a number of ratios, one for each criterion (Triantaphyllou, 2001). Both the WSM and the WPM methods are specially thought for singledimensional problems. Difficulty with these methods emerges when they are applied to multi-dimensional problems. The reason is that, when different dimensions are combined, the additive (or productive in the case of the WPM method) assumption is violated. This disadvantage results to be a quite big problem for the case that is being considered in this thesis as a set of criteria measured in different dimensional units is given. Therefore, this disadvantage doesn’t place these methods in a good situation in order to select them to carry out the problem described here.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 112 2.6 Conclusion A variety of experiments, for example (Hobbs & Meier, 1994) (Hobbs, Chankong, Hamadeh, & Stakhiv, 1992), have proved that the choice of the method may have a significant influence in the decision result. According to Hobs et al. (Hobbs, Chankong, Hamadeh, & Stakhiv, 1992), the choice of the method is as much important, or evens more, than the person who is using the methods. There are many possible explanations for these differences, the DM may not understand completely the method, or some methods may not offer a valid representation of the DM’s preferences. 2.6.1 Choosing an MCDA method Choosing a MCDA method means to choose a compensation logic (Guitouni & Martel, 1998). This may be a difficult choice, so there are many criteria to take into account (Hobbs, 1986). Between the most important ones is validity, that is, that the method measures what is supposed to be measured. Different methods can provide different results, so the method that reflects the ‘true values’ of the user with the highest possible precision in case of be chosen. However, is important to be conscious that different persons have different ways to think and to express the values (Hobbs & Meier, 2000). Consequently, the most appropriate method for a DM is not necessary as valid for other DMs as well. Another important property is the adequacy of the method, that is, that the method is compatible with the provided data and that the DMs can provide to the method all the information that it needs. The MCDA method must be also easy to use and to understand, even for the non-experts. If logic behind the method is not transparent, a DM can perceive the methodology like a black box. The result may be that the DM does not trust in the recommendations of the method. In this case, it has no sense spend time applying the MCDA method. In practice, the choice of the method usually depends on the DM’s and analyst preferences. Consequently, the most important criteria for choosing the MCDA method are frequently the familiarity and affinity with a specific method (Guitouni & Martel, 1998). Consequently, instead of looking for the most appropriate method, the decision problem is adapted so that it fits to the DM’s or analyst’s favourite method. The result is that important limitations and underlying suppositions of methods are usually ignored.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 113 The choice between the existent MCDA methods can be said to be a multicriteria problem in itself. Each one of the methods have their own advantages and disadvantages, and is not possible to assert that anyone of them, in general, is more appropriated than another one. However, some methods are more appropriated if the uncertainty is the main problem, while other methods are more appropriated if values in conflict are more important (von Winterfeldt & Edwards, 1986). It is important to take into account that the use of different methods will probably give different recommendations. 2.6.2 Indentifying the appropriate method Like has been mentioned in the last section, the choice of the MCDA method is a non-trivial task as the decision of the method that will be implemented can have an important influence on the decision result. So, the selection of the MCDA method is a decision problem in itself, that must be carried out in a detailed and carefully way. Therefore, the selection of the MCDA method is the first main goal that is addressed in this thesis, which must be realized in detail. That is the reason for which several methods from different MCDA method families have been described in this thesis. Once the main properties and performance of each approach has been studied, as well as the analysis and comparisons between each methodology families (and also between the methods in themselves) has been realized, then it is possible to find out which one can be the method that will fit better to the problem on which this thesis is focused on. First of all, remember that we can exclude the WSM and WPM methods as they are specially thought for single-dimensional multi-criteria problem and especially because these methods cannot work when for any attribute there are missing values (See Chapter 2.5.1). Taking into account that in the problem which this thesis faces, the criteria are multi-dimensional and there are several attributes with missing values, it is simple to realize that any of these two methods will be able to solve the problem which this thesis wants to solve. Then, the decision problem is now to choose between a utility based and an outranking methodology family.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 114 In the comparison between these two methodology families exposed in Chapter 2.5.1 was analysed the main properties of each one of these methods as well as the kind of problems on each one of these methodologies fit better in order to provide a satisfactory solution to the decision makers. Therefore, utility based models assign a score to each one of alternatives enabling, hence, the ranking of alternatives. These methods are quite intuitive and easier to understand by the analysts and DMs. However, these methods assume that the DM is able to provide precise answers to a wide range of questions. Unlike utility based models, outranking methods assume that the decision maker is not able to define tradeoffs between the criteria. In these approaches alternative are pair-by-pair compared to determine which one is the best for each criterion. When all comparisons are aggregated then it will be possible how much an alternative outranks another one for all the considered criteria. These methods are based on less restrictive assumptions than utility based methods and so, these methods correspond better to what the decision maker really thinks. Therefore, as also was mentioned in Chapter 2.5.1, outranking techniques are specially appropriated when criteria metrics are not easily aggregated, measure scales vary in wide ranges, and units are disproportionate or unique In terms of the problem that this thesis faces, in the data provided by the European Commission to the DSS’s laboratory, for the attributes of each alternative there are several values of different measure units (numbers, dates, words, codes, ...) that make the criteria difficult to be aggregated. Also, measure scales vary in wide ranges as for many attributes the values they can have are quite diverse. Also, as a data provided by an extern organism (in this case the data are provided from the EC) the DM may have some difficulties in order to give concrete answers to a big number of questions, what is a quite big disadvantage for the utility based methods. Therefore, considering the problem to solve in this thesis, it can be said that the MCDA methodology family that fits better in order to provide a satisfactory solution for the problem is the outranking methods. As all the attributes of the data provided are not measured in the same kind of units and so, criteria are not easy to aggregate, this family of MCDA methodologies are the most proper for the problem described in the beginning of this thesis.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 115 Then, the problem now is to decide which method among this methodology family is the most appropriate to implement for the problem tat is wanted to solve. As exposed in Chapter 2.5.1.2, among the MCDA outranking methods, MURAME is the one that performs better according to the advantages and disadvantages of each methodology. The main difference between the outranking methods is the calculation procedure. As the calculations in ELECTREE are found to be quite complex for analysts and decision makers, the PROMETHEE and, hence the MURAME methods are preferred. Moreover, unlike PROMETHEE, MURAME can even work with missing values. Due to the fact that in the data provided there are many missing values for some criteria, the MURAME method is the one from these outranking methods that fits better to the properties of the considered problem. In conclusion, taking in account the analyzes and comparisons carried out for each one of the different MCDA methodology families, and the main properties for each one of the methods among each method family it can be said that the MUlticriteria Ranking Method (MURAME) is the most appropriate method by considering the features of the described problem. Therefore, MURAME is the method that will be chosen to apply for the problem of this thesis and, according to the analysis that have been carried out; this method will be able to solve in a quite satisfactory way the given multi-criteria decision problem.
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National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 117 3. Proposed Methodology The Chapter 2 presented a set of Multi-Criteria Decision Analysis systems that might carry out the problem described in the beginning of this thesis. Each MCDA method was explained, by describing the main features of the method and also detailing the development of each proper method. For the methods on which different versions are available (like the ELECTRE and PROMETHEE methods) each one of these versions were described, and also differences between these versions of each methodology were explained. After the exposition of all the relevant methodologies that have been published and analysed by different authors in the last years, a comparison between these methods has been made (see Chapter 2.5). After analysing the WSM and the WPM methods, this thesis concluded that these two methods wouldn’t provide a satisfactory solution for the problem considered in this thesis. So, the comparison was then made between the utility based methods and the outranking methods, as the other MCDA methodologies (unlike the WSM and the WPM methods) analysed here belong to one of these method families. The performed comparison concluded that outranking methods fit better to the decision problem this thesis faces to, than the utility based models. Then, the problem was to select, among all the methods that belong to this methodology family, the one that might provide better results according to the purpose of the given problem that is wanted to solve. Then, it was necessary to compare the ELECTRE, PROMETHEE and MURAME methods, as these methodologies are the main ones inside the outranking methods family. The comparison between these methods concluded that the MURAME method is the most appropriate to carry out the multi-criteria decision problem provided to the DSS’s laboratory (see also chapter 2.5.2.2.3). As MURAME is a hybrid method of the ELECTRE and PROMETHEE, it excludes the main disadvantages of each one of these methods. Therefore, once the method that is going to be used for solving the multi-criteria decision problem is known, the next step is to realize a detailed analysis of this concrete method (the MURAME) in order to know how it can be implemented,
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 118 and the necessary steps that must be followed to perform a better implementation of the method. By performing a good analysis about how the implementation of a MCDA method must be carried out, the development of this method will become easier and the results provided by the methodology will be more satisfactory according to the necessities of the DMs. Therefore, the purpose of this chapter is to perform a specific analysis for the MURAME method according to the given problem. So, in this chapter will be explained the different steps that must be followed to perform a satisfactory implementation of this method. This analysis will include also the different main criteria that will be considered for the multi-criteria decision problem, as well as the weights that will be given to each one of the different attributes by discussing their importance and the way they can help to solve the problem in a proper way according to the needs of the EC.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 119 3.1 Introduction Once the MCDA method that will be used is know, the next step (which is also the purpose of this section) is to describe how to apply the selected method, in this case the MURAME method, and to describe which steps should be followed as well. As described in the Chapter 1 (Description of the Problem), the project proposals were collected from the EC, through the EuropeAid program. The source of information concerning projects, on which monitoring is wanted to carry out, is the CRIS database, a EuropeAid’s database (see Chapter 1.2.2). A big number (851) of project proposals coming from the EuropeAid program were identified. All the necessary information about the projects must be available in order to be able to perform a ranking of the projects in order to decide which ones should be monitored. For this reason, all the proposals of projects are codified in a systematic way with the use of data sheets of the projects. In this way, the 851 projects have a uniform “appearance” providing then a better management and recovery of information. Figure 12: Microsoft Excel document with the whole set of alternatives
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 120 Therefore, all the information about these 851 projects is collected in a spreadsheet, concretely in a Microsoft © Office Excel document. The Figure 12 and Figure 12 show the document available for the DSS’s laboratory in order to perform a multi-criteria decision problem that will allow the laboratory to choose, among the whole set of projects, the ones that are more interesting to monitor. Figure 13: Available information of projects After the collection and defining of the whole set of alternatives, that in this case are the different projects that are expected to be monitored, the next stage is to define the different steps that will be necessary to carry out in order to make possible the implementation of the MURAME method. As mentioned in previous sections, the MURAME method is implemented in two main phases, combining in this way the ELECTRE III and the PROMETHEE methods (see Chapter 2.3.7.1). In the first phase, the aggregation phase, is where the outranking relation gets constructed. Here, the key criteria are defined, as well as the different weights for each one of these defined criteria. Weights for the criteria must be assigned according to the importance of each one of them over the global decision process. Also, in this phase the thresholds for each one of the whole set of the criteria used to solve the decision problem must be defined. The thresholds that
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 121 must be calculated for each one of the criterion are the indifference (qj) and the preference (pj) thresholds. In the implementation of the MURAME method for the solution of the given problem, also the veto threshold (vj) will also be assigned to each one of the criteria, as it has been proved that the use of this threshold provides a better performance in the solution of the decision problems. In the second phase, the exploitation phase, the outranking relation, which includes the weights and the three thresholds (indifference, preference and veto thresholds) for each one of the criteria, used to solve decision problem, are used to produce a total pre-order. In this way the whole set of projects will be ranked according to the values for each one of the criteria. This modellisation of the problem is the one that must be carried out, as is the way the MURAME method performs, and is the method which resulted chosen after comparing it with the rest of the methods (see Chapter 2.6.2). However, before detailing the concrete steps that must be followed to carry out this modellisation, it is also important taking into account some aspects. First of all, as described in Chapter 1.6 is wanted to classify the set of projects into three different groups: the projects that should be monitored, the projects that should be considered to be monitored, and the projects that are not recommended to be monitored. As the method which resulted to be chosen is the MURAME method, then total preorders of the projects should be produced by it. Then, with a total preorder list of projects, assignment of each one of the projects to these three groups will become a simple task. Also, the use of the veto threshold vj is not strictly necessary for the implementation of the MURAME method. However, as in the identification of the critical criteria some of them can be of special importance, it will be quite useful to include this threshold in the modellisation of the problem. Moreover, the use of the veto ensures that an alternative with a bad performance in such a critical criterion will not receive high priority (Goletsis, Psarras, & Samoulidis, 2003). Once the main features of the MURAME modellisation are know as well as the parameters that must be valued (the weights of criteria and the indifference, preference and veto thresholds) for each criterion, it can then be possible to define the steps to follow to carry out a proper performance of the MURAME method. The first step will consist on identifying the relevant attributes. As the number of attributes available for each alternative is quite large (63) it will be necessary
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 128 18. Document type Enhance quality for the implementation of project Different scores according to the type of document 19. Sector code Promotion of the desired sector Different scores for each sector 20. Workflow type Secure the possibility for implementation of the project Higher scores for workflow types that are tested to perform better 21. Balance Secure viability of the project Amount of money Table 3: Ranking criteria Therefore, all these criteria were considered to be included in the criteria family. However, due to the lack of information over many alternatives (the proposed projects) it will be necessary to ignore, at this stage of the planning process, some evaluation criteria, for which there is no information for significant number of projects. In order to get a satisfactory result by the application of the MURAME method for the given decision problem, it will be recommendable to include just those criteria for which more than the 50% of the proposed projects (that is, the alternatives) are evaluated. The percentages of the evaluations among the proposed projects, for each one of the selected criteria were calculated. This task was carried out in order to know for which criteria the number of missing values is under 50%. The results obtained are shown below:
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 129 Criterion Number of missing values Percentage of missing values 1. Domain 0 0% 2. Nature 6 0.71% 3. Type of services 759 89.19% 4. Contracting party 56 6.58% 5. Geographical zone 61 7.17% 6. Nationality 168 19.74% 7. Former system reference 693 81.43% 8. Status 0 0% 9. Delegation 792 93.07% 10. Entity 83 9.75% 11. Contract type 0 0% 12. Expiry date 25 2.94% 13. Closing date 492 57.81% 14. Person in charge 0 0% 15. Procedure 6 0.71% 16. Negotiated procedure type 849 99.76% 17. Report deadline 426 50.06% 18. Document type 482 56.64% 19. Sector code 253 29.73% 20. Workflow type 0 0% 21. Balance 0 0% Table 4: Missing values for each criterion As was mentioned above it is recommended, for a good performance of the MURAME method, to exclude those criteria for which the 50% of the evaluations, or more, are missing (Goletsis, Psarras, & Samoulidis, 2003). According to the results showed in the table 4, there are 7 criteria for which the number of missing values exceeds the 50%. These criteria are: • Type of services • Former system reference • Delegation • Closing date • Negotiated procedure type • Report deadline • Document type
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 130 Then, these criteria will be excluded for the modellisation of the problem, as not enough evaluations of such criteria among the set of alternatives are available. So, the set of attributes that will be taking into account for the exploitation phase of the MURAME method are: 1. Domain 2. Nature 3. Contracting party 4. Geographical zone 5. Nationality 6. Status 7. Entity 8. Contract type 9. Expiry date 10. Person in charge 11. Procedure 12. Sector code 13. Workflow type 14. Balance Therefore, these 14 the criteria are the ones that will compose the criteria family. These remaining criteria will be used in the second phase (the exploitation phase) in order to produce the final total preorder list of the projects.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 131 3.3 Thresholds for the Different Attributes Once the criteria family for the decision problem has been established, next step is to assign the indifference qj, preference pj and veto vj thresholds to each one of these criteria. According to Goletsis et al. (Goletsis, Psarras, & Samoulidis, 2003), the purpose of the use the indifference, preference and veto thresholds is to reflect the DM’s preference in a realistic way. The three zones scheme (strict preference, weak preference, indifference) is modelled by the use of two thresholds for each criterion j: the indifference threshold qj and the preference threshold pj. The values of pj and qj may be constant or have the form: α * gij + b. In any case, qj (gij) ≤ pj (gij). Also, a veto threshold vj is retained for each criterion i. This threshold is used to reject the hypothesis ai S ak, if in one criterion alternative ai is much worse than ak, that gij + vj < gkj. Veto threshold cannot be less than pj (see chapter 2.3.7.2). Therefore, as an input for the MURAME method the set of these three thresholds (indifference, preference and veto thresholds) must be calculated for each criterion, in order to provide the methodology the required information to be able to produce the total preorder list of projects. It is not strictly necessary the calculation of the veto threshold, but as mentioned above its inclusion in the modellisation is recommended in order the MURAME method to provide a satisfactory solution for the decision problem. In order to assign the different thresholds values to each criterion the next guidelines were followed (Goletsis, Psarras, & Samoulidis, 2003): according to the approach published by Rogers and Bruen (Rogers & Bruen, 1998) the thresholds were not be interpreted as uncertainty, error or imprecision margins as was suggested by Roy et al. (Roy, Present, & Silhol, 1986), but the q threshold was defined as the point at which one alternative is distinguishable from the other under a specific criterion and the p threshold as the point at which one alternative is perceived to be clearly preferable to the other. In the following paragraphs, the way on which the qj, pj and vj thresholds were established for each one of the criteria is presented.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 132 C1 – Domain. This is an important criterion. Projects may want to be promoted according to the area on which they are destined to. As a result the indifference threshold q1 is small, with a value of 5 (i.e. 5%) while the preference threshold is three times more, i.e. p1 = 15. In the same way, v1 is only twice as p1, as is not wanted to promote a project which is destined to a sector that is not desired at the moment, instead of a project whose purpose is more desirable. C2 – Nature. This criterion determines the purpose of the project, but unlike the ‘Domain’ criterion (which determines the area on which the project is focused on: education, sanity, etc.), this criterion reflect if the project it will be carried out as an action grant, a specific service or whatever. Therefore, even is a less important criterion than the last one, this is also a criterion to take into account. The veto threshold has here a high value. As a result, q2 = 10, p2 = 20, v2 = 60. C3 – Contracting party. Knowing the company that will be the responsible of the development of the project may be also important to decide which projects must be promoted. However, this one is not a main attribute to consider for the decision problem. Therefore, q3 = 20, p3 = 40, v3 = 60. C4 – Geographical zone. The region on which the project will be carried out may be a significant criterion in order to decide if the considered project must be promoted. As may be wanted to give more importance to those projects that are developed in a specific zone, the veto threshold here will have a medium value, as veto should happen often. As a result, q4 = 10, p4 = 30, v4 = 50. C5 – Nationality. This criterion indicates the nationality of the project considered to carry out. In this case, this criterion cannot help from being an important decision parameter. In this cost evaluation q5 = 10, p5 = 20, v5 = 40. C6 – Status. Knowing the status of the project (if it’s ongoing, cancelled, provisional, etc.) is an important criterion in order to know the urgency of this project. By setting q6 = 0, p6 = 10, v6 = 50 the indifference zone is suppressed, what means that has a strict preference to occur early. However, the veto may happen often. C7 – Entity. Like the ‘Nationality’ of the project, this criterion is not considered to be one of the most important ones. However, unlike the nationality of the project, the entity that will carry out the project can provide more specific information. Therefore, q7 = 5, p7 = 15, v7 = 40. C8 – Contract type. The contract type of the project also doesn’t provide quite relevant information in order to decide if the project must be promoted. Then, q8 = 20, p8 = 40, v8 = 60.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 133 C9 – Expiry date. The expiration of the date to develop the project is an important criterion. In order to give preference to occur early, the indifference zone is suppressed here as well. As a result, q9 = 0, p9 = 20, v9 = 70. The high value of the veto will make rather hard to exclude the project. C10 – Person in charge. Knowing the person that will be the responsible of the development of the project it may be very useful to decide if the project must be promoted. The veto threshold here is high. q10 = 10, p10 = 30, v10 = 70. C11 – Procedure. This criterion indicates the procedure that must be followed to develop the project. As this criterion could not easily exercise a veto, the veto threshold takes here a high value. As a result, q11 = 10, p11 = 40, v11 = 90. C12 – Sector code. The sector code indicates the sector that the project belongs to. This information is considered to be important in order to decide if the project must be considered to monitor. As it may be possible that projects that belong to a specific sector are wanted to be promoted the indifference threshold should be small. On the other hand, the veto threshold must not have a quite high value, as probably it will be preferred to promote a project of another sector, instead of the sector that a project belongs to. As a result, q12 = 10, p12 = 20, v12 = 40. C13 – Workflow type. Like the procedure of the project, the workflow type indicates how to carry out a good performance in the develop process of the project. Therefore, knowledge of the workflow is of great value in the implementation phase. As a result, q13 = 10, p13 = 30. However, veto for these projects should occur rather than hard. Hence, the veto threshold is very high, v13 = 90. C14 – Balance. This criterion indicates the amount of money that is left to pay. In any case the balance of the project cannot be considered to be an important parameter. In this “quantitative” balance evaluation q14 = 10, p14 = 25, v14 = 40. Therefore, these are the indifference, preference and veto thresholds values that have been assigned to each one of the criterion. These set of thresholds values will be provided to the MURAME method in order to calculate, in the second phase of the methodology, the final preorder list for the whole set of projects. The values for the different thresholds of each criterion is summarised in the table 5.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 134 Once the three thresholds have been evaluated for each criterion, the next step is to calculate the weights for each one of the criteria. As not all the criteria have the same importance, will be necessary to establish in which measure each criterion is stronger (or weaker) than the others. The methodology followed to decide which ones are the proper weights for the different criteria is explained in the next section. Criterion q p v C1. Domain 5 15 30 C2. Nature 10 20 60 C3. Contracting party 20 40 60 C4. Geographical zone 10 30 50 C5. Nationality 10 20 40 C6. Status 0 10 50 C7. Entity 5 15 40 C8. Contract type 20 40 60 C9. Expiry date 0 20 70 C10. Person in charge 10 30 70 C11. Procedure 10 40 90 C12. Sector code 10 20 40 C13. Workflow type 10 30 90 C14. Balance 10 25 40 Table 5: Thresholds’ values for each criterion
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 135 3.4 Weights for the Different Attributes Once the criteria family has been identified and the thresholds to each one of the criteria have been evaluated, next step is to calculate the weights for each one of the criteria. The weight vector (which contains the weights for each one of the criteria family) provides the relative importance of each criterion. According to (Vincke, 1992), weights in an outranking relation must be considered like a vote in a vote process. It is thought by Goletsis et al. (Goletsis, Psarras, & Samoulidis, 2003) that a direct weighting usually cannot reflect the preferences in an effective way. Several special methods have been developed in the last years by many authors. It is suggested to study (Figueira & Roy, 2002) (Ramathanan & Ganesh, 1994) (Rogers, Bruen, & Maystre, 1999) (Roy B. , 1990) . In any case, the method to be follow must be – relative simple – and easily understandable. In the decision problem which this thesis focuses on, the method proposed by Rogers and Bruen (Rogers & Bruen, 1998), which is based on the personal construction of the theory published by G.A. Kelly (Kelly, 1955) was applied. The description of this method is detailed in the following paragraphs. The method proposed by Rogers and Bruen (Rogers & Bruen, 1998) is based on the Personal Construct Theory - PCT (Kelly, 1955) and its bipolar modellisation of the human preferences system. Without analysing the Kelly’s theories, finally, a bipolar construction (extreme) of the two possible cases is associated to each criterion, for example, by the cost: low cost/high cost. For each construction it must be selected which one of the two cases is the most preferable (for example, by low cost). In a pair-by-pair comparison between the constructs and assuming that the current state is the preferable one for each construct, it must be defined which one of the two constructions it is better to see changed to the non-preferable situation (or vice versa, that one resists to change). By the calculation of this resistance to change the criteria weights are calculated. A symmetrical matrix where rows and columns represent the constructions can then be created. Each cell inside this matrix represents the obtained result by using the following notation:
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 136 • An X determines that the column of the construction “resists to change”, • A blank indicates that the row of the construction “resists to change”, • An I indicates that the two modifications are equally undesired, • An e indicates that two constructs change at the same time. The resistance-to-change is calculated by adding the number of “blanks” in the rows and the X in the columns for each construct. This resistance-to-change is considered to be a measure of the importance of each criterion. Criterion weight wj is then $D6 .$D6 - (RtC: Resistance-to-Change). Therefore, by using the Personal Construct Theory – PCT for the calculation of the criteria weights, the following matrix was constructed: C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 RtC C1 - X X X e X X 7 C2 - X X X e X X X X X X 2 C3 - X X X X X X X X X 2 C4 - X X X X 8 C5 - X X X X X X X X 2 C6 - X X 11 C7 - X X X 5 C8 - X X X X X X 1 C9 - X 11 C10 - X X X 5 C11 - X X 8 C12 - X 9 C13 - X 5 C14 - 13 Total 89 Table 6: Criteria weights definition with the use of PCT Once the RtC value has been calculated for each criterion associated to the criteria family, is possible now to calculate the weights for each criterion by applying the formula that Rogers and Bruen (Rogers & Bruen, 1998) proposed in their method. Therefore, the resultant weights for the criteria are shown in table 7:
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 137 Criterion Weight w C1. Domain 7.9% C2. Nature 2.2% C3. Contracting party 2.2% C4. Geographical zone 9.0% C5. Nationality 2.2% C6. Status 12.4% C7. Entity 5.6% C8. Contract type 1.1% C9. Expiry date 12.4% C10. Person in charge 5.6% C11. Procedure 9.0% C12. Sector code 10.1% C13. Workflow type 5.6% C14. Balance 14.6% Table 7: Criteria weight values Therefore, these weights will be provided to the MURAME as inputs for the methodology. The set of weights of the criteria family, as well as the indifference, preference and veto thresholds for each criterion, and the scores of the alternatives for each one of them (the ‘evaluation matrix’) constitute the whole set of inputs, that will be provided to the MURAME method in order to be able to perform a total preorder list of the projects. The outputs that will be provided by the MURAME are described in the next section.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 144 5. Conclusions This section summarizes the main conclusions of the thesis: • Decision-planning problems, and hence the monitoring projectsplanning, are usually characterized by many conflicting criteria. • The multi-criteria decision analysis (MCDA) is designed for the identification of the best solution when several criteria are considered, by the calculation of numbers/scores or results that reflect the total value of each one of the proposed alternatives. o MCDA allows the decision maker (DM) to express his preferences over the different criteria in an explicit way. MCDA provides a representation of the DM’s values and subjective preferences. o With the use of MCDA, the DM is not limited to any basically fixed rules, but is free to include or exclude the different aspects of the analysis, based on his own suppositions about what is important. Moreover, MCDA allows tradeoffs to be nonlinear if is desired. o Many MCDA methods allow the including of qualitative criteria in a coherent way. • For this monitoring-planning project to be successful, it is essential to spend enough time and resources in the definition and structuring of the problem, in order to ensure that there will not be any kind of disagreements or confusion regarding to the nature of the problem and the desired goals. • Inside the MCDA methods there are several methodology families. Methods belonging to the same MCDA methodology family have the same main properties. However, it is not possible to say which one is the best MCDA family, as each one of the diverse families has different properties. But each family fits better to different decision problems. Therefore, the use of the MCDA method family will depend largely on the properties of the decision problem for which a satisfactory solution is wanted for it.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 145 • Between the whole set of MCDA method families the one that fits better to the problem described in this thesis, according to the properties of such problem, are the outranking methods. As a ranking of projects, in order to know which ones are better to monitor, is wanted, outranking methods are the most appropriate methods because they are able to produce a total preorder list between the set of alternatives available in the decision problem. • Considering the MCDA methods that belong to the outranking method family, the MURAME method was considered to be the most appropriate for the development of the decision problem. As hybrid between the ELECTRE and PROMETHEE methods, the MURAME method is able to combine the advantages of these two methodologies and to remove the main disadvantages of both of these methods. Moreover, the MURAME method is able to work even some values are missing. These are the main features for which this method was chosen in order to solve the decision problem. However, as was proposed in the previous chapter, it would be advisable to suggest the reader of this thesis, to study as many MCDA methods as possible in order to ensure that there is not any other method which will fit better to this decision problem. • Due to the large amount of data that was needed to study and analyze, and also the large amount of information about non-relevant criteria, it was necessary to select, from the whole set of attributes, those ones that were considered to be useful in order to obtain a satisfactory solution. As many irrelevant criteria were provided, it wouldn’t be right to use all the information available for the modellisation of the problem. Therefore, a detailed selection of the proper attributes was necessary in order to perform a sufficiently efficient development of the method • Usually, in the decision problems, like the one described in this thesis, not all the information has the same relevance. Because the information provided by some attributes may be more important than the information provided by other attributes, not all the attributes have the same importance. For this reason it was necessary to assign a weight for each criterion that was included in the modellisation of the problem. By weighting the different criteria it is ensured that each criterion has a difference importance with the others in order to reach a satisfactory solution for the decision problem.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 146 • In order to allow the DM to express his preferences and uncertainties for each one of the different criteria, the MURAME method includes the preference, indifference and veto thresholds. For the modellisation of the problem, it was necessary to assign a value for each threshold (among the whole set of the criteria family). In this way, the preferences and uncertainties for the different attributes were provided to the methodology. • By providing all the necessary inputs to the method, MURAME would be able, after calculating some parameters, in the exploitation phase to produce a total preorder list of the projects according to the importance of being monitored. The MURAME method will not ordered the list according to the importance of the projects on themselves. MURAME will order the projects according to their importance to be monitored.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 147
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 148 6. References Assimakopoulos, V., Charalambopoulos, C., & Samoulidis, J. (1991). Combining Decision Support Tools and Knowledge-Based Approach for the Development of an Integrated System for Regional Energy Planning. Energy Systems and Policy , 15 (4), 245-255. Beccali, M., Cellura, M., & Ardente, D. (1998). Decision Making in Energy Planning: The ELECTRE Multicriteria Analysis Approach Compared to a Fuzzy-Sets Methodology. Energy Conversion and Management , 39 (16-18), 1869-1881. Beccali, M., Cellura, M., & Mistretta, M. (2003). Decision-Making in Energy Planning. Application of the Electre Method at Regional Level for the Diffusion of Renewable Energy Technology. Renewable Energy , 28 (13), 2063-2087. Belton, V., & Stewart, T. J. (2002). Multiple Criteria Decision Analysis. Kluwer Academic Publishers. Bogetoft, P., & Pruzan, P. (1997). Planning with Multiple Criteria: Investigation, Communication and Choice. København: Handelshøjskolens forlag. Bouyssou, D. (1990). Building criteria: A prerequisite for MCDA. (C. Bana, Ed.) Readings in Multiple Criteria Decision Aid . Bouyssou, D. (1992). Ranking methods based on valued preference relations: A characterization of the net-flow method. European J. Oper. Res. , 60, 61-68. Brans, J. (1982). L'ingénièrie de la décision; Elaboration d'instruments d'aide à la décision. La méthode PROMETHEE. In R. Nadeau, & M. Landry (Ed.), L'aide à la décision: Nature, Instruments et Perspectives d'Avenir (pp. 183-213). Québec: Presses de l'Université Laval. Brans, J., & Vincke, P. (1985). A preference ranking organisation method - the PROMETHEE method for multiple criteria decision making. Managm. Sci. , 3(6), 647-656. Brans, J., Vincke, P., & Mareschal, B. (1986). How to select and how to rank projects: the PROMETHEE method. European Journal of Operational Research , 228-238. Bridges. (2005). Comparative Risk Assessment. Buchanan, J., & Sheppard, P. (2001). Ranking Projects Using the ELECTRE Method. Hamilton, New Zealand. Bui, X. (1987). Co-oP: A Group Decision Support System for Cooperative Multiple Criteria Group Decision Making. New York, New York, USA: Springer. Capros, P., Papathanassiou, S., & Samoulidis, J. (1988). Multicriteria Analysis of Energy Supply Decisions in an Uncertain Future. Omega , 16 (2), 107-115.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 149 Catrinu, M. (2006). Decision Aid for Planning Local Energy Systems: Application of Multi-Criteria Decision Analysis (Doctoral Theses). Trondheim: Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, Department of Electrical Power Engineering. Clauss, D., & Hall, M. (2009, Agosto 4). European Commission. Retrieved from European Commission: http://ec.europa.eu/europeaid/how/ensuringquality/rom/documents/rom_handbook2009_en.pdf Cook, W., & Seiford, L. (1982). On the Borda-Kendall consensus method for priority ranking problems. Managm. Sci. , 1721-1732. Chankong, V., & Haimes, Y. (1983). Multiobjective Decision Making Theory and Methodology. New York, New York, USA: Elsevier Science. Chen, S., & Hwang, C. (1999). Multiple Attribute Decision Making Methods and Applications. (G. Liang, Ed.) European Journal of Operational Research . Daellenbach, H. (2005). Management Science: Decision Making through Systems Thi. Basingstoke: Palgrave Macmillan. Diakoulaki, D., & Karangelis, F. (2007). Multi-Criteria Decision Analysis and Cost-Benefit Analysis of Alternative Scenarios for the Power Generation Sector in Greece. Renewable and Sustainable Energy Reviews , 11 (4), 716-727. Diakoulaki, D., Antunes, C., & Martins, A. (2005). MCDA and Energy Planning. (J. Figueira, S. Greco, & M. Ehrgott, Eds.) Multiple Criteria Decision Analysis: State of the Art Surveys . Dodgson, J., Spackman, M., Pearman, A., & Phillips, L. (2001). DTLR Multi-Criteria Analysis Manual. UK Dept. for Transport, Local Government and the Regions. Figueira, J. R., Greco, S., & Ehrgott, M. (2005). Multiple Criteria Decision Analysis: State of the Art Surveys. Boston, Dordrecht, London: Springer Verlag. Figueira, J., & Roy, B. (2002). Determining the weights of criteria in the ELECTRE type methods with a revised Simos' procedure. European J. Oper. Res. , 139, 317-326. Finlay, P. N. (1994). Introducing decision support systems. Cambridge: Blackwell Publishers. Gachet, A. (2004). Building Model-Driven Decision Support Systems with Dicodess. Zurich: VDF. Georgopoulou, E., Lalas, D., & Papagiannakis, L. (1997). A Multicriteria Decision Aid Approach for Energy Planning Problems: The Case of Renewable Energy Option. European Journal of Operational Research , 103 (1), 38-54. Georgopoulou, E., Sarafidis, Y., & Diakoulaki, D. (1998). Design and Implementation of a Group DSS for Sustaining Renewable Energies Exploitation. European Journal of Operational Research , 109 (2), 483-500.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 150 Goicoechea, A., Hansen, D. R., Duckstein, L., & Goicochea, A. (1982). Multiobjective Analysis With Engineering and Business Applications. Seattle, WA, U.S.A.: John Wiley & Sons Inc. Goletsis, Y., Askounis, D., & Psarras, J. (2001). Multicriteria judgments for project ranking: An integrated methodology, Economic Financial Modelling. Autumn Issue. Goletsis, Y., Psarras, J., & Samoulidis, J.-E. (2003). Project Ranking in the Armenian Energy Sector Using a Multicriteria Method for Groups. Annals of Operations Research , 120, 135-157. Greening, L., & Bernow, S. (2004). Design of Coordinated Energy and Environmental Policies: Use of Multi-Criteria Decision-Making. Energy Policy , 32 (6), 721-735. Guitouni, A., & Martel, J.-M. (1998). Tentative Guidelines to Help Choosing an Appropriate MCDA Method. European Journal of Operational Research , 109 (2), 501-521. Haag, Cummings, McCubbrey, Pinsonneault, & Donovan. (2000). Management Information Systems: For The Information Age. McGraw-Hill Ryerson Limited. Haettenschwiler, P. (1999). Neues anwenderfreundliches Konzept der Entscheidungsunterstützung. vdf Hochschulverlag , 189-208. Haralambopoulos, D., & Polatidis, H. (2003). Renewable Energy Projects: Structuring a MultiCriteria Group Decision-Making Framework. Renewable Energy , 28 (6), 961-973. Hobbs, B. (1986). What Can We Learn from Experiments in Multiobjective Decision Analysis? IEEE Transactions on Systems, Man and Cybernetics , SMC-16 (3), 384-394. Hobbs, B., & Meier, P. (2000). Energy Decisions and the Environment: A Guide to the Use of Multicriteria Methods. Boston, USA: Kluwer Academic Publishers. Hobbs, B., & Meier, P. (1994). Multicriteria Methods for Resource Planning: An Experimental Comparison. IEEE Transactions on Power Systems , 9 (4), 1811-1817. Hobbs, B., Chankong, V., Hamadeh, W., & Stakhiv, E. (1992). Does Choice of Multicriteria Method Matter - an Experiment in Water-Resources Planning. Water Resources Research , 28 (7), 1767-1779. Kangas, A., Kangas, J., & Pykalainen, J. (2001). Outranking methods as tools in strategic natural resources planning. Silva Fennica , 215-227. Keen, P. (1978). Decision support systems: an organizational prespective. Reading: AddisonWesley Pub. Co. Keen, P. G. (1980). Decision support systems: a research perspective. Decision support systems : issues and challenges. New York: Pergamon Press. Keeney, R. (1988). Structuring Objectives for Problems of Public Interest. Operations Research , 36 (3), 396-405.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 151 Keeney, R., & Raiffa, H. (1976). Decisions with multiple objectives: Preferences and value tradeoffs. (J. Wiley, Ed.) New York, New York, USA. Kelly, G. (1955). The Psychology of Personal Constructs (Vols. 1, 2). Norton, New York, USA. Kuhn, H., & Tucker, A. (1951). Nonlinear programming. (J. Neyman, Ed.) Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability , 481-492. Lehmann, E., & D'Abrera, H. (1998). Nonparametics: Statistical Methods Based on Ranks. New York: McGraw-Hill. Linkov, I., Satterstrom, F., Kiker, G., Batchelor, C., Bridges, T., & Ferguson, E. (2006). From Comparative Risk Assessment to Multi-Criteria Decision Analysis and Adaptive Management: Recent Developments and Applications. Environmen International , 32 (8), 1072-1093. Little, J. (1970). Models and Managers: The Concept of a Decision Calculus. Management Science . Løken, E. (2007). Multi-Criteria Planning of Local Energy Systems with Multiple Energy Carriers. Trondheim: NTNU-trykk. Loken, E., Botterund, A., & Holen, A. (2006). Decision Analysis and Uncertainties in Planning Local Energy Systems. The 9th International Conference on Probabilistic Methods Applied to Power Systems. Stockholm, Sweden. Macharis, C., Brans, J., & Mareschal, B. (1998). The GDSS PROMETHEE procedure. J. Decision Systems , 283-307. Marakas, G. M. (1999). Decision support systems in the twenty-first century. Prentice Hall. Mareschal, B., & Brans, J. (1988). Geometrical representations for MCDA. European Journal of Operational Research , 34, 69-77. Moore, J., & Chang, M. (1980). Design of Decision Support Systems. Data Base . Pohekar, S., & Ramachandran, M. (2004). Application of Multi-Criteria Decision Making to Sustainable Energy Planning - a Review. Renewable and Sustainable Energy Reviews , 8 (4), 365-381. Power, D. J. (2002). Decision support systems: concepts and resources for managers. Quorum Books. Power, D. J. (1997). What is a DSS? The On-Line Executive Journal for Data-Intensive Support . Ramanathan, R., & Ganesh, L. (1995). Energy Resource Allocation Incorporating Qualitative and Quantitative Criteria: An Integrated Model using Goal Programming and AHP. Socio-Economic Planning Sciences , 29 (3), 197-218.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 152 Ramathanan, R., & Ganesh, L. (1994). Group preference aggregation methods employed in AHP: An evaluation and an intrinsic approach for deriving members' weightages. European J. Oper. Res. , 249-265. Rogers, M., & Bruen, M. (1998). Choosing realistic values of indifference, preference and veto thresholds for use with environmental criteria within ELECTRE. European J. Oper. Res. , 107, 542-551. Rogers, M., Bruen, M., & Maystre, L.-Y. (1999). ELECTRE and Decision Support. Dordrecht, The Netherlands: Kluwer Academic. Roy, B. (1968). Classement et choix en présence de points de vue multiples (la méthode ELECTRE). Rev. Franc. Automatique Inform. , 57-75. Roy, B. (1985). Méthodologie multicritère d'aide à la décision. Paris: Economica. Roy, B. (1996). Multicriteria Methodology for Decision Aiding (Vol. 12). Dordrecht: Kluwer Academic. Roy, B. (1990). Sur la notion d'importance relative des critères. 12th Triennal Conference an Operations Research. Athens, Greece. Roy, B. (1990). The outranking approach and the foundations of ELECTRE methods. Readings in Multiple Criteria Decision Aid . Roy, B., Present, M., & Silhol, D. (1986). A programming method for determining which Paris metro stations should be renovated. European J. Oper. Res. , 24, 318-334. Saaty, T. (1996). Decision Making with Dependence and Feedback The Analytic Network Process. Pittsburgh: RWS Publications. Saaty, T. L. (1994). How to make a decision: the analytic hierarchy process. Interfaces , 19-43. Saaty, T. L. (1980). The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation. McGraw-Hill. Saaty, T. L. (2005). Theory and Applications of the Analytic Network Process: Decision Making with Benefits, Opportunities, Costs and Risks. Pittsburgh, Pennsylvania, USA: RWS Publications. Saaty, T. L., & Cillo, B. (2009). The Encyclicon, Volume 2: A Dictionary of Complex Decisions using the Analytic Network Process. Pittsburgh, Pennsylvania, USA: RWS Publications. Saaty, T. L., & Vargas, L. G. (2006). Decision Making with the Analytic Network Process: Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and Risks. New York, New York, USA: Springer. Seager, T. P. (2004). A taxonomy of metrics for testing the industrial ecology. J. Cleaner Production , 865-875.
National and Technical University of Athens Decision Support System for Project Monitoring Portfolio 153 Simpson, L. (1996). Do Decision Makers Know What They Prefer?: MAVT and ELECTRE II. Journal of the Operational Research Society , 47, 919-929. Siskos, J., & Hubert, P. (1983). Multi-Criteria Analysis of the Impacts of Energy Alternatives:. European Journal of Operational Research , 13 (3), 278-299. Sprague, R. H., & Carlson, E. D. (1982). Building effective decision support systems. Prentice Hall. Sprague, R., & Watson, H. (1993). Decision support systems: putting theory into practice. New Jersey, New York, USA: Prentice Hall. Sproles, N. (2000). Coming to Grips with Measures of Effectiveness. Systems Engineering , 3 (1), 50-58. Stewart, T. (1992). A Critical Survey on the Status of Multiple Criteria Decision Making Theory and Practice. Omega , 20 (5-6), 569-586. Triantaphyllou, E. (2001). Multi-criteria decision making methods: A comparative study. (L. M. Guzman, Ed.) Brussels, Belgium: Kluwer Academic Publishers. Turban, E. (1995). Decision support and expert systems: management support systems. Prentice Hall. Tzeng, G.-H., Shiau, T.-a., & Lin, C.-Y. (1992). Application of Multicriteria Decision Making to the Evaluation of New Energy System Development in Taiwan. Energy , 17 (10), 983-992. Vincke, P. (1992). Multicriteria Decision Aid. Wiley. von Winterfeldt, D., & Edwards, W. (1986). Decision Analysis and Behavioral Research. Cambridge: Cambridge University Press. Whitworth, W., & Felton, R. (1998). Measuring disagreement in groups facing limited choice problems. Proc. of the 32nd Hawai Internat. Conf. on System Sciences. Hawai: IEEE Computer Soc. Press. Yang, H., & S.L., C. (1989). Incorporating a Multi-Criteria Decision Procedure into the Combined Dynamic Programming/Production Simulation Algorithm for Generation Expansion Planning. IEEE Transactions on Power Systems , 4 (1), 165-175. Yoe, C. (2002). Trade-Off Analysis Planning and Procedures Guidebook. Zeleny, M. (1982). Multiple Criteria Decision Making. New York, New York, USA: McGraw-Hill. Zimmermann, H. (1996). Fuzzy Sets, Decision Making and Expert Systems. McGraw-Hill.