Using the hybrid fuzzy goal programming model and hybrid genetic algorithm to solve a multi-objective location routing problem for infectious waste disposal

Narong Wichapa; Porntep Khokhajaikiat Article Using the hybrid fuzzy goal programming model and hybrid genetic algorithm to solve a multi-objective location routing problem for infectious waste disposal Journal of Industrial Engineering and Management (JIEM) Provided in Cooperation with: The School of Industrial, Aerospace and Audiovisual Engineering of Terrassa (ESEIAAT), Universitat Politècnica de Catalunya (UPC) Suggested Citation: Narong Wichapa; Porntep Khokhajaikiat (2017) : Using the hybrid fuzzy goal programming model and hybrid genetic algorithm to solve a multi-objective location routing problem for infectious waste disposal, Journal of Industrial Engineering and Management (JIEM), ISSN 2013-0953, OmniaScience, Barcelona, Vol. 10, Iss. 5, pp. 853-886, https://doi.org/10.3926/jiem.2353 This Version is available at: https://hdl.handle.net/10419/188844 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/3.0/ Journal of Industrial Engineering and Management JIEM, 2017 – 10(5): 853-886 – Online ISSN: 2013-0953 – Print ISSN: 2013-8423 https://doi.org/10.3926/jiem.2353 Using the Hybrid Fuzzy Goal Programming Model and Hybrid Genetic Algorithm to Solve a Multi-Objective Location Routing Problem for Infectious Waste Disposal Narong Wichapa , Porntep Khokhajaikiat Khon Kaen University (Thailand) [email protected], [email protected] Received: May 2017 Accepted: September 2017 Abstract: Purpose: Disposal of infectious waste remains one of the most serious problems in the social and environmental domains of almost every nation. Selection of new suitable locations and finding the optimal set of transport routes to transport infectious waste, namely location routing problem for infectious waste disposal, is one of the major problems in hazardous waste management. Design/methodology/approach: Case study, which involves forty hospitals and three candidate municipalities in sub-Northeastern Thailand, is divided into two phases. The first phase is to choose suitable municipalities using hybrid fuzzy goal programming model which hybridizes the fuzzy analytic hierarchy process and fuzzy goal programming. The second phase is to find the optimal routes for each selected municipality using hybrid genetic algorithm which hybridizes the genetic algorithm and local searches including 2-Opt-move, Insertion-move and λ-interchange-move. Findings: The results indicate that the hybrid fuzzy goal programming model can guide the selection of new suitable municipalities, and the hybrid genetic algorithm can provide the optimal routes for a fleet of vehicles effectively. -853- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 Originality/value: The novelty of the proposed methodologies, hybrid fuzzy goal programming model, is the simultaneous combination of criteria in order to choose new suitable locations, and the hybrid genetic algorithm can be used to determine the optimal routes which provide a minimum number of vehicles and minimum transportation cost under the actual situation, efficiently. Keywords: multi-objective facility location problem, fuzzy analytic hierarchy process; fuzzy goal programming model, hybrid genetic algorithm, infectious waste disposal, multi-criteria decision making, location routing problem 1. Introduction Health-care waste management, including collection, transportation, treatment and disposal, is a very important issue as far as the hospital environment and public is concerned. Improper waste management will cause environmental pollution, unpleasant smells and growth and multiplication of insects, rodents and worms, and may lead to transmission of diseases like typhoid, cholera, and hepatitis through injuries from sharps contaminated with human blood (Abdulla, Abu Qdais & Rabi, 2008). Infectious waste material is one of the hazardous wastes generated at health-care facilities. The collection, transportation, treatment and disposal of infectious waste can cause substantial harm to human health and safety or to the environment when improperly handled (Hansakul, Pitaksanurat, Srisatit & Surit, 2010; Miyazaki & Une, 2005). Selecting locations for the construction of disposal facilities and finding the optimal set of routes for infectious waste disposal are the important steps for pollution control, minimizing environmental hazards and minimizing costs. Infectious waste management remains one of the major problems in the hazardous waste management in Thailand. The government is aware of this problem, and has set policies to manage this waste more effectively. Infectious waste management problems are often found, such as illegal dumping, delayed collection and delayed disposal because the existing incinerators are insufficient to meet demands. Although, in the past, many public hospitals had their own incinerators to dispose of their infectious waste, because of environmental concerns and protests by local residents and hospital staff members, these incinerators inside the hospitals have been shut down. Hence, these hospitals eventually require services from outside agencies. However, there are three serious problems which are often found from using the services of outside agencies. First, the existing outside agencies cannot dispose of all existing infectious waste. Second, waste collection by outside agencies can be delayed, which does not meet the requirements of hospitals. Finally, transporting infectious waste from public hospitals does not meet the regulatory requirements for safety, such as the illegal dumping and -854- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 illegal disposal in inappropriate places. Hence the Thai government has set up a policy to encourage the construction of new disposal facilities at areas of potential municipalities, in order to address the abovementioned problems and increase the efficiency of infectious waste disposal. These disposal facilities must be able to serve nearby hospitals and at the same time must reduce economic, environmental, health, and social factors. In order to achieve maximum benefit, new disposal facilities need to be planned along with suitable transport routes which provide the lowest transportation cost in accordance with the due date time. Therefore, building new, suitable, disposal facilities and finding the transport routes for infectious waste disposal more effectively is becoming an issue that is particularly important to consider. Community hospitals, with forty hospitals in sub-Northeastern Thailand, are one type of public hospital that has often found the abovementioned problems, because they are far from the existing disposal facilities of outside agencies. To address such problems, the government has set policies to locate the new sites for infectious waste disposal at areas of potential municipalities. Selecting new suitable sites in this case is a complex problem which is difficult to address using any existing techniques alone, because there are relevant factors which must be considered, including infrastructure, geological, environmental, social and cost factors. Certainly, all factors must be considered simultaneously in designing an optimal transportation network. Finally, in order to achieve maximum benefit, we need to find suitable transport routes which provide minimum transportation cost for each selected municipality. From the literature reviewed and due to the complexity of this issue, the solution approach for the location routing problem (LRP) for infectious waste disposal consists of the following stages: (i) suitable municipalities are first selected by combining the fuzzy analytic hierarchy process (FAHP) and the fuzzy goal programming model (FGP model), namely the hybrid fuzzy goal programming model (HFGP), and (ii) the vehicle routing problem (VRP) based on the selected municipalities sequentially. Firstly, selecting new, suitable municipalities for infectious waste disposal is an issue with many relevant factors (both tangible and intangible) that need to be considered simultaneously. The facility location problem (FLP) in this case is one of the multi-criteria decision making problems (MCDM problems), namely the multi-criteria/objective facility location problem (MCFLP/MOFLP). This problem is a complex problem which is difficult to solve and interpret. Using only one tool may not be sufficient to solve this problem. From the literature reviewed, FAHP is a powerful tool to solve multi-attribute decision making (MADM) problems which are difficult to interpret, and the FGP model is a suitable tool to solve multi-fuzzy objective problems. Hence, combining FAHP and FGP models should make a suitable model to solve location selection in this case, in order to maximize total priority weight and total cost. Finally, after obtaining the new suitable municipalities from the HFGP model, finding the vehicle trips for each selected municipality is one of the vehicle routing problems (VRPs). The VRPs belong to an NP-Hard problem in combinatorial optimization which is hard to solve by exact solution techniques. Hence, the -855- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 Genetic algorithm (GA) is one of various meta-heuristic algorithms which are often used to solve the VRPs in the literature because it is a simple, flexible and powerful algorithm to solve NP-hard problems. However, in order to increase the efficiency of this algorithm, a new hybrid genetic algorithm (hybrid GA) is developed to solve the VRP in this case study, instead of the traditional GA. The major difference between the traditional GA and the hybrid GA in this case is that three local searches (2-Opt-move, Insertion-move and λ-interchange-move) are added to increase the efficiency of the algorithm. This is the major reason why hybrid GA is chosen as a suitable algorithm for solving the VRP in this paper. The rest of the paper is organized as follows. Sections 2, 3 and 4 are Literature review, Methodology and Application of the proposed methodology respectively, and finally, Section 5 is the Conclusion. 2. Literature Review The facility location problem (FLP) has been studied for over one hundred years. Even though it is old, applications of these models to real world problems are getting more attractive. The FLP is a classic problem, originating from Pierre de Fermat, Evagelistica Torricelli, and Battista Cavallieri (Drezner & Hamacher, 2004). However, it is formally accepted by all scientists that Alfred Weber’s book is the most important historic origin of location science (Farahani, SteadieSeifi & Asgari, 2010). Traditional FLP is a single objective/criterion problem, and objectives that are usually considered in location problems can be different. These objectives can be as follows: minimizing the longest distance from the existing facilities, minimizing the total setup cost (Vasko & Wilson, 1986), minimizing the tour total cost (Gendreau, Laporte & Semet, 1997), minimizing the total cost (Nozick, 2001) and minimizing the number of located facilities (Toregas, Swain, ReVelle & Bergman, 1971). Although facility location theory has a long history in single objective/criterion problems, it seems that since the origin of multi-criteria decision making theory (MCDM theory) in management sciences, this theory has been applied in the real word problems of location selection. The MCDM problems are divided into multi-attribute decision making (MADM) and multi-objective decision making (MODM) problems. In the MADM problem there is a limited number of predetermined alternatives and a single goal/objective. MADM aims to select the best from the predetermined alternatives. There are several common tools which are used to tackle the MADM problems, such as simple additive weighting (SAW), hierarchical additive weighting, elimination and choice expressing reality (ELECTRE), technique for order preference by similarity to an ideal solution (TOPSIS), analytical hierarchy process (AHP) and data envelopment analysis (DEA) (Kuo, Yang & Huang, 2008). One tool often suggested for solving MADM problems is AHP (Majumdar, Mangla & Gupta, 2010), because it is a flexible and powerful tool for handling both qualitative and quantitative data (Ünal & Güner, 2009). Since the traditional AHP still cannot reflect the human thinking style, the fuzzy -856- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 analytic hierarchy process (FAHP) based on the fuzzy set theory of Zadeh (1965a) was developed in order to overcome this weak point for solving fuzzy problems (Kahraman, Cebeci & Ruan, 2004). Nowadays this tool is widely used for solving MADM problems instead of traditional AHP as shown in literature (Shaverdi, Ramezani, Tahmasebi & Rostamy, 2016; Verma & Chaudhri, 2014; Wang, Lestari & Tran, 2017). Since the MADM tools alone cannot handle the multi-existing environmental restrictions of the MODM problems, such as selecting the locations for hazardous waste disposal, choosing the plants for nuclear power and choosing the suitable locations for infectious waste disposal, a group of researchers have taken MADM tools combined with mathematical techniques in order to simultaneously deal with environmental restrictions. Goal programming (GP), proposed by Charnes, Cooper and Ferguson (1955), has been often combined with the MADM tools for solving MODM problems in the literature (Badri, 1999; Blake & Carter, 2002; Fang & Li, 2015; Karsak, Sozer & Alptekin, 2003; Kengpol, Tuammee & Tuominen, 2014). However, in practice, determining exactly the target value of each goal is difficult for decision makers; a decision maker does not have sufficient information related to the different goals. To overcome the weakness, the fuzzy set theory initially introduced by Zadeh (1965b) has been applied to MODM problems with imprecise data. Zimmermann (1976) and Zimmermann (1978) proposed the fuzzy set theory to a linear programming (LP) problem with single and multiple objectives. Narasimhan (1980) first proposed fuzzy set theory to GP, namely the fuzzy goal programming (FGP) model, to specify imprecise aspiration levels of each fuzzy goal. This research first considers a symmetrical FGP model, having equal important weights for each objective. Later, Hannan (1981) simplified the Narasimhan approach by using the interpolated membership functions, and then this model could be solved using the LP. Because various problems in the real world often have different levels of each objective, the solution approach is extended to the case of asymmetrical FGP, having unequal important weights for each goal. Although several asymmetrical FGP models (Lin, 2004; Tiwari, Dharmar & Rao, 1987; Yaghoobi & Tamiz, 2007; Yücel & Güneri, 2011) have been proposed in the literature, the weighted max-min model based on Lin (2004) was developed to solve asymmetrical FGP problems effectively; this model can properly reflect the views of experts, unlike other methods (Amid, Ghodsypour & O’Brien, 2011). Therefore, in this paper, a weighted FGP model based on the max-min FGP model of Lin (2004) has been developed for solving the new MOFLP model for infectious waste disposal in this case study, by taking the priority weights of each candidate municipality into this weighted max-min FGP model. This new fuzzy model enables decision makers not only to consider the imprecision of information but also to take the limitations of available resources into account in calculating new suitable municipalities for infectious waste disposal from each candidate municipality, unlike the traditional FLPs. For this reason, selecting this fuzzy model will enhance the confidence of decision makers for choosing the suitable locations for infectious waste disposal. -857- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 The vehicle routing problem (VRP) consists of determining a set of vehicle trips, including customers, a single depot and routes. Each vehicle trip starts and ends at the same depot with known location and capacity, each customer with known location and demands is assigned to exactly one vehicle, and any vehicle cannot carry over its capacity. Each vehicle may also be limited in the total distance (maximum allowed distance). The objective is to determine a set of vehicle routes for each vehicle that will often minimize the total distance/transportation cost. The basic models of VRP were proposed in papers of Dantzig and Ramser (1959) and Clarke and Wright in (1964). Later, the VRP has been very extensively studied in literature because of its wide applicability and its importance to many real world situations for reducing operational costs in transportation networks. The VRP is extended with variants for each problem such as VRP with time windows (Anghinolfi, Paolucci & Tonelli, 2016), VRP with pick-up and delivery (Tasan & Gen, 2012), VRP with backhauls (Brandão, 2006), VRP with multi-depot (Zhang, Zhong, Liu & Wang, 2014) and VRP with multi-objective (Alexiou & Katsavounis, 2015). These VRP models are known to be the NP-hard problems (Meryem & Abdelmadjid, 2015; Narasimha, Kivelevitch, Sharma & Kumar, 2013), and it is difficult to solve large NP-hard problems by exact solution techniques. Hence, when the problems become too large for exact solution techniques, recent meta-heuristic techniques (Montané & Galvão, 2006; Baker & Ayechew, 2003; Goksal, Karaoglan & Altiparmak, 2013; Liu, Xie, Augusto & Rodriguez, 2013; Nagy & Salhi, 2005) are often used for solving various VRP models. However, there are no meta-heuristic techniques to confirm which is best, depending on the variant of each problem and individual preference. The genetic algorithm (GA) is one of the meta-heuristic techniques which is often employed to solve the various VRPs in the literature (Baker & Ayechew, 2003; Potvin, Duhamel & Guertin, 1996) because this algorithm is easy to understand, has great flexibility and is applicable to many kinds of real world problems (Ho, Ho, Ji & Lau, 2008). However, in order to improve the solution efficiency, nowadays the GA technique is often integrated with other tools/techniques for dealing with various VRPs. The various new algorithms of hybrid genetic algorithm (hybrid GA) (Jeon, Leep & Shim, 2007; Shi, Boudouh & Grunder, 2017; Vidal, Crainic, Gendreau, Lahrichi & Rei, 2012) have been continuously developed for solving real world VRPs, depending on the preferences and expertise of each researcher. Hence, combining GA with other tools/techniques, namely hybrid GA, is one of the most popular techniques for solving VRPs in literature, which is appropriate and adequate for solving the VRPs in this case study. This is the major reason why hybrid GA was chosen as an appropriate technique in this paper. -858- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 3. Methodology The solution approach for this case consists of the following stages. (i) The first phase of this research is to select suitable municipalities for infectious waste disposal from candidate municipalities, for which location selection in this case is a complex problem, a multi-objective facility problem. The HFGP model is formed in the first phase by combining FAHP and FGP models in order to achieve the lowest total cost and maximum total priority weight. (ii) After that, the VRP model and hybrid GA are used in the second phase in order to achieve the lowest transportation cost/minimum total distance by using the optimization techniques with LINGO13 and Visual studio 2015 (C++) respectively. The details of selecting the new suitable municipalities and finding the suitable transport routes for minimizing transportation cost/minimizing total distance are as follows: •Define the most important criteria for selection of locations for infectious waste disposal, •Evaluate the global priority weights for each candidate municipality using FAHP, •Formulate and compute a HFGP model, •Select the new suitable municipalities for infectious waste disposal. •Build and compute the VRP model using an optimization technique (LINGO13) and meta-heuristic technique with Visual studio 2015 (hybrid GA with C++), and •Select the optimal routes for each selected municipality. The first step is to define the most important criteria for selection of locations for infectious waste disposal, and determining candidate municipalities is considered by using legislation, regulations and expertise. After that, these important criteria and candidate locations are decomposed into a multi-level hierarchical structure. The second step is to evaluate the priority weights of elements in the proposed hierarchical structure using FAHP. The third step is to formulate and compute the HFGP model which takes the weights of candidate municipalities into this model for extension to consider needed criteria for this problem. The fourth step is to choose the suitable municipalities from results of the HFGP model. Another step is to build and compute the VRP model using LINGO13 and hybrid GA, and then the proposed hybrid GA is used to solve the VRP model for a large size problem in this case. The final step is to choose the optimal routes for each selected municipality from results of the proposed hybrid GA. -859- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 3.1. FAHP From the literature reviewed, FAHP is a flexible and powerful tool to solve MADM problems. Hence, using FAHP should make a suitable approach to evaluate the global priority weights of each candidate municipality, in order to take these weights into a HFGP model in Section 3.2. In this paper, we calculated the priorities weights of elements in each level of hierichy via the geometric means method of Buckley (1985) and Buckley, Feuring and Hayashi (2001); see also in similar papers of Cebeci (2009) and Meixner (2009). In this paper, the fuzzy arithmetic operations on triangular fuzzy numbers (TFNs) can be expressed as follows: Addition: F1  F2 = (l1 + l2, m1 + m2, u1 + u2)(1) Multiplication: F1  F2 = (l1 · l2, m1 · m2 ·m2, u1 · u2)(2) Division: F1 / F2 = (l1 /u2, m1 /m2, u1 /l2)(3) Reciprocal: F1–1 = (1/u1, 1/m1, 1/l1) (4) where l1 and l2 are the least possible value; m1 and m2 are modal value and u1 and u2 are highest possible value respectively. F1 and F2 are two TFNs; TFNs will be applied in order to compare a priority scale between criteria/elements as shown in Table 1. TFNs Definition (1,1,1) Equal importance (2,3,4) Moderate importance (4,5,6) Strong importance (6,7,8) Very strong importance (8,9,9) Extreme importance Intermediate values between the two adjacent judgments Table 1. The 9 - point scale of TFNs The steps of the FAHP are as follows. -860- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 N is a set of hospitals and municipalities, N = {1, 2, 3, ..., n}. qk is the capacity of each vehicle k (kg). dj is the amount of waste collected from hospital j (kg). tij is the travel time from node i to j (min.) that is symmetrical (tij = tji). D is the maximum permitted travel time per vehicle (min.). Each vehicle travels from node i to j at a speed of 60 kilometers per hour (tij = dtij). Decision variables: Xijk =1, if vehicle k drives from hospital i to j, Xijk = 0, otherwise. Zk =1, if vehicle k is used to service hospitals, Zk = 0 otherwise. Objective function: (30) Constraints: (31) (32) (33) (34) (35) (36) (37) (38) -867- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 Xijk  {0, 1} i  N , j  N , k  K (39) Zk  {0, 1} (40) Yi – Yj + N · Xijk ≤ N – 1 i = 2, 3, 4, …,n; j  = 2, 3, 4, …,n; i  j; k  K(41) The objective is to minimize the total distance, as shown in Equation (30). Equation (31) guarantees that the number of arcs from node i and node j does not exceed n nodes. Equation (32) and Equation (33) guarantee that a vehicle must start at a selected municipality to hospitals only once. Equation (34) guarantees that if a vehicle visits a hospital j, it also leaves that hospital j. Equations (35) and (36) guarantee that all hospitals are visited only once. Equation (37) guarantees that the amount of infectious waste of each hospital will be fulfilled by vehicles k but does not exceed the capacity of the vehicle itself. Equation (38) ensures that every vehicle k cannot travel more than the tour length restriction. Equation (39) and Equation (40) guarantee the decision variables xijk and zk to be binary decision variables. Equation (41) guarantees that there will be no sub tours. In this case study, hybrid GA will be used to solve the VRP model for infectious waste disposal in this case as shown in the next section. 3.4. Hybrid GA Genetic algorithms (GA), which were firstly proposed by Holland (1992), are very easy to understand, have great flexibility and are applicable to many kinds of actual problems (Ho et al., 2008). GA is a stochastic and parallel search technique that imitates the principles of evolution and natural selection by using genetic operators (Li, 2011). The process of traditional GA usually starts with a randomly generated population of n chromosomes, called an initial population. According to the nature of VRPs, different positions in each chromosome are often encoded as numbers, and these positions are randomly changed within a range during evolution. The simplest form of GA involves three operators: selection, crossover and mutation. After obtaining population of size p, parents are randomly chosen from the current population for reproduction, on the basis of a value of probability distribution. Any chromosomes with fitter values (higher values of fitness function) are given more opportunities to reproduce by crossover and mutation. After the reproductive process, some parents and some offspring will be chosen to be the new generation in accordance with their fitness values, and by rejecting others to maintain the size of the population constant. After the number of generations is predetermined, the algorithm converges to the best chromosome, which is expected to be the best solution of the problem. GA performance depends -868- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 on relevant parameters such as probability of crossover, probability of mutation, population size, repetition number, and algorithm. A hybrid genetic algorithm (Hybrid GA), which integrates GA and three local searches (insertion-move, 2-opt-move and λ-interchange-move), was proposed to solve the VRP in this case. The first objective of the hybrid GA is to minimize the number of vehicles (NV) and the second objective is to minimize the total distance (TD), under the limits of existing resources. The algorithm is shown in Figure 3. Figure 3. Flow chart of solution of VRP using hybrid GA -869- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 Figure 3 can be described as follows. Let n be the size of the population at each generation. An initial population will be randomly generated until the size is equal to n. After that, the chromosomes in the initial population are sorted by fitness, and then a pair of chromosomes is randomly chosen for mating using the ranking-based selection of Correa et al. (Correa, Steiner, Freitas & Carnieri, 2001), as shown in Equation (42). (42) OS is an ordered list of solutions sorted by fitness. P is the position in the OS to be selected as the chromosome Sp. rnd (M) is a random distribution in the range 0 to M-1. After that, with crossover probability (pc), exchange parts of a pair of parents and create two offspring as shown in Figure 4. Figure 4. Crossover procedure •Randomize indices cut1 and cut2, where cut1 < cut2 •Step 1: Copy hospitals in parent-1 (P1) from indices cut1 to cut2 to child-2 (C2) starting at index 0. Also hospitals in parent-2 (P2) from indices cut1 to cut2 to child-1 (C1) starting at index 0. •Step 2: mask hospitals in P1 that already are contained in C1 and also mask hospitals in P2 that already are contained in C2. •Step 3: fill hospitals that unmask in C1 to P1 and C2 to P2. In the mutation procedure, with the mutation probability pm, hospitals in the two offspring chromosomes will be randomly swapped as shown in Figure 5A. The mutation procedure is repeated until the size of the new population is equal to 100. After that, offspring and the old population (current population) will -870- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 be combined and n chromosomes picked to be the new population using fitness. If a new chromosome is better than any chromosome in the current population, the new chromosome will be included and the worst one in the current population will be removed. Finally, the chromosomes in the new population will be improved by three local searches, insertion-move, 2-opt and λ-interexchange, as shown in Figure 5B, Figure 5C and Figure 5D respectively. Figure 5. Mutation and three local searches (Insertion, 2-Opt and λ-interchange) The selection is still a rank-based selection and selects chromosomes n times for each local search. This procedure is repeated until the stopping criteria are satisfied. Implementation and computational results of the hybrid GA are reported in the next section. 4. Application of the Proposed Methodology In Section 3, the proposed methodology was used to identify the suitable locations and transport routes for a case study on the selection of a transportation network for infectious waste disposal in sub-Northeastern Thailand. There are three candidate municipalities, including Nong Bua Lam Phu Town Municipality (NLTM), Nong Khai Town Municipality (NKTM), and Loei Town Municipality (LTM). These candidates were extracted from legislation, regulation and expertise by experts. Therefore, the suitable municipalities were chosen from three candidate municipalities to serve the forty community hospitals, namely H1, H2, ..., H40 (see details in Figure 6), given the resource restrictions and preferences. The steps of the calculation are shown in Sections 4.1, 4.2 and 4.3. -871- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 Figure 6. The transportation network of the candidate municipalities and hospitals 4.1. Estimate the Priority Weights of Municipalities Using FAHP This section presents the steps to determine the priority weights of elements at each level. Firstly, a multi-level hierarchical structure was constructed by consulting six decision makers, who have worked in the field for more than fifteen years, and stakeholders (see Figure 1). In the hierarchy, level 0 was the goal, the new suitable municipalities for infectious waste disposal, and level 1 was three main criteria, infrastructure (C1), geological (C2) and environmental & social (C3). Level 2 was ten sub-criteria, public utilities (SC11), traffic (SC12), area size (SC21), features of area (SC22), flooding in the past (SC23), density of population (SC24), municipal administrators (SC31), ability of municipalities (SC32), distance from communities (SC33) and distance from public water resources (SC34). Level 3 had three candidate municipalities, L1 = NLTM, L2 = NKTM and L3 = LTM. Secondly, fuzzy comparison matrices were constructed from the six decision makers who have worked in the field for more than fifteen years using the 9scale of FAHP (Table1), as shown in Table 2. Third, the fuzzy comparison matrices of the decision makers were aggregated into a FAHP combined matrix ( ) using Equation (5), and the priority weights of level 1 were estimated using Equations (6-10), shown in Table 3. In level 2 and level 3 were estimated in the same way as the first level 1. Finally, the global priority weights were computed, as shown in Table 4. -872- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 Goal C 1 C 2 C 3 C1 (1.00, 1.00, 1.00), (1.00, 1.00, 1.00), (1.00, 1.00, 1.00), (1.00, 1.00, 1.00) (1.00, 1.00, 1.00), (1.00, 1.00, 1.00) (0.25, 0.33, 0.50), (0.17, 0.20, 0.25), (1.00, 1.00, 1.00), (2.00, 3.00, 4.00), (0.25, 0.33, 0.50), (1.00, 1.00, 1.00) (0.11, 0.11, 0.13), (0.11, 0.11, 0.13), (0.13, 0.14, 0.17), (0.13, 0.14, 0.17), (0.11, 0.11, 0.13), (0.17, 0.20, 0.25) C2 (2.00, 3.00, 4.00), (4.00, 5.00, 6.00), (1.00, 1.00, 1.00), (0.25, 0.33, 0.50), (2.00, 3.00, 4.00), (1.00, 1.00, 1.00) (1.00, 1.00, 1.00), (1.00, 1.00, 1.00), (1.00, 1.00, 1.00), (1.00, 1.00, 1.00), (1.00, 1.00, 1.00), (1.00, 1.00, 1.00) (0.13, 0.14, 0.17), (0.13, 0.14, 0.17), (0.13, 0.14, 0.17), (0.13, 0.14, 0.17), (0.13, 0.14, 0.17), (0.17, 0.20, 0.25) C3 (8.00, 9.00, 9.00), (8.00, 9.00, 9.00), (6.00, 7.00, 8.00), (6.00, 7.00, 8.00), (8.00, 9.00, 9.00), (4.00, 5.00, 6.00) (6.00, 7.00, 8.00), (6.00, 7.00, 8.00), (6.00, 7.00, 8.00), (6.00, 7.00, 8.00), (6.00, 7.00, 8.00), (4.00, 5.00, 6.00) (1.00, 1.00, 1.00), (1.00, 1.00, 1.00), (1.00, 1.00, 1.00), (1.00, 1.00, 1.00), (1.00, 1.00, 1.00), (1.00, 1.00, 1.00) Table 2. The comparison matrix of criteria with respect to goal by the six experts Combined comparison matrix C 1 C 2 C 3 wiCR C1(1, 1, 1) (0.52, 0.64, 0.79) (0.12, 0.13, 0.15) (0.08, 0.09, 0.12) 0.10 0.03C2(1.26, 1.57, 1.91) (1, 1, 1) (0.13, 0.15, 0.18) (0.11, 0.13, 0.17) 0.13 C3(6.48, 7.50, 8.09) (5.61, 6.62, 7.63) (1, 1, 1) (0.65, 0.79, 0.95) 0.77 Table 3. The combined comparison matrix of six decision makers Candidate municipalities Global priority weights ( wi ) Nongbua Lamphu Town Municipality (NLTM) 0.55 Nong Khai Town Municipality (NKTM) 0.21 Loei Town Municipality (LTM) 0.24 Table 4. Global priority weights of candidate municipalities 4.2. Compute the Suitable Locations Using HFGP Model The wi of each candidate municipality are found based on Section 4.1 to be w1 (global priority weight of NLTM) = 0.55, w2 (global priority weight of NKTM) = 0.21 and w3 (global priority weight of LTM) = 0.24. In order to solve the MOFLP in this case, set wG1>wG2 according to experts’ opinions; the sensitivity analysis of the HFGP was also performed for different levels of objective weights. The actual distance matrix and demands of three candidate municipalities and forty hospitals are shown in Table 5 as dj, dtij. The values of u and DT are 4.3 baht/km and 240 km respectively. In Table 6, fk (k = 1 and k = 2) are 13,248 and 24,395 baht per week, and ok are 69,090 and 130,508 baht per week respectively. The values of sk are about 3,000 and 6,000 kg per week. The data set for membership functions of each goal in Equation 26 and Equation 27 need to be evaluated first, the max-min total cost (Z1) and max-min total weight of opened municipalities (Z2) are shown in Table 7. -873- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 ID Hospital name NLTM (km) NKTM (km) LTM (km) Amount of infectious waste (kg/week) H1 Nahaeo 190.00 275.00 128.00 80.50 H2 Pakchom 187.00 162.00 71.00 178.50 H3 Dansai 168.00 253.00 106.00 350.00 H4 Erawan 55.70 140.00 61.90 119.00 H5 Tha Li 156.00 240.00 122.00 147.00 H6 Phurua 132.00 216.00 69.30 56.00 H7 Na Duang 65.00 150.00 52.30 91.00 H8 Chiang Khan 148.00 202.00 31.20 105.00 H9 Wang Saphung 78.40 163.00 44.30 210.00 H10 Phu Kradung 94.40 168.00 96.40 108.50 H11 Phu Luang 102.00 187.00 70.00 112.00 H12 Pha Khao 78.60 148.00 98.50 105.00 H13 Sangkhom 142.00 99.00 134.00 112.00 H14 Phon Phisai 154.00 75.40 264.00 217.00 H15 Si Chiang Mai 103.00 60.20 173.00 105.00 H16 Sakhrai 89.60 6.00 200.00 49.00 H17 Tha Bo 102.00 44.00 192.00 217.00 H18 Suwannakhuha 53.00 102.00 145.00 133.00 H19 Si Bun Rueang 40.70 114.00 154.00 185.50 H20 Na Klang 26.80 111.00 90.70 147.00 H21 Na Wang 43.90 125.00 76.40 91.00 H22 Non Sang 55.60 129.00 169.00 105.00 H23 Kumphawapi 95.70 82.00 209.00 80.50 H24 Si That 120.00 106.00 233.00 175.00 H25 Chai Wan 109.00 89.50 222.00 350.00 H26 Wang Sam Mo 147.00 134.00 261.00 189.00 H27 Phibun Rak 94.00 47.50 207.00 217.00 H28 Nong Han 90.20 70.80 204.00 59.50 H29 Kut Chap 52.10 81.80 166.00 91.00 H30 Nong Wua So 27.00 61.70 140.00 108.50 H31 Ban Dung 138.00 71.50 251.00 210.00 H32 Sang Khom 124.00 49.00 237.00 108.50 H33 Non Sa-at 107.00 93.30 220.00 112.00 H34 Nam Som 80.90 95.70 83.90 105.00 H35 Phen 96.10 21.20 209.00 115.50 H36 Nong Saeng 81.60 81.20 195.00 217.00 H37 Thung Fon 121.00 101.00 231.00 105.00 H38 Ban Phue 95.70 82.00 209.00 49.00 H39 Na Yung 120.00 106.00 233.00 217.00 H40 Huai Koeng 109.00 89.50 222.00 42.00 Total 4,074.00 4,633.30 6,281.90 5,575.5 Table 5. The resource data for the HFGP model -874- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 Details of the cost (baht/week) Size of incinerator (kg/week) 3,000 6,000 1. Facility cost 1.1 Incinerator 1.2 Landfill 1.3 Storage 1.4 Infectious waste tank 1.5 Cleaning system 1.6 Emergency generator 1,918 479.5 6,902 1,725.5 115.5 2,107 3,836 959 13,811 3,451 231 2,107 Total facility cost (baht/day) 13,248 24,395 2. Operating cost per day 2.1 Labor cost 2.2 Maintenance costs (6% of incinerator) 2.3 Cost of measuring air pollution 2.4 Cost of IWD (3.3 Baht/kg ) 51,026.5 1,151.5 7,672 9,240 102,053 2,303 7,672 18,480 Total operating cost (baht/day) 69,090 130,508 Table 6. Details of the cost µ = 0 µ = 1 µ = 0 Min. total cost, G1 – 172,421.2 495,848.3 Max. total weight, G2 0.45 1 – Table 7. Data set for membership functions These relevant parameters were taken to place into the HFGP model (Equation 25 to 29). Afterward, the LINGO 13 software was applied, and the optimal solutions for different objective weights were as shown in Table 8. WG 1 = 0.80, WG 2 = 0.20 WG 1 = 0.70, WG 2 = 0.30 WG 1 = 0.60, WG 2 = 0.40 WG 1 = 0.50, WG 2 = 0.50 NLTM NKTM LTM Selected (Size = 3,000) Selected (Size = 3,000) Not selected Selected (Size = 3,000) Selected (Size = 3,000) Not selected Selected (Size = 3,000) Not selected Selected (Size = 3,000) Selected (Size = 3,000) Selected (Size = 3,000) Selected (Size = 3,000) Total cost (Baht/week) 178,950.30 178,950.30 182,361.0 259,105.2 Total priority weights 0.76 0.76 0.79 1.00 Table 8. Sensitivity analysis for different values of objective’s weights As seen in Table 8, the sensitivity analysis of the HFGP model was performed for different levels of objective weights. The sensitivity analysis is conducted to evaluate the influence of objective weights on the MOFLP. It can be seen that by increasing wG1 and decreasing wG2 at the same time, the total cost goal has a decreasing trend. On the other hand, it can also be seen that by decreasing wG1 and increasing wG2 at the -875- Journal of Industrial Engineering and Management – https://doi.org/10.3926/jiem.2353 same time, the number of locations and total cost have an increasing trend. Finally, the optimal solutions from the sensitivity analysis for different values of objective weights were offered to the four decision makers. The four decision makers made the decision to choose the NLTM and NKTM as suitable municipalities for infectious waste disposal, with the following reasons: “Although total priority weight of selected municipalities is not equal to the maximum predefined value (Target = 1), the total cost is a minimum total cost. If we choose the others, the total cost will be very high, which is not according to experts’ opinions (wG1 > wG2)” The results show that the suitable candidate municipalities were NLTM and NKTM (selected by wG1 = 0.70 and wG2 = 0.30). It can decrease the total cost by selection of NLTM and LTM by about 3,410.7 baht/week. Although the weight of NKTM was slightly lower than the weight of LTM, by about 0.03, the total cost objective was achieved using the new proposed model. Details of optimal solution of HFGP model are shown in Table 9. Opened location Size of location (kg/week) Hospitals NLTM 3,000 H1, H3, H4, H5, H6, H7, H8, H9, H10, H11, H12, H18,H19, H20, H21, H22, H29, H30, H34, H36 NKTM 3,000 H2, H13, H14, H15, H16, H17, H23, H24, H25, H26, H27, H28, H31, H32, H33, H35, H37, H38, H39, H40 Total cost = 178,950.30 baht/week Total priority weight = 0.76 Table 9. Optimal solution of HFGP model Therefore, this model can lead to the selection of new suitable locations for infectious waste disposal by considering both tangible factors and intangible factors simultaneously. In addition, the decision makers believed that our work can provide essential support for decision makers in the assessment of infectious waste disposal problems, in this case study and other areas of Thailand and, they also believe that the proposed methodology can be applied to other complex problems. 4.3. Find the Routes for Each Selected Municipality Using Hybrid GA Based on the actual situation of this case study, the hospitals were determined to be served by each selected municipality (NLTM and NKTM) once a week, and any special vehicle used to pick up the infectious waste should be of a suitable size, appropriate with the design of the transport routes and mobility of the service. 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