A synergy value analysis of sustainable management projects: Illustrated by the example of the aesthetic medicine industry

Lin, Tyrone T.; Yen, Hui-Tzu; Hsu, Shu-Yen Article A synergy value analysis of sustainable management projects: Illustrated by the example of the aesthetic medicine industry Journal of Risk and Financial Management Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Lin, Tyrone T.; Yen, Hui-Tzu; Hsu, Shu-Yen (2022) : A synergy value analysis of sustainable management projects: Illustrated by the example of the aesthetic medicine industry, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol. 15, Iss. 8, pp. 1-16, https://doi.org/10.3390/jrfm15080348 This Version is available at: https://hdl.handle.net/10419/274870 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/4.0/ Citation: Lin, Tyrone T., Hui-Tzu Yen, and Shu-Yen Hsu. 2022. A Synergy Value Analysis of Sustainable Management Projects: Illustrated by the Example of the Aesthetic Medicine Industry. Journal of Risk and Financial Management 15: 348. https://doi.org/10.3390/jrfm15080348 Academic Editor: Thanasis Stengos Received: 4 July 2022 Accepted: 2 August 2022 Published: 5 August 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Journal of Risk and Financial Management Article A Synergy Value Analysis of Sustainable Management Projects: Illustrated by the Example of the Aesthetic Medicine Industry † Tyrone T. Lin , Hui-Tzu Yen * and Shu-Yen Hsu Department of International Business, National Dong Hwa University, Hualien 97401, Taiwan *Correspondence: [email protected]; Tel.: +886-3-890-3051 † This manuscript is modified and revised from part of Hui-Tzu Yen’s doctoral dissertation. Abstract: This study aims to construct a mathematical model to determine the dimensions of an economic, social, and environmental project with the goal of sustainable management. By identifying the optimal weights, the synergy values for sustainable management can be maximized. Taking aesthetic medicine companies as examples, this study attempts to construct the index projects of the economic, social, and environmental dimensions of sustainable management in an uncertain environment. Linear relationships (a combination of fixed synergistic values and varying synergistic values) are used to calculate the import optimal weight under optimistic, normal, and pessimistic circumstances. This study helped companies to introduce triple bottom line (TBL) indices to plan their issues under sustainable management and development, thus, enabling the parent company to achieve the optimal weight for the project costs to put in its subsidiaries. Additionally, this study prioritizes the weight of the influence on the management of the aesthetic medicine industry according to the risk probabilities, to minimize the uncertainties of risk management in corporate management and reduce the possibility of direct and indirect cost losses caused by financial distress, functional fluctuations, and negative impact on the medical equipment market, thereby maximizing the estimated total project value under sustainable management. This study constructs an aesthetic medicine-specific mathematical model concept using the triple bottom line model as the basis for sustainable corporate management and proposes an approach to obtain sustainable weight in uncertain conditions. By doing so, companies can add various managerial methods for the same industry, and new ideas are provided to the academic community to discuss the development of decision-making assessment criteria for risk assessments in sustainable management. Keywords: sustainability; risk and financial management; functional training time; medical errors/dispute incidences; aesthetic medicine industry 1. Introduction Any inappropriate management strategy of an enterprise may endanger society or the environment and directly threaten the economic gains of the enterprise or even its survival; this is especially true with regard to risk management under uncertain circumstances (Brandenburg and Rebs 2015). Risks of Doing Business (2019), pointed out the five global risks that enterprises are most worried about when operating in their own countries in the next ten years are the economy, geopolitics, and environmental, social, and technological concerns. The requirements of the environment, the customers, and the supply chain change constantly, which adds fuel to the current market competition. Sustainable management and development is an important requirement for the management strategy or business model of any enterprise, as lacking a goal of sustainable development will result in weakened competitiveness and make long-term operation unlikely for an enterprise (Nosratabadi et al. 2019). A sustainable management strategy enables a company to rise above its rivals and reposition itself in social and environmental aspects (Dragomir 2020). Additionally, from the perspective of sustainable management, in order to achieve J. Risk Financial Manag. 2022,15, 348. https://doi.org/10.3390/jrfm15080348 https://www.mdpi.com/journal/jrfm J. Risk Financial Manag. 2022,15, 348 2 of 16 sustainable development goals, it is necessary to make good use of the new concept of the three key dimensions of corporate strategies. The greatest challenge for sustainable management is to seek management value in project values according to the TBL indices regarding social, economic, and environmental dimensions (Baumgartner and Rauter 2017). Furthermore, an orientation towards social and environmental sustainability may help generate higher corporate confidence among key stakeholders, which identifies market demands according to economic, social, and environmental dimensions, thereby boosting and improving sustainable corporate performance (Kraus et al. 2017) and creating opportunities for sustainable management. Since 2019 and the onset of COVID-19, the world has faced increasing issues. The pandemic has brought about tremendous uncertainty and exerted an unimaginable influence on the economy, social development, business, risks, financial management, and financial markets (Chang and McAleer 2020). Aesthetic medicine is a customized medical service industry (Glogau et al. 2015). Under an economic depression and an uncertain business environment, the aesthetic medicine industry has understood that sustainable development is the only way to enhance its competitive advantages. Furthermore, innovations in management strategies (Filser et al. 2021) are the key to the sustainable management, profit-making, and growth of aesthetic medicine enterprises. When pursuing sustainable management in the healthcare industry, the aesthetic medicine industry is becoming aware of the necessity of sustainable development and of consulting the TBL model according to the stage of its own development and growth. If suitable indices can be established in the social, economic, and environmental dimensions of the TBL model specific to the aesthetic medicine industry, it could allow enterprises to operate sustainably and obtain the maximum operating value, thus, increasing the opportunities for their sustainable development. 2. Literature Review In 1987, the United Nations defined the concept of sustainable development as development that meets contemporary needs without compromising the future generation (United Nations 1987). The 2002 Earth Summit Report pointed out it is crucial to harmonize the three core elements of sustainable development, namely, economic growth, social development, and environmental protection, as interconnected pillars (United Nations 2002). Elkington (1997) proposed the spirit of the TBL, and Vanclay (2004) pointed out that the sustainable management of enterprises must take into consideration the sustainable management performance from the economic, social, and environmental dimensions. Business managers are faced with tremendous pressure to compete in the various aspects of management strategies, management models, human resource management, research and development, the quality of services, and the establishment of brands, in which industries are expected to exhibit their values of sustainable management (Pugna et al. 2019). In order to adapt to the rapidly changing commercial environment, enterprises must maintain and improve their performance by continually improving their modes of management to the point of achieving the goal of sustainable management and development (Kang and Na 2020). From the perspective of sustainable management for enterprises, to achieve the goal of sustainable development, enterprises must make good use of the new concepts concerning the three key dimensions mentioned in the enterprise management strategy. Many scholars have discussed the subject of sustainable management of enterprises from the perspective of TBL (Barbosa et al. 2020;Kuo and Smith 2018;Garbie 2015;Wiesner et al. 2018;Majid and Koe 2012). Table 1summarizes the literature concerning the indexes related to sustainable development. J. Risk Financial Manag. 2022,15, 348 3 of 16 Table 1. Literature concerning indices related to sustainable development. Indexes Related to Sustainable Development The Global Sullivan Principles 1. Encourage equality and fairness among employees regardless of their economic and social status. 2. Equal pay for equal work in the workplace, regardless of race. 3. Respect human rights and provide equal work opportunities for everyone. 4. Incorporate the principles into all levels of business operation. Global Reporting Initiative 1. Environmental Performance 2. Economic Performance 3. Social Performance 4. Integrate Performance World Business Council for Sustainability Development 1. Economic 2. Social 3. Environmental The World Economic Forum 1. Economic 2. Social 3. Environmental 4. Politics 5. Skills Ministry of Health and Welfare 1. Social 2. Economic 3. Environmental Principles for Responsible Investment 1. Environmental 2. Social 3. Corporate Governance COVID-19 has disrupted sustainable development goals, namely, society, the economy, and the environment (Thorp 2020). Many enterprises, especially small and middle-sized enterprises, lack plans and strategies regarding sustainable management. The pandemic has resulted in the suspension of operations, lack of personnel, and supply chain disruptions. In the face of such problems, business management must not solely focus on the economic aspects of creating revenue or profit but should consider the extrinsic risk factors for society and the environment (Hermundsdottir et al. 2022). Mitchell et al. (2010) wrote that responding to the market has long been the most basic strategy of enterprise management. The overall sustainable management values of an enterprise comprise social, financial, and environmental dimensions. The social dimension refers to the social benefits of the stakeholders in an enterprise, such as the employees, customers, manufacturers, and any other entities that may be affected by the business operations (Gopalakrishnan et al. 2012) the economic dimension refers to generating and maintaining long-term profits (Kleindorfer et al. 2005), and the environmental dimension refers to minimizing the negative impact of business operations on the environment (Hassini et al. 2012). The greatest challenge for the sustainable management of an enterprise is to find management value in project values according to the TBL indices concerning the social, economic, and environmental dimensions (Baumgartner and Rauter 2017). An orientation towards social and environmental sustainability may help generate more confidence in the enterprises on the part of key stakeholders, while meeting market demand in the economic, social, and environmental dimensions, thus, stimulating the enterprise’s sustainable performance (Kraus et al. 2017) and providing an opportunity for maintaining the sustainable management of the enterprise. More and more enterprises are including factors regarding sustainable development in their management strategies, and are establishing sustainable management policies to address those issues (Searcy 2016). Of course, this argument also stands for healthcare en- J. Risk Financial Manag. 2022,15, 348 4 of 16 terprises. The above studies mostly focused on improving sustainable management values, while aesthetic medicine-related literature chiefly investigated medical disputes in crisis management, service quality, discussions on medical technology, strategic analysis, medical project management, and innovation. However, research on the sustainable management values of aesthetic medicine and exploration of aesthetic medicine sustainable management using the TBL model is relatively rare. To fill these gaps in existing literature, this study aimed to explore the new thinking on issues related to the sustainable operation of aesthetic medicine through the realization of the transformation of the knowledge ecosystem, in order to construct an aesthetic medicine-specific mathematical model (Aquilani et al. 2020). On the basis of literature regarding sustainable development and its relevant indexes, this study discussed which model the aesthetic medicine industry should adopt when implementing sustainable management, and which model suits the plans and strategies of the aesthetic medicine industry. It discussed the uncertain environment faced by business managers in the aesthetic medicine industry, especially at times when instability threatens the global economy. It analyzed literature relevant to the goals, including the Studies on the Project Value under an Enterprise of Aesthetic Medicine with Sustainability (Yen 2021), an Optimal Advertising Strategy in Aesthetic Medicine Budgets with Uncertain Income (Yen and Lin 2021), the Criteria of Optimal Training Cost Allocation for Sustainable Value in the Aesthetic Medicine Industry (Lin and Yen 2020), and the Modified Binomial Options Pricing Model and the Revised Replicating Portfolio Approach with the Concept of Sustainability Options (Lin et al. 2020). According to the 2019 Taiwan and Asia Pacific Sustainability Reports Analysis, some regional hospitals in Taiwan announced their social responsibility and sustainability frameworks and targets, including the various indices regarding operations and management, happy workplace, medical services, environmental security management, medical quality and safety, talent cultivation, supply-chain systems, information security, and innovative management (CSRone Sustainability Report Platform 2019). Based on the abovementioned literature and using the aesthetic medicine industry as an example, this study determined the dimensions of the TBL assessment model with regard to sustainable management in the aesthetic medicine industry, as well as their corresponding indices and functions, as shown in Table 2. Table 2. The dimensions of sustainable management in aesthetic medicine, with corresponding indices and functions. Dimensions of Assessment in the TBL Model Indexes Issues The Project Value of Sustainable Management in the Aesthetic Medicine Industry Social Dimension 1. Employee Rights 2. Consumer Rights Functional Training Economic Dimension 1. Shareholder Rights 2. Social Wealth Advertising and Marketing Environmental Dimension 1. Environmental Indexes 2. Regulatory Indexes 3. Supplier Indexes Green Healthcare Procurement Hendiani et al. (2020a,2020b) studied ways to obtain the optimal ratio to achieve sustainability under uncertain circumstances in different TBL dimensions and came up with an overall sustainable synergy index for manufacturing enterprises. Abdullah et al. (2018) focused on the relationship between the three factors of TBL, investigated the practice of sustainable management and marketing among customers, and concluded by means of finding the suitable ratio that the economic scale is the most important factor influencing sustainable marketing. Govindan et al. (2013) discussed sustainable supply chain projects, calculated the weight ratio by means of TBL, and selected effective models for suppliers in the supply chain. Sartori et al. (2017) studied and evaluated the sustainable development J. Risk Financial Manag. 2022,15, 348 5 of 16 performance of the Brazilian electricity industry by calculating the weight ratios. ranked suppliers based on their sustainable development performance and proposed a way to select sustainable suppliers using ratios. From the above literature, it could be concluded that enterprises can use ratios to determine the most suitable total project value in each dimension when making sustainable business management decisions. This study attempted to construct a generalized mathematical model of sustainable management value using indices regarding the three elements of the TBL model. After considering the synergistic value of sustainable management, this study determined the optimal ratio of the indices in the economic, social, and environmental dimensions, to fulfil the goal of maximizing project value. The aesthetic medicine industry provides professional medical services; therefore, improving medical professionalism (Musina et al. 2016), providing excellent medical technical services and enhancing the quality of employee services (Garg et al. 2020), and providing medical expertise and proficiency, as well as transparent medical information, are all critical factors that could trigger medical disputes. According to Wolf et al. (2010), functional training for medical teams can help improve medical companies’ sustainable management, reduce medical delays, and improve medical teamwork and patient safety. Therefore, functional training for employees and the time invested in such training will reduce medical disputes and increase the project values of the indices concerning the social dimension. According to Hanaysha and Hilman (2015); Vlasova et al. (2016), an unstable global economy may increase the complexity of sustainable development factors in corporate finance. As a result, advertising may be considered a supporting tool for acquiring public wealth to achieve economic sustainability and growth, with the aim of improving a company’s economic development and investment attractiveness, as well as brand value. Therefore, the project value of social dimension indices in the aesthetic medicine TBL model focuses on the discussion of optimizing the advertising budget to increase earnings given uncertain revenue. Furthermore, the environment is the key to sustainable development, and sustainable development in the context of the environment involves the sustainable acquisition of natural resources (Szegedi et al. 2017). Numerous studies have shown that an orientation toward environmentally sustainable development indirectly enhances a company’s competitiveness (Danso et al. 2019). Regarding the green equipment for a product’s life cycle, sustainability and the environment are important elements for individuals and organizations in procurement, waste management, and energy-saving practices (Wilson and Garcia 2011). In the environmental dimension of aesthetic medicine’s sustainable development, green costs, supply chains, environmental protection in the product life cycle, and environmental pollution are all considerations related to sustainable capital, management costs, and sustainable development (Montabon et al. 2007). Therefore, given the uncertain environment, the project value of the environmental dimension indices in the aesthetic medicine TBL model lies in the green input instrument procurement project and the medical equipment procurement project. 3. Research Method and Model Formulation 3.1. Research Method The aesthetic medicine industry also regards sustainable management as a long-term pursuit. Enterprise managers have realized that if the aesthetic medicine industry is to operate sustainably and remain unbeatable in the medical field, the management of aesthetic medicine enterprises has to be strengthened. After integrating human resource management, marketing software, and hardware equipment, the corresponding indexes of the economic, social, and environmental dimensions of the TBL model were introduced into subsidiaries. Projects should be proposed for each index to improve the sustainable management of the enterprise and find the optimal total project value for sustainable management. The relevant structure is shown in Figure 1. Through the value-added synergy in enterprise management can the enterprise value be improved, thus maximizing the goal of sustainable management and development in enterprises. This study used J. Risk Financial Manag. 2022,15, 348 6 of 16 linear relationships (the fixed synergistic value, varying synergistic value, and combined synergistic value) to introduce the external environment in an attempt to evaluate the optimal ratio in the social, economic, and environmental dimensions under optimistic, normal, and pessimistic circumstances. It aimed to find the optimal weighting ratio between the synergistic value of the sustainable management project in the aesthetic medicine industry and the optimal resource input, thereby working as a defensive strategy to avoid risk and actively improve the synergistic value of sustainable management projects in the aesthetic medicine industry. J. Risk Financial Manag. 2022, 15, x FOR PEER REVIEW 6 of 17 relationships (the fixed synergistic value, varying synergistic value, and combined synergistic value) to introduce the external environment in an attempt to evaluate the optimal ratio in the social, economic, and environmental dimensions under optimistic, normal, and pessimistic circumstances. It aimed to find the optimal weighting ratio between the synergistic value of the sustainable management project in the aesthetic medicine industry and the optimal resource input, thereby working as a defensive strategy to avoid risk and actively improve the synergistic value of sustainable management projects in the aesthetic medicine industry. Project value in the social dimension Project value in the economic dimension Project value in the environmental dimension Economic and environmental synergistic value Economic and social synergistic value Project values under sustainable management Optimistic (0) Normal (n) Pessimistic (p) Expected project values under sustainable management ()VM ()VO ()VQ 1 1 1 1 1 1 (g , ; ) ( ) ( ) MO V z e g MV M zQV O e= + + 2 2 2 2 2 2 (g , ; ) ( ) (Q) MQ V z e g V M z V e= + + ( , , ) ( ) (1 ) ( ) (1 ) 1 2 1 12 (1- ) ( ) (1 ) ( ) 2 1 2 12 - V M O Q V M g g V O z T e e V Q z e e ee   =  + + +  + +   + + + ( , , ) ( ) (1 ) ( ) (1 ) 1 2 1 12 (1- ) ( ) (1 ) ( ) 2 1 2 12 - V M O Q V M g g V O z Tee ii i i V Q z e e ee i   =  + + +  + +  + + + ( , , ) ( ) ( , , ) ( ) ( , , ) (1- ( )- ( ) ) ( , , ) E V M O Q p o V M O Q p n V M O Q rr T T T on p o p n V M O Q rr Tp =  +  +   M ( , , ) , 12 ( ) ( , , ) ( ) ( , , ) M ,(1- ( )- ( ) ) ( , , ) 12 ax E V M O Q T ee p o V M O Q p n V M O Q rr TT on ax p o p n V M O Q ee rr Tp    +  =+        Figure 1. Optimal evaluation structure of synergy value and weight in sustainable management projects. 3.2. Model Explanations The main definitions in the model are, as follows: Let the project value in the economic dimension under sustainable management be ()VM , and the weight of the assets to be invested in advertising be , 0 1 11 ee   . Let the project value in the social dimension under sustainable management be ()VO , and the weight of the assets to be invested in functional training be , 0 1 22 ee   . Let the project value in the environmental dimension under sustainable management be ()VQ , and the weight of the assets to be invested in healthcare equipment be 1 1 2 1 2 (1 ), 0 1 e e e e     − −  − − . With different investment amounts, the weight of the assets to be invested in advertising is 1 e  , that of the assets to be invested in functional training is 2 e  , and that of the assets to be invested in healthcare equipment is 12 1ee  −− . 1 e is the set weight reflecting the synergy value of the economic and social dimensions, and 2 e is the set weight reflecting the synergy value of the economic and environmental dimensions. 1 g is the reaction coefficient reflecting the project value in the economic dimension ()VM and the economic and social synergy value 1 1 1 ( , ; ) MO V g z e , and 1o g , 1n g and 1p g Figure 1. Optimal evaluation structure of synergy value and weight in sustainable management projects. 3.2. Model Explanations The main definitions in the model are, as follows: Let the project value in the economic dimension under sustainable management be V(M) , and the weight of the assets to be invested in advertising be ωe1 , 0≤ωe1≤ 1. Let the project value in the social dimension under sustainable management be V(O) , and the weight of the assets to be invested in functional training be ωe2 , 0≤ωe2≤ 1. Let the project value in the environmental dimension under sustainable management be V(Q) , and the weight of the assets to be invested in healthcare equipment be ( 1 −ωe1−ωe2) , 0≤ 1 −ωe1−ωe2≤ 1. With different investment amounts, the weight of the assets to be invested in advertising is ωe1 , that of the assets to be invested in functional training is ωe2 , and that of the assets to be invested in healthcare equipment is 1 −ωe1−ωe2. e1 is the set weight reflecting the synergy value of the economic and social dimensions, and e2 is the set weight reflecting the synergy value of the economic and environmental dimensions. g1 is the reaction coefficient reflecting the project value in the economic dimension V(M) and the economic and social synergy value VMO(g1 , z1 ; e1) , and g1o , g1n and g1p are respectively the reaction coefficients reflecting the project value in the economic dimen- J. Risk Financial Manag. 2022,15, 348 7 of 16 sion V(M) and the economic and social synergy value VMO(g1 , z1 ; e1) under optimistic (o), normal (n), and pessimistic (p) circumstances. g2 is the reaction coefficient reflecting the project value in the economic dimension V(M) and the economic and environmental synergy value VMQ(g2 , z2 ; e2) , and g2o , g2n and g2p are respectively the reaction coefficients reflecting the project value in the economic dimension V(M) and the economic and environmental synergy value VMQ(g2 , z2 ; e2) under optimistic (o), normal (n), and pessimistic (p) circumstances. z1 is the reaction coefficient reflecting the project value in the social dimension V(O) and the economic and social synergy value VMO(g1,z1;e1), and z1o,z1nand z1pare respectively the reaction coefficients reflecting the project value in the social dimension V(O) and the economic and social synergy value VMO(g1 , z1 ; e1) under optimistic (o), normal (n), and pessimistic (p) circumstances. z2 is the reaction coefficient reflecting the project value in the environmental dimension V(Q) and the economic and environmental synergy value VMQ(g2 , z2 ; e2) , and z2o , z2n and z2p are respectively the reaction coefficients reflecting the project value in the environmental dimension V(Q) and the economic and environmental synergy value VMQ(g2 , z2 ; e2) under optimistic (o), normal (n), and pessimistic (p) circumstances. The definitions of parameters are shown in Table 3. Table 3. Definitions of parameters. Parameter Definition VTTotal project value under sustainable management VTo Total project value under sustainable management in optimistic circumstances VTn Total project value under sustainable management in normal circumstances VTp Total project value under sustainable management in pessimistic circumstances E[VT]Estimated total project value under sustainable management V(M)Project value in the economic dimension under sustainable management V(O) Project value in the social dimension under sustainable management V(Q)Project value in the environmental dimension under sustainable management ωe1 Weight of the assets to be invested in advertising in the economic dimension under sustainable management ωe2 Weight of the assets to be invested in functional training in the social dimension under sustainable management 1−ωe1−ωe2=ωe3 Weight of the assets to be invested in healthcare equipment in the environmental dimension under sustainable management e1Set ratio reflecting the synergy value of the economic and social dimensions e2Set ratio reflecting the synergy value of the economic and environmental dimensions g1o,g1n,g1p g2o,g2n,g2p Respectively the reaction coefficient reflecting the project value in the economic dimension and the economic and social synergy value under optimistic, normal, and pessimistic circumstances z1o,z1n,z1p z2o,z2n,z2p Respectively the reaction coefficient reflecting the project value in the social dimension and the economic and social synergy value under optimistic, normal, and pessimistic circumstances iOptimistic / normal / pessimistic pr(o)Probability of occurrence of optimistic circumstances regarding total project value under sustainable management pr(n)Probability of occurrence of normal circumstances regarding total project value under sustainable management 1−pr(o)−pr(n)= pr(p) Probability of occurrence of pessimistic circumstances regarding total project value under sustainable management J. Risk Financial Manag. 2022,15, 348 8 of 16 Given g1 , g2 , z1 , z2 and the corresponding original project values in the economic, social, and environmental dimensions V(M) , V(O) and V(Q) , the economic and social synergy value VMO(g1,z1;e1)can be represented as: VMO(g1,z1;e1) = g1V(M) + z1V(O) + e1(1) The economic and environmental synergy value VMQ(g2 , z2 ; e2) can be represented as: VMQ(g2,z2;e2) = g2V(M) + z2V(Q) + e2(2) The natural restrictive conditions are: VMO(g1,z1;e1)>0, VMQ(g2,z2;e2)>0. Based on the above definitions, the total project value under sustainable management VT(M,O,Q)can be defined as: VT(M,O,Q) = ωe1V(M)×(1+g1+g2) + ωe2V(O)×(1+z1) +(1−ωe1−ωe2)×V(Q)×(1+z2) + (e1+e2)(3) The total project model under sustainable management in optimistic (o), normal (n), and pessimistic (p) circumstances VTi(M,O,Q),i=o,n,p, is: VTi(M,O,Q) = ωe1V(M)×(1+g1i+g2i) + ωe2V(O)×(1+z1i) +(1−ωe1−ωe2)V(Q)×(1+z2i) + (e1+e2)(4) The estimated total project value under sustainable development E[VT(M,O,Q)] , in which the possibility of occurrence of optimistic circumstances pr(o) , the possibility of occurrence of normal circumstances pr(n) , and the possibility of occurrence of pessimistic circumstances po(p) = 1−pr(o)−pr(n)can be represented as: E[VT(M,O,Q)]=pr(o)×VTo(M,O,Q) + pr(n)×VTn(M,O,Q) +(1−pr(o)−pr(n) ) ×VTp(M,O,Q)(5) The objective function of this model was to determine the most suitable weight of the assets to be invested in advertising ( ωe1 ), that of the assets to be invested in functional training ( ωe2 ), and that to be invested in medical equipment ( 1 −ωe1−ωe2) when the estimated total project value under sustainable management E[VT(M,O,Q)] reaches its maximum, which can be represented, as follows: Max ωe1,ωe2 E[VT(M,O,Q)] =Max ωe1,ωe2pr(o)×VTo(M,O,Q) + pr(n)×VTn(M,O,Q) +(1−pr(o)−pr(n) ) ×VTp(M,O,Q)(6) The restrictive conditions are 0≤ωe1≤ 1, 0 ≤ωe2≤ 1, and 0 ≤( 1 −ωe1−ωe2)≤ 1. Within a given range of applicable total investment amounts, the weight of the assets to be invested in advertising ( ωe1 ), that of the assets to be invested in functional training ( ωe2 ), and that to be invested in medical equipment ( 1 −ωe1−ωe2) can be found where the estimated total project value under sustainable management E[VT(M,O,Q)] reaches its maximum with different total investment amounts. This was taken as a basis for determining the most suitable weight of the assets to be invested in advertising ( ωe1 ), that of the assets to be invested in functional training ( ωe2 ), and that to be invested in medical equipment (1−ωe1−ωe2), within an applicable range of the total investment amounts. 4. Numerical Example 4.1. 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