The facility location problem from the perspective of triple bottom line accounting of sustainability

Abstract Design of facilities network, allocation of customers to be served from the facilities and their operations have strong economic, environmental and social impacts. Although the decisions in the facility location problem may have varying effects on these impacts, simultaneous consideration of these effects in the early stages of decision-making for facility location selection and network plan has attracted limited attention in the facility location decision literature. Specifically, the social dimension and mathematical modelling are rarely used. In this paper, we present a decision support framework for the facility location problem that incorporates the triple bottom line accounting of sustainability. The framework is a valuable integration of mathematical modelling embedding the criteria with proper measurement indicators in a multi-objective model, perspectives of the related stakeholders, any thresholds and assumption, model analysis, and the decision-maker strategy to find the best-fit alternative. We demonstrate our methodological approach to establish a supply network for digital products in Turkey using real data. The results indicate that the method can balance the economic, environmental and social pillars, based on limitations of the three pillars and strategic perspective of the decision-maker. The decision-maker can interpret the interactions among the three pillars of sustainability and can make his decision by analysing the balance between them.


Introduction
The design of supply networks is a fundamental problem in supply chain management where the location of facilities and the connections among these facilities are determined to establish an efficient network (Farahani, SteadieSeifi, and Asgari 2010). Due to far reaching impacts of these decisions, the optimal solution of the facility location problem is very interesting for both private and public sectors. While, the private sector traditionally focuses on minimising the costs, the public sector aims to maximise the social impact. Considering the financial factors only in the location decisions is no longer sufficient in the current business environment; population growth, competition and technological progress force the decision-makers to be more critical and sensitive to environmental and social impacts (Dou and Sarkis 2010;Seuring and Müller 2008). Addressing all of these issues simultaneously in the facility location has become an important aspect of the decision-making process. Sustainability is the concept that addresses this need. A common approach in analysing sustainability is the concept of triple bottom line (TBL) accounting; the TBL accounting concept states that for a system to be sustainable, a minimum performance should be achieved in the economic, environmental and social aspects (Jeurissen 2000).
The selection of facility location is a strategic level decision due to the time scale and costs associated with construction of these facilities. The facility location problem cannot be treated from a pure economic perspective, due to strong environmental and social effects of establishing facilities and interconnections among these facilities. The waste treatment facilities and management of emissions (solid, liquid or gas) can show large variations depending on the location of the facilities. Moreover, corporate social responsibility has become one of the most critical business factors on the global policy agenda in the age of globalisation. Establishment of a facility in a location has varied impact of the local level depending on the size of the facility, as well as the demographic and population characteristics of the location. Also, the social performance of companies affects the corporate social image and the brand preferences of customers. Besides, the public authorities force the companies to consider sustainability and limit environmentally and socially detrimental activities. These facts necessitate considering the economic, environmental and social dimension of sustainability, while developing new facilities to reduce waste and emission, promoting better life conditions to the community and a less risky business practice.
Recently, more companies have started to feel the economic costs of the negative environmental and social effects increasingly and realise that preventing a social and ecological problem is usually cheaper in the long-term than mitigating the adverse effects after it happens (Vanclay 2003). Corporations have realised that putting the corporate objectives, the stakeholder preferences and public interests together makes win-win-win situation for the company, stakeholders and community (Marcel 2003).
The sustainability requirement in the location decisions of companies motivated us to review the sustainability factors, decision parameters, and decision models in the literature. We then try to fill the existing gaps and improve the current models and approaches. Our integrated framework considers the systems issues, decision-maker strategy and sustainability concerns in three dimensions, simultaneously and employs mathematical programming to solve a complex multi-objective problem. It improves the lack of systematic incorporation of the three pillars of sustainability in the design structure to decide on the best configuration of desirable network in supply chain. The paper is organised as following: in the next section the literature is discussed in detail, then the existing gaps and our proposed contribution is summarised. Section 3 presents our proposed approach and developed framework, Section 4 shows the application of the method on a realistic case and its results, and Section 5 summarises the conclusions.

Related work
In this section, we review the recent work in supply chain management, network design and location analysis that consider sustainability. Particularly, we focus on the work that study the social and/or environmental concerns in addition to economic dimension. Most studies on sustainability employ descriptive models which are not able to find the feasible alternatives when there is large volume of data. Furthermore, these methods work on a limited number of predefined alternatives. Among the descriptive methods, the analytic hierarchy process (AHP) and analytic network process (ANP) are two of the most widely used methods. The AHP has some limitations such as one-way relation among factors and neglecting interactions among different factors (Saaty 1990). Although ANP dominates AHP, it becomes too complex to analyse as the number of alternatives increases, and the need for more effort from the analysts and decision-makers reduces its application speed and accuracy (Jharkharia and Shankar 2007).
Among the work that focuses on economic and environmental dimensions of sustainability, Accorsi et al. (2016) present a framework that supports strategic decision-making on agriculture and food distribution issues, while addressing climate stability. Their framework includes an original land-network problem solved with a linear programming model that optimises costs and balances carbon emissions within the agro-food ecosystem. Babazadeh et al. (2017) and Talaei et al. (2016) consider two objectives as the minimisation of the total cost and the environmental impact. The former uses a multi-objective possibilistic programming model for designing a second-generation biodiesel supply chain network. The latter investigate a facility location/allocation model for a multi-product closed-loop green supply chain network. Banasik et al. (2017) propose a multi-objective mixed integer linear programming model to redesign the logistical structure and close loops in the mushroom supply chain based on economic and environmental parameters. They show that adopting closing loop technologies in industrial mushroom production can improve total profitability by almost 11% and the environmental performance approximately by 28% . Nurjanni, Carvalho, and Costa (2017) incorporate a closed-loop network to accommodate the reprocessing model of disposal products and a multi-objective optimisation mathematical model to minimise overall costs and carbon dioxide emissions, while setting the supply chain. They use weighted sum method, weighted Tchebycheff and augmented weighted Tchebycheff to perform the optimisation process. Genovese et al. (2017) compare the performances of traditional and circular production systems based on some indicators such as total life-cycle emissions, waste recovered, virgin resources use and carbon maps. Circular economy is a method that concerns creation of self-sustaining production systems where materials are used over and over again. They use Hybrid LCA methodology to utilise the assessment in two case studies in chemical and food industries and demonstrate the environmental advantage of circular economy principles integration within supply chain management. Minimising the total system cost and environmental impact are two objectives considered by Skriver and Andersen (2003) and Vaillancourt and Waaub (2002) in their selection process.
Some papers have focused on economic and social pillars, with mostly investigating the service level and cost of unsatisfied demand as their social consideration. Among them, Ho (2007) investigate the customer service as part of the social capital and economic criteria without covering environmental dimension. Nagurney and Masoumi (2012) develop a multi-criteria system-optimisation framework for the network design of a sustainable blood banking system. Their model captures the product perishability, the medical waste discarding costs, the demand uncertainty and the product procurement risk. Stummer et al. (2004) determine the location/size of medical facilities in a hospital network with the objectives of the total travel cost for patients, the total costs of hospital plan location/allocation, the number of rejected patients in a department at a time and the number of necessary relocations to rebuild the current allocation.
Few papers have considered the three pillars of sustainability. Govindan et al. (2016) aim at prioritising alternative potential locations for manufacturing firms with respect to the three dimensions of sustainability. The rank of alternative potential locations using Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The performance of each alternative potential location is assessed by Analytical Hierarchical Process (AHP). Golini et al. (2016) consider the supply chain(SC) as a whole, identifying the drivers and contingent variables that foster the adoption of sustainable practices. They conduct a set of case studies at different stages of the SC before focusing on the meat processing stage. Then analyse how these companies leverage SC management practices to develop sustainable supply chains and highlight the interdependences across various stages of the meat SC. Türkay, Saraçoglu, and Arslan (2016) present the aggregate planning problem from sustainability perspective that considers the financial, environmental and social impacts of planning operations on the manufacturing environment. Among the social considerations, employee job security and morale-motivation, employee health and work-family balance, and customer satisfaction were considered. The concepts and models were illustrated on a home appliance manufacturing system. Fard and Maryam (2016) develop a range of technical and sustainability criteria to evaluate the sustainability characteristics of alternative sites to locate a new cement plant in the state of Florida. They use AHP and GIS (geographic information system) techniques to utilise the criteria weight and evaluate the predefined alternatives. Finally, without emphasis on network design and sustainable development (Lentes et al. 2017) propose sustainable manufacturing by means of ultra-efficient factories in urban surroundings. They identify criteria to assess the maturity of companies aggregate into a comprehensive maturity model which enables the determination of potentials for advancements of companies. None of these works deal with mathematical models to design the sustainable network and quantifies the social concerns to embed into a mathematical model.
In addition to the papers that present new models and illustrate these models on a variety of problems, the literature includes a number of review papers that were published recently. Chan and Nan Li (2016) classify the mathematical problems dealing with the management of sustainable manufacturing systems with emphasis on the environmental protection. Terouhid, Ries, and Fard (2012), Seuring and Müller (2008), Ramstetter (2011), Chen, Olhager, andTang (2014), Srivastava (2007), Gold, Seuring, and Beske (2010) and Seuring (2013) review the sustainability considerations in supply chain management. According to these papers, the sustainability consideration from the social dimension received limited attention in the network design and facility location literature. Literature does not effectively address sustainable development requirements from TBL perspective to help the decision-maker (Terouhid, Ries, and Fard 2012;Chen, Olhager, and Tang 2014). Seuring (2013) emphasises that there are only 36 papers using quantitative models in sustainable supply chain that do not take into account the social factors of sustainability. Finally, among the 87 papers reviewed in a very recent paper (Eskandarpour et al. 2015), only 13 papers included the social dimension in their analysis. We analyse all these papers and summarise the social factors considered in Table 1.
The analysis of Table 1 shows that minimising the cost of the network is the most commonly used economic objective. In the category of forward supply chain, only one paper (Santibañez-Aguilar et al. 2014) deals with three objectives simultaneously and considers the number of jobs created only as social criteria. The number of jobs created is the most important criteria that some papers focus, while some papers consider worker safety, medical facility access, hazardous product, the land-use incompatibility and level of user satisfaction as their social factors. Regarding the environmental dimension, all the papers in this category evaluate the air emission, while Pishvaee, Razmi, and Ali (2012) only consider waste because of different technologies and Beheshtifar and Alimoahmmadi (2015) do not include the environmental dimension. Also, none of the papers consider the customer relationships, business practice and human rights, while only two of them evaluate the social commitment. Only two papers (Bouzembrak et al. 2010;You et al. 2012) consider the transportation mode to configure the transportation network. This analysis shows that the papers in the forward supply chain category, do not include the society and related community concerns in sufficient detail that addresses the changing perspectives of all stakeholders involved and macro-level concerns of community.
The papers in the category of reverse logistics do not consider the three objectives (corresponding to TBL accounting of sustainability) simultaneously and do not consider the transportation mode in the network configuration. While most of them do not consider social criteria, Tuzkaya, Gülsün, and Önsel (2011) consider the job creation and political opposition without quantifying it. Dehghanian and Mansour (2009) investigate the number of jobs created (for different technologies), local development, worker safety from damage and recycled product usage risk. The two later criteria are related to work conditions and product type that is not necessarily the criteria in forward supply chain with fixed work force strategy. Also, they aggregate four social criteria into a single indicator with AHP, use expert judgment to evaluate the criteria for different methods. In the closed loop supply chain category, none of papers include the transportation mode in the model configuration. While both of them deal with three pillars simultaneously, only Mota et al. (2015) employ an exact solution method; but only investigate the job distribution equity as the social criteria.
The literature review shows that the social aspects are almost completely missing or rarely included in a very simplified manner, not only in the objective function, but also in problem constraints and even definition of decision variables. Also they are ignored in mathematical models. The environmental aspect usually focuses on reducing the emission or waste production. The population density and geographical characteristic of location to evaluate the waste/emission effect are ignored in all papers. The literature on location analysis does not effectively address all sustainable development requirements in the  decision process. Finally, there is not an integrated framework which captures all related concerns in a reliable way and considers all the pillars simultaneously based on mathematical model. In this paper, we propose to fill these gaps in the literature aiming to have a comprehensive reliable sustainable solution. We design an integrated framework that can address these gaps by addressing the economic, social and environmental concerns, not only by adding social and environmental objectives to the economic one, but also projecting the new concerns on the variable definition and constraints, having an improved and reliable method of parameter definition and effect measurement, designing a good mathematical model, solving the model with proper method, engaging decision-maker strategy and guiding him/her with solution analysis. The framework determines location of facilities, their production amount, multi mode network configuration. The decision variable for product flow includes the transport mode and affected by the real multi-transport network. Both the product flow and open facility variables are affected by all the concerns of the three pillars. We try to engage the social concerns in a comprehensive manner and deal with both the amount and effect of environmental concerns. While, none of papers conduct an evaluation of criteria for their compatibility and suitability with the problem assumptions and stakeholder perspectives, our framework conducts a validation process to evaluate reliability and relevance of every investigated criteria. Defining the indicator to measure the social and environmental parameters is one of important innovation in the framework. The mathematical programming model and exact method to simultaneously address the economic, environmental and social concerns of sustainability is another innovation in our framework. The multiobjective mathematical model optimises the network configuration with multiple available transport mode to obtain minimum GHG emissions, cost, waste and maximum expected security level (reducing expected security problems), level of access to medical facility, level of access to education facility, level of development distribution equity, level of job distribution equity. The framework involves thresholds and restrictions and some concerns are directly defined in the mathematical model as constraints. Resource availability, work-family balance and complete demand satisfaction are defined as constraints, while some restrictions such as carbon cap affect the final selection. Finally, rather than existing studies this framework engages the decision-maker in the parameter definition, criteria evaluation and finally, with its specific strategy to define the preferred solution. This engagement helps her/him to make informed decisions by understanding the benefits/costs of different strategies and interrelation between pillars.
In summary, this paper propose to derive a sustainable and reliable solution with improvement in every stage of the facility location selection problem with an integrated framework and is distinguished from previous papers as follows: • Investigates a more comprehensive social utility analysis, for a 'generic model', • Models different social aspects quantitatively alongside environmental and economic issues in a compact mathematical model as a constraint or objective, working with exact methods and real trade-off among objectives, • Deals with real multi-mode network configuration, sensitive to different locations characteristics, • Incorporates the decision-maker strategy and stakeholder points of views, • Presents a framework flexible to adopt with problem modification, • Promotes social responsibility and business practice, rather than just thinking the work condition and customer satisfaction, • Improves the lack of systematic incorporations of the three pillars of sustainability together with interrelation among them in the decision structure to decide on the best configuration of the desirable locations in a supply network, • Fills the gap of empirical research on sustainable location decision, linking the real data to formal assessment by quantitative models, • Quantifies the qualitative criteria with proper metrics to calculate the effects with accessible reliable data, and ability of working with big data to produce reliable alternatives.

Proposed framework
In this section, we present a framework that is able to address conflicting objectives, optimise the values of decision variables in the Pareto optimal set and engage strategy of the decision-maker. The schematic representation of the proposed decisionmaking framework is given in Figure 1. Although this framework can be for any problem that incorporates sustainability, we provide details of the framework for the facility location problem for the manufacturing facilities in a supply network.

Defining the assumptions, system boundary, spatial scale and related capital owners/stakeholders
The facility location problem requires definition of the system boundary, determination of the spatial and time scale and identification of the capital owners (Neumüller et al. 2015). We consider the national level, land/water resources and years as system boundary and scale. We consider community, customers, employees, capital providers, government, suppliers and contractors as the capital owners. Also defining the problem assumptions is important in the sense that they can affect the problem model and parameters. For example, here, we assume that the suppliers and contractors have the same support level for each location that is considered. This lead us to exclude them from the capital owners. The expectations of the capital owners should be considered when defining the parameters in order to assess the system risks and satisfy them to reduce the probability of system failure.

Defining economical, environmental and social parameters
The identification and valuation of the parameters are critical in the model development: the more accurate parameters are defined, the more reliable the solution of the model will be. We define the criteria with respect to their impacts on three pillars of sustainability, capital, expectations of the stakeholders and the system assumptions. We ignore factors that the company has the same policy measure for them or their provision costs are the same for all locations, because they do not influence our decisions.

Economic parameters and their metrics
The cost and profit of the investor are the primary considerations for parameter selection in the economic dimension. We focus on reducing the cost assuming that the company has the same market demand and revenue regardless of the facility location and consider the following parameters in the life cycle of facility: Set-up cost (as pre-operation cost): The facility set-up cost that includes equipment cost, construction cost and land cost. We assume to use the same equipments in each location. The construction cost is dependent on labour cost and material cost. However, we assume to outsource the construction to a construction company and consider a final price (land price + construction cost) for each square metre of land we buy in each location. Equation (10)  Transportation cost (as operational cost): The transportation cost between the facilities and the customers differ depending on the distance and also the transportation mode. In this paper, we consider sea, rail, road and air transportation as four different modes that have different cost and distance. Equation (11) quantifies this cost based on unit transportation cost of each mode per product multiplied the total shipment and total distance travelled by each mode.
Labour cost (as operational cost): The labour cost (Chen, Olhager, and Tang 2014) is different for candidate locations. Equation (12) quantifies the labour cost based on labour cost per unit production multiplied the total production in each location.
Utility Cost (as operational cost): The cost of utilities (Chen, Olhager, and Tang 2014) usually differ among the candidate locations. Equation (13) quantifies the total utility cost based on utility cost per unit product multiplied the total production in each location.

Environmental parameters and their metrics
We consider the following environmental parameters in life cycle of facility: Resource Consumption(as pre-operation effect): We consider availability of land and fresh water and eliminate the potential locations without enough land for construction and water for production. Constraints (6) and (7) force the model to meet the resource limitations in each location.
Air pollution from transportation (as operational effect): Air pollution is a critical factor in the environmental sustainability (Neumüller et al. 2015) that affects both ecosystem and human health negatively. Equation (14) quantifies the air pollution produced based on the amount of emission per product per kilometre on a transport mode(g m ) multiplied by total amount of product shipment of each transport mode(sum of X mi j ) and its corresponding distance(d mi j ). The total emission can be reduced using the network design and diversity of transport modes.
Water and land pollution: The water and land pollution are the two important factors affecting both the ecosystem and the human health. The liquid and solid waste generated from construction of the facility(as pre-operation effect) (Wise and Trantolo 1994) and during operation of the facility (as operational effect) (Neumüller et al. 2015) are the main sources of land and water pollution . In general, the average waste from construction is recorded to be 6.9kg/m 2 (Moyano and Ramírez 2011). Equation (15) quantifies the effect of waste generated during construction for all opened facilities. The effect is quantified for selected locations (Y i ), based on the amount of land we use (L N ), amount of waste generated per m 2 of land construction (DW ) and sensitivity of each location for produced waste (W S i ). Since the construction waste is high for a long-term it is depreciated over a long-term (DepY). Equation (16) quantifies the effect of operation waste for all opened facilities based on waste generated per unit product (w) and for all products in each location (sum over x mi j ) multiplied by the waste sensitivity of that location (W S i ). The important factor here is the different sensitivity of locations. We define this sensitivity based on the population density of each location and location ranking of aquifers and dry soil among the candidate locations. A location with higher population density and higher aquifers level is more sensitive to waste. We assume that waste treatment technology be the same in all locations.

Social parameters and their metrics
The social responsibility is a multidisciplinary and multi-stakeholder issue and measuring all of the related aspects is challenging. 'International Guidance Standard on Social Responsibility-ISO 26000' ISO (2010) is a good reference for social criteria published by International Standard Organisation (ISO). ISO 26000 defines seven core subjects for Social Responsibility: organisational governance, human rights, labour practices, the environment, fair operating practices, consumer issues, community involvement and development. Also, Gauthier (2005) divides the social factors into two categories: internal and external social criteria. The internal social criteria such as work conditions are in the category of company policies, and we assume them to be the same for all locations. Therefore, we focus on external criteria that can influence the location decisions. We investigate the external social parameters based on ISO 26000 core aspects and the five categories we defined in the Section 2.
Demand satisfaction (as operational criteria): The main social consideration for customers is the demand satisfaction (Neumüller et al. 2015). While unsatisfied demand worsens economic performance of the companies, it is also a social criteria regarding the fact that customers might suffer from unsatisfied demand in certain cases. Therefore, fill rate is an appropriate metric for quantifying customer satisfaction. Equation (2) forces the model to completely satisfy the demand of each demand point (R j ).
Resource equity (as pre-operation and operational criteria): The consumption of local resources may lead to conflicts with the local population who own or use them. As discussed in environmental part, the model considers sufficiency of water/land resources for the local needs and needs of current operating companies as well as the requirements of the new facility in constraints (6) and (7).

Job opportunity distribution (as operational criteria):
Job creation, fair distribution of employment opportunities and helping to improve income of local employees (Terouhid, Ries, and Fard 2012) are important issues. In this problem, the number of jobs created does not differ with the network configuration. The equity in distributing the created jobs is considered to fairly reduce the jobless rate; the more product is produced in a facility, the more contribution in job opportunity creation in that location. Equation (18) quantifies the social impact of company in providing job opportunity in the following way: The higher the unemployment rate(J L R i ) and the higher the population density of location(P O D i ), the more urgency to jobs in that location. The accurate effect is quantified with production share of company in each location ( j m Xmi j/ j R j ). Dividing over population density of country (P O DC) helps to have a coordinated magnitude with other criteria.
Regional development (as operational criteria): Welfare, housing (Terouhid, Ries, and Fard 2012) and community development (Neumüller et al. 2015) are among the important factors in sustainable development with the idea that all people have the right of living in a developed location. Promoting a fair distribution of development helps to reduce immigration and its consequence problems. We consider the regional development value of each location (DV i ) as a parameter encompassing these factors. Equation (19) quantifies the project social effect in regional development. Establishing in the locations with lower development value (100 − DV i ) will gain more social value. The quantification becomes accurate with considering the production share in corresponding location( j m Xmi j/ j R j ) and dividing over highest development value (H I DV ) to have a coordinated magnitude with other criteria.
Security level at the location (as operational criteria): The security at a location is important for the company to have access to materials, distribute its products and operate without major security risks (Neumüller et al. 2015). It is also important for the employees to live in a safe location, improve their social life for maintaining their performance. Equation (20) quantifies the project outcome regarding security. The locations with better security level (H SL − SL i ) (SL i is quantified using crime rate, number of problems,... available in country statistical data-sets. Higher SL i means it has lower security) will have better outcome. The total effect is quantified with production share in each location ( j m Xmi j/ j R j ) and gets a coordinated margin by dividing over range of security levels (RO SL).

Medical facility access level (as operational criteria):
Health is a priority in people's life (Neumüller et al. 2015). The negative impact of facility on people's health is considered in the environmental dimension. The important parameter here is a satisfaction level of access to the medical facility for employees; since low level of access would face the company with the employee retention problem. Locations with higher level of access are usually developed locations. Hence, if we give higher value to them, we are forcing the model to select developed locations which is in contrast with our social responsibility. To satisfy both sides, as shown in Equation (21), we define (M AG i ) as the social value that project gains from each location access level (M AL i ) and give a higher value for locations with medium access level (consider the way we treat ω m ). Hence, we promote social responsibility, while satisfying the necessary access level. Education level (as operational criteria): General education level is another important factor (Vurro, Russo, and Perrini 2009) for the company to hire well-educated workers, and for the incoming employees to have access to good education. With the same strategy and quantification method for medical access level we give higher value to locations with medium access level. Number of schools (N O S i ), number of teachers (N OT i ) and capacity of universities (U NC i ) divided by their respective population size are used to quantify the value that project gains regarding its effect on access to education.
The social criteria we consider emphasise the development of undeveloped locations, the equity in job distribution, fair use of resources, paying attention to health, education and security of employees, community equity, and equal work condition to satisfy the human rights. Equations (11)-(22) expresses the evaluation approach described for each criteria considered in this paper.

Validation of the parameters and indicators
It is important to establish proper parameters for quantifying the impact. In any realistic model, the parameters and their corresponding indicators must be validated before using in a model. This validation ensures that the system is sensitive to defined parameters and the conflicts between managers and others can be addressed at early stages of the decision-making process. As shown in Section 2, the validation process is ignored in most of the previous publications on sustainability. We validate the parameters including their measurement indicators using the algorithm shown in Figure 2  The validation algorithm starts by checking whether the parameter (including the indicator to quantify it) is previously defined or not. If it was defined, we check for the possibility of direct use in this specific problem. Otherwise, it is designed as a new parameter. If it is directly usable and previously validated, is applied directly. If it is not directly usable, it is adopted if is adoptable or is redesigned if is not adoptable. Finally, any output of the newly designed, adapted or previously not validated parameter (indicator) goes into 3S validation process that includes self, scientific and social validation stages. If the parameter passes all three stages, it is ready to be used in the problem. The self-validation stage is done by the working team to verify the quality of parameters and indicators. The scientific validation stage checks for objectivity and validation of parameters/indicators based on the experience and judgment of independent experts. In the social stage, those who are affected from the project give their opinion, even though they are not experts. The validation core is defined as a multicriteria multi-expert decision problem using a questionnaire based on three coherences: conceptual coherence, operational coherence and utility investigate. The AHP method (Saaty 1990) is used to evaluate the value of each parameter/indicator using coherences criteria and their priority weights. The parameter is defined as 'validated' if it passes a certain threshold. The parameters we defined in Section 3.2 have passed the evaluation threshold. We used an expert panel from different disciplines for the scientific part, and the population samples of locations for the social part. We defined 3.8 as our threshold based on Likert scale and opinions of experts. More details about the validation process and validation results for the social parameters are given as a supplementary material.

The optimisation model
The defined parameters as output of Process Analysis Method (PAM) (see Figure 1) are used as the input to the modelling part of the decision-making process to develop the optimisation model. We assume that there is a centralised decision-maker in this model for designing the macro-level network. The potential facility locations are known, the network links for transport modes have a flexible capacity and may be absent based on the existing network. The facility capacity is limited with the available resources and demand quantities. The initial material is assumed to be available at the facilities and the customer demand must be satisfied completely. The following multi-objective mixed-integer linear programming (MO-MILP) model is formulated. The notation for the parameters and sets can be found in 2. The model tries to minimise the economic cost and environmental effect, and maximise the social utility simultaneously: subject to: Customer demand satisfaction is quantified by the fill rate and is incorporated into the model with Equation (2), which states that demand of each customer should be satisfied completely. Equation (3) allows flow from a facility to a demand location by a transportation mode only if that mode is available. Equation (4) ensures that the amount of shipment from any facility location to any demand location is positive if the facility is open, and at most it is equal to the corresponding demand. Equation (5) opens the facility if any product is produced in that location. Equations (6) and (7) check the land and water resources sufficiency and satisfies resource equity criteria. The last two are decision variable definitions (Equations (8) and (9)), limiting the flow decision variable to be positive and the decision variable of opening a facility to be binary. The economic objective Z E is expressed as summation of objectives (Equations) (10)-(13).

Setup cost
c m X mi j d mi j (11) The environmental objective Z G is formulated as summation of Equations (14)-(16)

T ransportation carbon emission
The social utility of the total network is defined as the weighted sum of Equations (18)- (22): where p k is the weight and S k equals to value of corresponding social factor. Z S is the social contribution of the designed network, composed of: where where , ω e = RO E AL/3 The optimisation model presented in this paper is in the category of multi-objective decision-making problems that have conflicting objectives and set of Pareto solutions instead of optimal solution, regardless of their solution method. We found generation methods that can give the exact solutions and the whole Pareto set, the most appropriate solving method regarding our aim to generate non-dominated exact solutions. The most widely used generation methods are the weighting method and the -constraint method where the latter has several advantages over the former especially in the presence of discrete variables, finding the whole Pareto set, and no need for common scale (Mavrotas 2009). In the literature, several versions of the -constraint method have appeared trying to improve its performance or adapt it to a specific type of problems like MOIP problems (Ehrgott and Ryan 2002;Laumanns,Thiele, and Zitzler 2006;Hamacher, Pedersen, and Ruzika 2007;Mavrotas 2009;Mavrotas and Florios 2013). Among them AUGMECON2 proved to have better performance (Mavrotas and Florios 2013). Therefore, we use AUGMECON2 as our solving algorithm. Using the method, the model is transformed in following model where optimise f 1 and uses f 2 and f 3 as constraints: Subject to: x ∈ S and S i ∈ R + Where S 2 , S 3 are the surplus variables of the respective constraints, f min i and f max i are the minimum and maximum value of objective functions from the payoff table (when they are considered as single objective), f max i − − f min i is the range of f i , t is the counter for the specific objective function and q i is the number of equal intervals in the range of f i and eps ∈ [10 −6 , 10 −3 ]. With this formulation the solver will find the optimal for f 1 and then it will try to optimise f 2 then f 3 . Also the method reduces number of redundant solution with bypass coefficient as: When b >=1, implies that in the next iteration the same solution will be obtained. This makes the iteration redundant and we can bypass it. The bypass coefficient actually indicates how many consecutive iterations we can bypass. We implement the model in GAMS 24.1.3 to generate the set of Pareto solutions.

Reducing the efficient set and embedding strategy of the decision-maker
Selecting the preferred (or the best-fit) one in the Pareto set is a major concern that can be improved with reduction of set. A method for reducing the set is the pruning (Wismans et al. 2014) that applies filters to select the most relevant solutions. Another method is reducing the set based on restricted regulation and financial, environmental and social limitations. These two methods can also be used in combination. Then, the strategic objectives of the decision-maker are embedded to reduce the remaining results. The decision-maker may be able to have his/her preferred choice. For example, if her/his goal is the minimum cost, he/she can choose the solution with the minimum cost among the feasible solutions which is in the range of TBL accounting consideration. If the decision-maker cannot select his/her preferred solution from the reduced set, then our method continues to the next step.

Selecting the best-fit alternative
We use the ranking methods to select the best-fit alternative. Weighted Sum Method (WSM) and AHP are the most commonly used methods, while Elimination and Choice Expressing REality (ELECTRE) III is suitable to deal with inaccurate or uncertain data (Wismans et al. 2014). The ranking methods are flexible with the priority weight of objectives based on the strategy of decision-maker. Hence, a sensitivity analysis can be applied to see how the solution set changes with different weights in the objectives of the corporate strategy. The Equations (28) and (29) show the related formulas of WSM and AHP. The score is calculated for each Pareto solution by summing the normalised values of each objective multiplied by its relative weight. The AHP is dimensionless and differs with WSM in normalisation using the sum of objective values. The minimisation and maximisation objective value are multiplied with +1 and −1, respectively. The solution with a lower score is ranked better.

Case study
We illustrate our methodological framework on a case study with real data and analyse the results. We study the location decisions for a digital product manufacturer in Turkey. The real data with all parameters are provided as supplementary material. We consider the same priority for cost parameters in the economic pillar, since the cumulative cost is important for the investor. In the environmental pillar, air and waste emission have the same weight, since both are very important for the environment and society. The priority weights for employment opportunity, regional development, security level, education access level and medical access level in the social pillar are considered as 21. 3, 11.62, 29.85, 15.91 and 21.3%, respectively. A panel of sociologists are interviewed with to define the weights for social parameters using AHP. The defined weights may differ for other cases. Although we illustrate our approach on a facility location problem, the same methodological framework is applicable to other problems and other cases in different countries. We implemented and ran the model on a notebook computer with a 2.5 GHz Intel core i5 CPU and 8 GB RAM running Windows 7. The network topology consists of seven potential facility locations and eight demand locations in Turkey. The facility locations are Istanbul, Bursa, Samsun, Gaziantep, Ankara, Adiyaman and Trabzon, and the demand locations are Konya, Sivas, Antalya, Izmir, Van, Adana, Erzurum and Malatya. The real network, available connections, detailed list of metrics and their values are given in the supplementary file. The solution of problem generates 77 unique Pareto optimal solutions. Table 3 presents the model statistics and solution report. Figure 3(a) shows the economic cost versus environmental effect. The environmental effect decreases as the economic cost increases, in a non-linear way. Starting from the lowest possible costs, with a small increase in the cost, a large improvement occurs in the environmental effect. However, in the last steps, reaching lowest value in environmental dimension has a high cost. Also, reaching zero cost and zero emission is impossible. Figure 3(b) shows the economic cost versus the social utility.  The improvement rate of social dimension is higher than the rate of increase in cost. This shows that a small increase in cost leads to higher improvement in the social utility value, in a non-linear way. Starting from least possible costs, some more cost has a high improve in social value, but reaching the highest level of social value is more costly to the company. A small improve in social value requires a higher increase in the cost. Figure 4 shows the 77 unique Pareto optimal solutions. Each solution has a unique value for economic, environmental and social utility. Additionally, each unique Pareto optimal solution includes the locations of facilities opened, the corresponding transportation network, the allocated demand, the set-up and operation costs, the amounts of emission and waste, and the social criteria values. The detailed values captured in each of the Pareto optimal solutions are provided in the supplementary file.
Since the decision-maker does not have a strategy to select the solution or reduce the set, ranking methods are employed to select the best-fit solution. The WSM and AHP curves for different priority weight of objectives for this example are shown in Figure 5(a) and (b). The figures show how the WSM and AHP values change according to the decision-maker's strategies to select the best-fit solution. Hence, this method guarantees solution feasibility, while allowing selection of the most preferred solution. The higher-ranked solution in each curve is identified by a square.
In another analysis, we compare the selected best-fit solution with the ideal solution. As shown in Figure 5(a) and (b), equal weights for objectives chooses the 10th solution. The suggested solution is 8% higher than the ideal cost, 25% higher than the ideal environmental impact and 3% lower than the ideal social utility. When the priority weight is 10, 80 and 10 for each objective, respectively, the 11th solution is selected. While, the cost and social objectives are 17 and 4% away from the ideal values, respectively, the environmental dimension is in its ideal level. The distance from the ideal value in environmental objective decreases 25% compared to the equal weight strategy, in return for 9 and 1% away from economic and social dimension values, respectively.   Figure 6(a) shows the general structure of supply chain. In the facility location problem we consider the manufacturing facility and the regional distribution centres (RDC which is responsible for each demand point) as two part of chain to focus. We assume, we have available supply and the same support of suppliers regardless of manufacture location. The details of 10th Pareto solution are shown in Figure 6(b) to give an idea about the detailed values captured in each of the Pareto optimal solutions. The points shown by a triangle are the selected locations and round points are demand locations. The links show the demand allocation of the demand locations with a transportation mode from the opened facility. In another analysis detailed in Table 4, we compare the preferred 10th solution against the solution of problem with single objective of minimising the economic cost. We realise 65% less environmental effect and 16% more social value creation in return to 8% higher cost in the 10th solution. These results are valuable due to higher rate of improvement in environmental and social pillars for a small increase in cost, and show the positive results of the proposed sustainable factors. The responsible development rewards can also be returned as economic benefits due to the reduced cost of treating emission/waste and increased profit of loyal customers and employees. The analysis shows that the amount of production share in developed, medium-and less-developed locations changes from 29, 46 and 23% for single-objective model into 12, 55 and 32%, for multi-objective model, respectively. The transport mode share also changes from 79% to 0 for truck, 15 to 87% for train, 5% to 0 for air and 0 to 12% for sea.
These values show that sustainable development tends to use more green transport mode and investigate on more medium-and low-developed locations to promote sustainability. The decision-maker can also make a higher contribution in environmental/social utility without necessarily a very high cost for the company. Although we demonstrate the availability of our mathematical model and solution method with a case study and analyse the outcome, we examine two other medium and large scale problems to reflect the complexity of the problem. The medium scale problem (MSP) has 11 facility locations and eight demand locations based on real data. The large scale problem (LSP) has 50 facility points and 20 demand points based on randomly generated data. The model and solution statistics for these problems are described in Table 3. While our case study and MSP are solved very fast, the LSP took 88 minutes. The facility location is a macro-economic problem that does not need immediate solution, hence, our method is applicable even for large problems. The MSP and LSP result in 63 and 458 solutions, respectively.

Managerial Insights.
We summarise the following managerial insights based on the experiments we conducted: • The social utility increases according to the cost. Even though we observe higher social value in locations with lower labour and fixed costs, they usually have higher transport cost (no access to low-cost transportation). The environmental effect improves as the cost increases. There are usually (not always) two reasons: First, the locations with access to low-emission transportation modes usually have higher set-up cost. Second, we observe more cost and less emission as the number of open facilities raises. The environmental effect is further affected by the waste sensitivity of locations and amount of waste due to number of facility. Moreover, improving the social utility worsens the environmental effect. • The environmental effect and social utility improvement rate becomes high with some more cost up to a point after which it begins to decrease. This shows that the improvement is considerable and valuable until some level, but it will not be economically attractive afterwards. • The lowest-cost network is a network with an average fixed cost and low transportation cost rather than the one with a lower fixed and labour cost. • The model tends to investigate a higher production share in medium-developed locations.
• Managers can define the budget needed to apply a special strategy or effect.
• Companies can expect a reduced cost of conflict, an increased support of stakeholders (government, NGOs, local communities), and a better reputation due to the greater transparency their impacts and considering stakeholders' concerns. • The method helps the management team to define and quantify sustainability criteria in their way to achieve sustainability and promote corporate responsibility. • The framework helps the business to figure out its ability to make better decisions, operate smoothly, reduce risk, improve efficiency and generate more value for stakeholders/shareholders, making a basis for value creation that is aligned with sustained growth.

Conclusions
We presented a methodological approach and an integrated comprehensive framework to include the TBL accounting of sustainability in the facility location problem. Employing mathematical modelling, the framework is reliable in the criteria involvement and all stakeholder concerns, and flexible with the decision-maker strategies, while guaranteeing the satisfaction of each dimension thresholds. It also provides Pareto optimal solutions and a clear image of the network. The solutions are more reliable than the comparison-based analysis of descriptive methods. This framework promotes the corporate social responsibility and shows new trends in the business practice. The decision-maker can make a decision with improved social and environmental outcome, while satisfying the economic objective of the business. Also the results of the model and the trade-off between the objectives can be easily followed and balanced. We demonstrated our methodological approach in selecting the location of a manufacturing network for production and distribution of digital products in Turkey. The analysis showed that the social utility increases as the economic cost decreases, the environmental effect reduces as the cost increases, and the social utility and the environmental effect move in the same direction. We also examined the distance of each objective from their ideal solutions. We observed that even though the best-fit solution may not be exactly the ideal solution of each objective, it is not very far from, and the method can perfectly balance the three pillars. The decision-maker can improve the social and environmental pillars by a marginal increase in the economic cost. Moreover, this cost will be returned in the long-term as customer loyalty and competitive benefit. We further applied the different priority weights and observed the flexibility of method with different strategy scenarios of the decision-maker. The empirical application showed how this method can satisfy different stakeholders, while selecting a solution that is flexible with the decision-maker strategy.
This work is a starting point for developing frameworks towards promoting sustainable development. It can be improved in many different directions. In order to be more precise and capture all related effects in an entire supply chain, the method can be extended to include the other echelons of supply chain. We mention that the parameters included in the model and their priority weights are based on our model assumptions, but the pillars are very dynamic and sensitive to particular settings. As a future extension, new assumptions can be considered to check for new relations and parameters definition. A field study would be beneficial to define the correlation among criteria. The dynamic nature of the variables and uncertainty in the parameter values are the other important aspects for future extension. We used standard values that are not expected to differ in short-term and do not have large effect on our macro-level decisions. However, the uncertainty associated with parameters and model assumptions can be analysed using stochastic or robust optimisation and working with statistical data.
To have a more comprehensive analysis and a global picture of the company's success, preferences of the related stakeholders, government perspective and their power to affect the company activities can be incorporated in the sustainabilitybased frameworks. Using an innovative view and adding some innovative business relations and operation activities in the supply chain to provide a more sustainable development and analysing their effect would also be an interesting extension. Finally, creation of a competitive pressure due to achieving extra value by businesses who have applied the sustainable decision-making frameworks, can be analysed as another step.

Disclosure statement
No potential conflict of interest was reported by the authors.

Supplemental data
Supplemental data for this article can be accessed at: https://doi.org/10.1080/00207543.2017.1341064