Master Thesis
A Social Responsible Facility Location Model:
Assessing the impact of the facility location decision on stakeholders rather than shareholders alone
Vincent van Megen
first supervisor dr. Stuart X. Zhu second supervisor dr. ir. Stefano Fazi
June 24, 2018
Sustainability has become an increasingly important topic for companies and corporate social responsibility (CSR) is embedded in business practices more and more. To maximize a firm’s sus- tainability and corporate social responsibility effectiveness, all aspects of business, including the facility location decision, have to be taken into account. Currently, sustainable facility location models that include aspects concerning both the social and ecological environment are lacking presence. This thesis presents a social responsible facility location model that prioritizes five as- pects: cost, emission, water usage, quality of life and demand satisfaction.
In order to develop the social facility location model, goal programming, a multi-criteria deci- sion making approach, is used. Here, the goal is to minimize the sum of the negative deviations from the individual objectives. To check the applicability of the model, it is subjected to multiple test scenarios. These scenarios are not specific to a single company, but they represent different industries and company preferences. Also, a sensitivity analysis is done on some important pa- rameters and on the level of importance (weights) of the individual goals.
The model shows that a general facility location model delivers different results than the social responsible model: the general model opens facilities in cost effective, but far away countries, resulting in high emission and a high water stress level. The social model has a significant lower total negative deviation for all weight combinations; the emission and water stress level are sig- nificantly lower while the costs are marginally higher. The model can serve as a decision-making tool for companies that have a broad view on the business case for CSR, to help assess the impact of their facility location choices and improve the inclusion of CSR in the decision making.
1 Introduction 3
2 Theoretical Background 5
2.1 Facility location models . . . . 5
2.2 CSR . . . . 6
2.2.1 CSR factors to include in the model . . . . 6
2.3 Goal programming . . . . 9
3 Methodology 10 3.1 Goal Programming . . . . 10
3.2 Modelling Description . . . . 10
3.2.1 Assumptions . . . . 11
3.2.2 Parameters . . . . 11
3.2.3 Decision variables . . . . 13
3.2.4 Objective function . . . . 13
3.2.5 Goals (Constraints) . . . . 13
3.2.6 Data . . . . 16
4 Numerical Study 17 4.1 Initial Values . . . . 17
4.1.1 Cost-focused facility location model . . . . 18
4.1.2 Emission-focused facility location model . . . . 18
4.2 Social responsible facility location model . . . . 19
4.2.1 Weights . . . . 19
4.3 Scenarios . . . . 21
4.3.1 Country or company specific scenarios . . . . 21
4.3.2 Industry scenarios . . . . 22
4.4 Scenario Outcomes . . . . 23
4.4.1 Country specific . . . . 23
4.4.2 Industry specific . . . . 25
4.5 Sensitivity Analysis . . . . 26
4.5.1 Parameters . . . . 26
4.6 Results . . . . 28
5 Discussion 29 6 Conclusion 31 Appendix A Parameter Values 36 A.1 Values . . . . 36
A.2 Data Collection . . . . 39
Appendix B Additional Suppliers 42
Appendix C Scenarios 43
C.1 Country specific scenarios . . . . 43
C.1.1 Objective function . . . . 43
C.1.2 Country selection . . . . 45
C.1.3 Absolute values . . . . 46
C.2 Industry scenarios . . . . 47
C.2.1 Objective function . . . . 47
C.2.2 Country selection . . . . 49
C.2.3 Absolute values . . . . 50
C.3 Sensitivity analysis . . . . 51
Introduction
For many companies, the decision where to open a new facility is of great importance. They face the facility location problem (FLP), which deals with the selection of a facility’s location to meet the demanded constraints in the best possible way. This decision is of high strategic importance as the decision is usually set for a long period of time and the facility location decision does not just affect the concerned company, its suppliers and clients, but also the wider environment of the facility, such as the people living close to the facility or its transportation routes, the employees and their families and governments and organizations. Because of this importance of determining the optimal facility location, the FLP is a well established problem in literature, where a wide range of facility location models have been developed (Melo et al., 2009).
When deciding on the optimal facility location there are numerous factors that can be taken into consideration, but despite the availability of multiple models, the factors related to corporate social responsibility (CSR) are underrepresented in current models. CSR is the notion of respon- sibility of a company towards the community and both the social and ecological environment.
Traditionally, most of the facility location models are tasked with the objective to minimize the total cost, maximize the profit or minimize the total transportation distance in relation to the location of the customers and suppliers. However, with the increasing emphasis of CSR from com- panies and governments, more elaborate facility location model, or models that are CSR-focused, are required (Chen et al., 2014).
It has become increasingly important for companies to embed (social) sustainability in their business practices. Motivated by the adoption of United Nations 2030 Agenda for Sustainable De- velopment with the corresponding Sustainable Development Goals (SDGs), and by the knowledge that well implemented CSR practices positively influence financial performance (Orlitzky et al., 2003; Wang et al., 2017), companies increasingly prioritize CSR practices. This phenomenon can be seen in the widespread voluntary adaptation of environmental standards such as ISO 140011, ISO 260002and the Global Reporting Initiative (GRI) Standards3.
With the increasing interest in CSR, facility location models are getting more focused towards models that include environmental and social factors instead of just the traditional cost and dis- tance factors (Chen et al., 2014). However, Farahani et al. (2010) still mention ‘Sustainability’ as a topic that requires more research within facility location problems and Chen et al. (2014) identi- fied that when it comes to sustainable frameworks, the social aspect, such as the quality of life, is lagging compared to sustainability (emission) aspects. An extended, improved or new facility lo-
1ISO 14001 is an environmental management system certification, with over 345000 certificates issued until 31 December 2016 (The ISO Survey of Management System Standard Certifications 2016 2017)
2ISO 26000 is a guidance to all types of organizations on social responsibility
3The GRI Standards are global standards for sustainability reporting which are widely acceptable reporting guidelines (Samy et al., 2010)
cation model, with more emphasis on the social aspect, can contribute to filling this literature-gap.
Therefore, the goal of this thesis is to develop a generic facility location model that considers relevant CSR factors. This model can contribute to a more well-considered facility location de- cision to optimize social welfare alongside companies’ profits. The model will focus on a global, cross-country setting with country specific environmental and social parameters. For the model, the optimization program called goal programming (GP) will be used. With goal programming, multiple, competing, objectives of different importance can be selected and a facility location can be chosen that minimizes the violations of the objectives (constraints) relative to their importance.
In this research, the objectives are related to costs and quantifiable (social) factors such as quality of life and environmental performance. These factors will be derived from facility location models, sustainable supply chain management (SSCM), green logistics, and other relevant literature.
The thesis is organized in the following parts. It starts with a theoretical background on the facility location problem and on CSR, followed by the methodology, where the the model overview will be presented. A thorough explanation will be given for all CSR-parameters included in the model. Next, the results obtained from the model will be compared to a the results of a general, cost based, model. The final chapters describe the discussion and conclusion.
Theoretical Background
This chapter presents a more detailed explanation on the facility location problem, with an em- phasis on the facility location models in combination with CSR practices. Here, the research-gap is identified and the goal this thesis is set. After this, more information is provided on CSR and social welfare, including the relevance of incorporating CSR practices in the facility location deci- sion. The CSR factors that will be included in the model are presented and explained. Finally, a short introduction on the use of goal programming is given.
2.1 Facility location models
As mentioned in the introduction, the FLP deals with the selection of a facility’s location. The goal is to maximize (or minimize) a given objective while satisfying the demanded constraints.
These objectives are mostly related to minimizing the costs, maximizing the profit or minimiz- ing the total transportation distances in relation to the location of the customers and suppliers (Terouhid et al., 2012; Chen et al., 2014). The facility location decision is usually associated with high initial time and monetary investments and it has a high impact on, among others, logistical and operational decisions. This makes the decision long term, difficult to reverse and strategically important (Snyder, 2006; Owen et al., 1998). This importance makes the FLP a well-mentioned subject in literature (Melo et al., 2009).
While the traditional focus of decision makers used to be on the economic aspects of the facility location problem, the focus has been shifting towards models that also include environmental and social factors (Chen et al., 2014; Terouhid et al., 2012). Although this shift has started to take place, there are still flaws in the new, more inclusive models. First, ”Sustainability” is mentioned by Farahani et al. (2010) as a topic for further research within the FLP. As mentioned before, Chen et al. (2014) identified that when it comes to sustainable frameworks, the social aspect is lagging compared to sustainability aspects. This point is reinforced by Tang et al. (2012) who state that models focusing on the social aspect of CSR, thus dealing with ‘people’ performance measures, create excellent research opportunity to make important contributions to help corpo- rations to achieve CSR objectives, but these “models that examine the people measure” are still lacking. Additionally, a study by Klassen et al. (2012) shows that managers agreed that it proves difficult to deal with social issues, and that they were only able to control a few, out of many, factors that linked social management capabilities with risk and performance. Finally, a study by Gabriel et al. (2004) shows that companies and households prefer different cities, which can lead to facility location decisions that favour business-preferences, but potentially harm the quality of life of employees.
The lack of social factors in sustainable facility location models, or even the little presence of sustainable facility location models in general, is identified as a gap in literature. This thesis aims to contribute to closing this gap by suggesting a new facility location model. The goal of this thesis is set as: Developing a generic social responsible facility location model. The model should contains country specific environmental, as well as social, factors.
2.2 CSR
In a comprehensive review on CSR by Aguinis et al. (2012), CSR is defined as “context specific organizational actions and policies that take into account stakeholders expectations and the triple bottom line of economic, social, and environmental performance” (Aguinis, 2011). It can be iden- tified as the benchmark and centerpiece of the socially conscious business movement (Carroll, 2015). Nowadays it is considered necessary for companies to apply social and ethical standards to their business practices and to define their roles in society (Lindgreen et al., 2010).
Carroll et al. (2010) note that there are two views of the business case for CSR: a narrow view and a broad view. The narrow view is a business case model that recognizes CSR when there is a direct relationship between CSR initiatives and the firm’s financial performance, while the broad view recognizes both the direct and indirect relationships between the firm’s performance and CSR. The broad view has, among others, the advantage that the complex relationship between the firm’s performance and CSR can be valued and that it enables to exploit opportunities outside the scope of the narrow view (Carroll et al., 2010). A broad view on the business case for CSR will be required for the adaptation of the social model, as not all benefits might be directly related to the firm’s financial performance: The total cost might be slightly higher, but this can result in improved performance for other aspects.
CSR consists of four factors (economic, legal, ethical and discretionary) which in turn all appear in three domains: the institutional, organizational, and individual domain (Wood, 1991, Table 3).
In all three domains, companies have different predictors and outcomes of the engagement in CSR practices. At an institutional level, the engagement in CSR can be explained by stakeholders’
pressure. The stakeholders can be, among others, the clients, the shareholders, the media and local communities, where often the focus lies on impacts of government (regulations) (Tang et al., 2012). Their reasons for pressuring firms to engage in CSR practices can be instrumental, institutional and moral. The extent to which companies implement CSR practices can be affected by institutional forces such as regulations, standards and certification. The outcome of adapting CSR practices at an institutional level is often an improved reputation. At an organizational level, companies engage in CSR for financial reasons and because it goes along with their values. When implemented right, there is a positive influence of CSR governance on the financial performance of a firm (Orlitzky et al., 2003; Wang et al., 2017). Lastly, at the individual domain level, motives such as individual concerns and personal values influence CSR engagement on a personal level. Consequently, engagement in CSR practices influences individual performance, behaviours, attitude, engagement, commitment and identification (Aguinis et al., 2012). The positive effects of adapting CSR practices are self-evident, thus implementing CSR practices in all facets of business, including the facility location choice, will be beneficial to the business.
2.2.1 CSR factors to include in the model
Wood (1991, Table 3), shows the three domains and four factors mentioned above. From this table, the organizational and individual economic principles such as “reflect costs by incorporat- ing all externalities” and “use low polluting techniques” and ethical institutional principles such as “follow fundamental ethical principles” could be quantified and used in a facility location model.
The review of Wood (2010, table 1) shows a number of ways on which corporate social perfor- mance within companies can be measured. The rating is measured through different reports, score- cards and ratings done internally or by third-party experts. The review concludes with a remark that, at the time of research, new resources are becoming available, such as the Global Reporting Initiative Standards. Samy et al. (2010) use these GRI ratings to measure the CSR-performance of 20 British multinationals. The GRI Standards are global standards for sustainability reporting which are widely acceptable reporting guidelines. A lot of these measures can not be used in the context of this model, as they are not location dependent. However, factors that can be included in the model can be identified by looking at the criteria of the CSR measurement systems. More, environmental outcomes and impacts as presented by Wood (2010, table 4) can be location and distance dependent and they can be included in the facility location model. Location dependent CSR factors, of which a number are identified by Terouhid et al. (2012), that will be included in the model are mentioned in the following sections.
Quality of life
From a CSR perspective, social aspects are underrepresented in CSR frameworks (Chen et al., 2014) or it is covered in a far too simplified manner (Seuring, 2013). More, social dimensions need much better integration with the environmental and economic aspects of sustainability (Seuring, 2013). For this reason, the quality of life aspect will be part of the social responsible model pro- posed in this thesis. It will not be possible to fully cover the effect of the facility location decision on the quality of life of the direct surroundings. However, factors that contribute the a higher, or lower, quality of life will be included. More, the quality of life of the region in which the facility is going to be located will be factored into the model to ensure a maximum quality of life for employees. This is important as cities that have a high quality of life tend to have a lower quality of business environment and vice versa (Gabriel et al., 2004) and if only business measures are considered, the quality of life of the employees might fall behind.
Factors that influence the quality of life are, among other, the crime rate, accessibility to goods and services, air quality and the noise level (Austin, 1974). For the model, the quality of life index computed by numbeo1 is used. This index is computed by taking into account the account purchasing power index, pollution index, house price to income ratio, cost of living index, safety index, health care index, traffic commute time index and climate index.
Air quality
Air quality has a huge influence on the quality of life of people; research by Luechinger (2009) shows that in the Western hemisphere the air quality has improved impressively over the last two decades, which resulted in large increases in human welfare. In developing countries, the situation does not always look as good; it is often getting worse. For example, air pollution is a huge prob- lem in large areas of China. Here, the Joint Prevention and Control of Air Pollution proposed a number of basic principles to integrate economic development with environmental protection:
” (1) Optimizing structure and layout of regional industry.
(2) Intensifying efforts to control key pollutants.
(3) Strengthening cleaner use of energy.
(4) Intensifying efforts to control vehicle pollution.
(5) Improving supervision system of regional air quality.
(6) Reinforcing support ability of air quality improvement.
(7) Intensifying organization and coordination. ” (Zhang et al., 2016) Similar actions have been proposed by Wang et al. (2012).
1https://www.numbeo.com/quality-of-life/rankings_by_country.jsp
The emission of air pollutants can be quantified and expressed in costs for society; this has been done by E. Buunk (2016), who calculated that the closure of the seven Dutch coal-fired power plants would increase welfare by 4.7 billion euros, and Smith et al. (1995), who determined the marginal willingness to pay for a one-unit reduction in total suspended particulates (in micro grams per cubic meter) lies between zero and $98.52 (in 1982-84 dollars).
Similar to the quality of life, the direct effect of air pollution on life satisfaction as presented by Luechinger (2009) will not fully be covered in this thesis, but as the importance of air quality is clear, the following aspects will be covered: Looking at the basic principles mentioned before, number (1) to (4) can be related back to the manufacturing facility location problem and influ- ence the those principles the following way: (1), (2), environmental facility location models can influence the layout of regional industry. (3) by choosing a location that has a low carbon inten- sity or investing in clean energy sources, such as solar panels or electric vehicles. (4) minimizing transportation distances and again use electrical (or comparable) vehicles or stimulate the use of public transportation by employees.
CO2 emissions and electricity consumption
As mentioned before, environmental factors are most represented is CSR related frameworks. The emission of CO2, or CO2 equivalent, is mostly used when addressing a firm’s environmental im- pact. Factors that can be included in the facility location context are the CO2 emission related to the total distance travelled, the mode of transportation, and the fixed and flexible emissions of a facility.
Electricity consumption can also be included in the model. The electricity consumption will relate to the fixed and variable consumption used during production. The impact of the energy consumption in terms of emission differs per country because different methods for generating elec- tricity are used. To tie back the CO2emission related to electricity consumption to the countries, country specific aspects such as the global warming potential per kWh of electricity consumed (Reich-Weiser et al., 2009) and the carbon intensity of electricity (Moro et al., 2017) can be used.
These scores can be linked to the CO2per kWh per country as done by Jochem et al. (2015) and Casals et al. (2016). For this model, the carbon intensities will be used.
In the model, there is a possibility to invest in a sustainable factory in stead of a regular factory.
There is also the option to invest in sustainable transportation. For sustainable transportation, the specifications of the new Tesla Semi trucks2 are used as guidelines. Investing in a sustainable truck will not always be more environmental effective, based on the carbon intensity of a country.
For regular truck transportation, the emission-data of the trucks will be obtained from a report by Ligterink et al. (2016). For transportation between a supplier and a factory the CO2emission of a heavy duty truck will be used, and for the transportation between the factories and warehouses the CO2 emission of a medium duty truck will be used.
Water consumption and availability
The consumption of water will also be included in the model, as the impact of water usage differs per country. The water consumption which is used during production will be tied back to the water stress of a country by using data from the FAO.3 Water stress affects countries all around the world; it hinders the sustainability of natural resources and it obstructs economic and social development, where the most disadvantaged people tend to be affected disproportionately (Food et al., 2018). Water stress is used as indicator of SDG 6: clean water and sanitation. It is measured
2https://www.tesla.com/semi
3FAO. Review of water resource statistics by country. Food and agriculture organization of the United Nations.
http://www.fao.org/nr/water/aquastat/data/query/index.html.
by taking the freshwater withdrawal as a proportion of available freshwater resources:
Water Stress = 100[Total freshwater withdrawal (primary and secondary)]
[Total renewable water resources]-[Environmental Flow Requirements]
(Food et al., 2018)
Social investments
It is assumed that companies want to make a positive impact on the community in every country where a new facility is opened. For this reason a target level of impact of social investments is set. The required investment to reach the desired level is different for each country as it is based on the county’s standard of life. The higher the standard of life of an area, the more it will cost to create the same social impact compared to a country with a lower standard of life.
To assess the impact of social investment in a country, several community factors as addressed in the quality of life survey (Eurofound, 2017) will be taken into account. The average percentage of the following negative factors that can be influenced by social investments is taken:
• Percentage of people that do not participate in social activities of a club, society or associ- ation once a weak
• Percentage of people that do not receive training for non-professional reasons
• Percentage of people that experience major problems with litter and rubbish on the street in their neighbourhood
• Percentage of people that has difficulty to access to green or recreational areas
2.3 Goal programming
The proposed modelling technique for this thesis is goal programming, which is previously used in studies by, among others, Lee et al. (1981), Lee et al. (1979) and Badri (1999). It is a branch of multi-criteria decision analysis (MDCA) (Tamiz et al., 1995) and it can be seen as an extension of linear programming used to handle multiple conflicting objectives. This makes it ideal to use in the context of this thesis, as there are multiple (possible) conflicting objectives such as minimizing cost, minimizing emissions and maximizing social welfare. Goal programming as solution approach is used to solve complex real case problems (Brandenburg et al., 2014), but they are limited used in SSCM (Brandenburg et al., 2014; Ansari et al., 2017) and for the FLP. This limited use leads to a focus on less complicated case problems due to modeling complications (Ansari et al., 2017).
A more detailed description of goal programming is given in section 3.1.
Methodology
The methodology used in this thesis will be explained throughout this chapter. The chapter starts with a continuation of section 2.3, as goal programming will be explained in more detail. Then the model is described. This description starts with the assumptions, followed by the parameters, decision variables, the objective function, the constraints and it concludes with an explanation on the data collection.
3.1 Goal Programming
Goal programming is a branch of multi-criteria decision analysis (MDCA) (Tamiz et al., 1995).
Within the multiple criteria decision making (MCDM) paradigm, it is one of the oldest and most widely used approaches. GP is used with the purpose of satisfying multiple goals at the same time, where the goals are relevant to the considered decision-making process (Romero, 2014). With GP, multiple objectives are transformed into a single objective by a weighted sum of the criteria (Melo et al., 2009); the sum of the unwanted negative deviation from the separate goals (constraints) is minimized. For this reason, goal programming is especially useful in the context of this thesis.
3.2 Modelling Description
In the model, all goals are awarded a weight. This weight has two components: it is based on their importance, and it is used to normalize the goals’ different values. In order to make the goals compatible, and the scores comparable, with each other, coefficients of impact are determined via the framework used by Neto et al. (2008), which consists of the following three steps:
1. Assessment of the environmental, social or economic impact in each activity: evaluate the effects of choices that can be made on the model and quantify the consequences accordingly 2. Normalization: the scores will be normalized by dividing them by a reference level.
3. Weighting: select a weight of importance for each of the goals
At every goal, deviation variables are included. These can indicate positive (pi) or negative (ni) quantified deviations from the goal; if there is a positive pi, the goal has been satisfied and it passed its target. The opposite holds for the negative deviation variables. The normalization will be done by dividing the negative deviation of a goal by the minimal or maximal value of that goal. This way the negative deviation will be presented as a percentage making it possible to compare the negative deviation of the different goals. The weighting is something that is done based on (company) preferences. In this thesis, different weight combinations will be used on different scenarios. The outcomes will be compared to the outcome when only the cost constraint is activated.
3.2.1 Assumptions
For this model, a few assumptions are made, the assumptions are:
• The demand is constant
• Every product in the model equals a truckload
• The amount of supplies equals the amount of production (both in truckloads)
• The initial investment amount for sustainable trucks can be expressed in the number of produced products in a factory
3.2.2 Parameters
Table 3.1 contains the parameters used in the model. A product stands for a full truckload.
The parameters are related to the different goals/ constraints and the objective function. The parameters’ choices relate back to the explanations given in section 2.2.1.
Parameter Symbol Unit Data Type
Weight of constraint g αg Real
Minimum social investment score Imin Real
Initial cost value Mmax Real
Initial emission value Emax gram CO2 Real
Initial water stress level value Wmax Real
Initial quality of life score Qmin Real
Shortest distance from suppliers to factory j sj km Real
Distance from factory j to warehouse i dij km Real
Demand per warehouse Di Products Integer
Number of employees in factory j bj Employees Integer
Maximum capacity of facility j fj Products Integer
Initial cost for opening a regular factory at j Fj Euro Real
Initial cost for opening a sustainable factory at j Fj0 Euro Real Initial cost for sustainable transportation at factory j per product Fj00 Euro Real
Fixed cost regular factory j hj Euro Real
Fixed cost sustainable factor y j h0j Euro Real
Cost per product in factory j Cj Euro Real
Cost per product in factory j when invested in sustainability Cj0 Euro Real
Governmental incentives in country j Gj Euro Real
Environmental incentives for buildings in country j Sj Euro Real Environmental incentives for transport in country j per product S0j Euro Real
Transportation cost per product per km cj Euro Real
Transportation cost per product per km (clean transportation) c0j Euro Real
Penalty per product if not delivered P Euro Real
Fixed kWh usage of factory j Ej kWh Real
Fixed kWh usage of factory j (green energy/ sustainable building) E0j kWh Real
kWh usage per product of factory j kj kWh Real
kWh usage per product of factory j (sustainable building) kj0 kWh Real
Quality of life in country j Qj Real
Social investment payback rate in country j rj % Real
Water Stress level per country j Wj % Real
Water usage per product w Liter Real
Carbon intensity of electricity consumed at low voltage aj CO2 g/kWh Real
Emission per product per km (normal truck) e CO2g/km Real
Emission related to raw material delivery per km e00 CO2g/km Real Electricity consumption per product per km (sustainable truck) e0 kWh/km Real
Table 3.1: Parameters
3.2.3 Decision variables
The list of decision variables of the model is captured in table 3.2:
Decision variable Symbol Data Type
Opening of a regular factory at location j Xj binary
Opening of a sustainable factory at location j Xj0 binary Investing in sustainable trucks for the transportation from factory j yj binary Number of products transported from factory j to warehouse i xhij integer Negative deviation from goal g, where g ∈ 1..4 ng real Positive deviation from goal g, where g ∈ 1..4 pg real
Negative deviation from goal 5 (demand) n5i real
Social investment in the country j Ij real
Table 3.2: Decision variables
As there is the possibility to invest in a sustainable building, and or sustainable transportation methods, there are four production options. For this reason the three dimensional array xhij is created, where h represents the investment choices:
h =
1 if the factory and transportation are regular
2 if the factory is sustainable and transportation is regular 3 if the factory is regular but transportation is sustainable 4 if the factory and transportation are sustainable
3.2.4 Objective function
The goal is the minimization of the total relative negative deviation from the individual goals.
This is done by taking the sum of all the normalized negative deviation for the goals multiplied by the importance (αg) of the goal. The objective function will look like:
minimize Z = α1 n1
Mmax + α2 n2
Emax + α3 n3
Qmin + α4 n4
Wmax + α5X
i∈I
n5i
Di (3.1)
Where ni is the negative deviation of the constraints defined in equation 3.2 till 3.5.
3.2.5 Goals (Constraints)
The constraints, or goals, will be formulated in the same way as the following constraints:
f (x) + ng− pg = bg , ∀ i = 1..k xi, ng, pg ≥ 0 , ∀ i = 1..k Where bg is the target value of the constraint.
Initially, there will be five constraints, categorized by value types. The constraints will be cost (euro), emission (gram CO2), quality of life, water stress, and demand (products).
Cost
The first part of the cost function consists of the initial investments, either with sustainability efforts of without, and the governmental subsidies:
Fixed Cost =X
j∈J
Xj(Fj+hj)+X
j∈J
Xj0(Fj0+h0j)+
4
X
h=3
X
i∈I
X
j∈J
xhij(Fj00−Sj0)+X
j∈J
Ij−X
j∈J
Xj0Sj−X
j∈J
(Xj0+Xj)Gj
The next part consists of the variable costs related to production and transportation:
Variable Cost = X
h∈1,3
X
j∈J
X
i∈I
Cjxhij+ X
h∈2,4
X
j∈J
X
i∈I
Cj0xhij+
2
X
h=1
X
j∈J
X
i∈I
cjdijxhij+
4
X
h=3
X
j∈J
X
i∈I
c0jdijxhij+
4
X
h=1
X
j∈J
X
i∈I
(Di− xhij)P
This results in the first, money related, constraint:
Fixed Cost + Variable Cost = Mmax+ n1− p1 (3.2) Environment
The first part of the environmental function consists of the fixed emissions, either with sustain- ability efforts of without:
Fixed Emission =X
j∈J
ajXjEj+X
j∈J
ajXj0Ej0
The next part consists of the variable emission related to transportation from and to the suppliers and customers and the variable emission related to production.
Variable Emission = X
h∈1,3
X
j∈J
X
i∈I
ajkjxhij+ X
h∈2,4
X
j∈J
X
i∈I
ajk0jxhij+
2
X
h=1
X
j∈J
X
i∈I
edijxhij
+
4
X
h=3
X
j∈J
X
i∈I
aje0dijxhij+
4
X
h=1
X
j∈J
X
i∈I
e00sjxhij
Both formulas are expressed in emission of CO2 equivalent emission through the use of table 2 and 3 from Moro et al. (2017). The emission related constraint is:
Fixed Emission + Variable Emission = Emax+ n2− p2 (3.3) Quality of life
The constraint related to the quality of life is made up of the quality of life of a country, combined with the number of employees required in each factory: This leads to the quality of life constraint:
Quality of life impact = X
j∈J
(Xj+ Xj0)bQj
X
j∈J
(Xj+ Xj0)bjQj = Qmin− n3+ p3 (3.4)
Water usage
Water related constraint is made up of the water consumption and the water stress level of a county:
4
X
h=1
X
i∈I
X
j∈J
xhijwWj = Wmax+ n4− p4 (3.5)
Demand
The demand related constraint is as follows:
4
X
h=1
X
j∈J
xhij= Di− n5i , ∀i ∈ I (3.6)
Additional constraints
The following additional constraints are required:
Only if a facility is opened, a sustainable transportation alternative can be chosen:
Xj+ Xj0 ≥ yj , ∀j ∈ J
If a facility is opened, either the facility can be sustainable, or not:
Xj+ Xj0 ≤ 1 , ∀j ∈ J
The maximum production capacity cannot be exceeded and the production capacity is 0 if no factory is opened. As there are four combinations for h, four sets of constraints are required.
h = 1: x1ij can only be higher than 0 if a regular factory is opened and no sustainable trans- portation is chosen. This results in the following constraints:
P
i∈Ix1ij≤ fjXj , ∀j ∈ J P
i∈Ix1ij≤ fj(1 − yj) , ∀j ∈ J
h = 2: x2ij can only be higher than 0 if a sustainable factory is opened and no sustainable transportation is chosen. This results in the following constraints:
P
i∈Ix2ij≤ fjXj0 , ∀j ∈ J P
i∈Ix2ij≤ fj(1 − yj) , ∀j ∈ J
h = 3: x3ij can only be higher than 0 if a regular factory is opened and sustainable trans- portation is chosen. This results in the following constraints:
P
i∈Ix3ij≤ fjXj , ∀j ∈ J P
i∈Ix3ij≤ fjyj , ∀j ∈ J
h = 4: x4ijcan only be higher than 0 if a sustainable factory is opened and sustainable trans- portation is chosen. This results in the following constraints:
P
i∈Ix4ij≤ fjXj0 , ∀j ∈ J P
i∈Ix4ij≤ fjyj , ∀j ∈ J
For every country that a factory is opened, the minimal social investment score must be met:
Ijrj≥ Imin(Xj+ Xj0) , ∀j ∈ J
At least 85% of all demand has to be met:
P4 h=1
P
j∈Jxhij≥ 0.85Di , ∀i ∈ I All variables should be non-negative:
Xj, n1, p1, yj, xhij ≥ 0 , ∀j ∈ J, ∀i ∈ I
3.2.6 Data
In order to run the model, the location of a number of potential factories, distribution centres and suppliers has been selected. Figure 3.1 gives an overview of the situation used as basis for the testing of the model. There are 12 potential facilities that can be opened in 12 countries across Europe. There are also four warehouses that all have a demand and there are two suppliers.
The model presented in this thesis is created to be general and applicable in multiple situation.
The model has a number of different parameters (see table 3.1), these parameters can be divided into two categories: parameter values based on literature, and parameters with chosen values. In the last category another division is made: parameters with chosen values and parameters with chosen values that are influenced by existing data and literature. Table A.4 in Appendix A shows the division of the parameters used in the model. In a normal situation, the ’chosen’ parameters will be based on the use-case of the model. However, in this thesis the model will not be tested against a ’real-world’ case, thus data is created. This data is influenced by literature to test the model against a scenario that depicts reality as good as possible. A detailed explanation of the data collection method per parameter and the values of the parameters can be found in Appendix A:
table A.1 to A.3 show the values of the parameters, and section A.2 gives the detailed explanation on the origin of the data.
Figure 3.1: Locations of warehouses, suppliers and potential facilities
Numerical Study
The goal of this thesis is to design a generic social responsible facility location model. This model, that is presented in chapter 3, has multiple conflicting goals, of which some are related to relevant CSR factors. In order the check the applicability and robustness of the model, and to better understand its behaviour, a numerical study is conducted on the model. This chapter presents an overview of the results of this numerical study on the aforementioned model.
This chapter starts with the calculation of the initial values (Mmax, Emax, Wmax and Qmin).
These initial values are required for running the model. The calculation of every single one minimum initial value also results in accessory values for the other three goals. A comparison is made between the minimal values and the other corresponding values to see the effect on the goals of only focusing on one aspect. Next, the results for a cost-focused and emission-focused model are given and explained. This is done to give a first insight on difference between the use of a regular facility location model and the presented social responsible model. From section 4.2 onwards, the social model presented in this thesis will be discussed. First, a number of combinations for the weights used by the model are presented. This is done to test if the model works for different weight combinations and to show the impact of choosing the right combinations within a certain bandwidth. These weight combination represent different possible company preferences. To test the applicability of the model in multiple situations, a number of scenarios are described that are going to be applied to test the model. These scenarios describe different industries, or they anticipate on changing country specific values. In section 4.4 the results of applying the different weight combination and the different scenarios are presented and analyzed. The chapter concludes with the results of a sensitivity analysis on some of the parameter values. This sensitivity analysis is done to see how the model reacts to parameter value changes. This insight in the model can help to identify which parameters to improve in order to improve the overall results most.
4.1 Initial Values
The proposed model, as described in section 3.2, requires initial values for the minimum quality of life score and maximum investments, greenhouse gas emission and water score. The maximum initial investments, greenhouse gas emission and water score are created by setting all weight to 0 except the weight (αi) related to the concerned constraint. For the initial values, the demand must fully be met. Therefore the following constraint is added:
4
X
h=1
X
j∈J
xhij= Di , ∀i ∈ I
To obtain the minimum quality of life score, the objective is set to maximizing n3. For this, the QOL constraint is temporarily changed to:
X
j∈J
(Xj+ Xj0)bjQj= n3
To prevent that too many factories are opened the extra constraint that at least 90% of the production capacity of an opened factory is used:
4
X
h=1
X
i∈I
xhij≥ 0.9fj , ∀j ∈ J
Table 4.1 gives an overview of the optimal initial values and the differences with the optimal values: in each row, the optimal initial values (cost, emission, QOL, water and distance) are displayed. When a minimal value is calculated, the corresponding values for the other goals are calculated as well and the percentage difference with the optimal value from the other rows is presented.
Cost Emission Quality of Life Water Score Distance
Minimum Cost 80,197,700 143% -9% 242% 76%
Minimum Emission 36% 21,945,500 -15% 234% 43%
Maximum QOL Score 29% 127% 390,344 176% 149%
Minimum Water Score 41% 197% -11% 86,125 207%
Minimum Distance 20% 57% -17% 331% 15,646,000
Table 4.1: The initial values and the percentage deviation
4.1.1 Cost-focused facility location model
From table 4.1 can be seen that a policy that focuses entirely on the minimization of costs, results in 143% extra emission compared to the best case. Also the water score and the total distance are significantly worse than the optimal value. The absolute values of the facility location model that is only tasked with cost minimization can be found in table 4.2:
Total Cost
Total Emission
Total
Quality of Life
Total
Water Score Total Distance 80,197,700 53,242,900 355,601 294,750 27,550,000
Table 4.2: Absolute values of the cost based approach
In this situation, a regular factory is opened at location 1, 6 and 8 and a sustainable facility factory is opened at location 9. At location 1 and 6, there is a investment in sustainable trans- portation methods. The factories are opened in Bulgaria, Poland, Romania and Spain. These countries are generally low-cost countries in terms of wages, utilities and investments. However, these countries, except from Spain, are further away from the demand points than other countries, which results in higher CO2 emissions.
4.1.2 Emission-focused facility location model
The situation that only focuses on the minimization of the emissions results among others in a 36% higher cost and 43% bigger total distance compared to the optimal values. The absolute values for this situation are as follows:
Total Cost
Total Emission
Total
Quality of Life
Total
Water Score Total Distance 108,972,000.00 21,945,500 330,391 287,425 22,320,500
Table 4.3: Absolute values of the cost based approach
In this situation, a sustainable factory is opened at location 2, 3, 5, 6 and 10. At location 2 and 10, there is a investment in sustainable transportation methods. The countries in which a factory is opened are France, Germany, the Netherlands, Poland and Sweden. These countries are closer to the demand points and their carbon intensity is relatively low. Only in Sweden and France the option of sustainable transportation is chosen. This is because the carbon intensity in these countries is very low: in Sweden, 83% of electricity production comes from nuclear and hydroelectric power and 7% of the electricity comes from wind power1. In France, 80% of the electricity generation comes from nuclear power generation and 14% from sustainable sources. In the other countries, the regular truck transportation is chosen as the carbon intensity is too high making sustainable truck an option that results in more emission.
4.2 Social responsible facility location model
The optimal initial values (table 4.1), and the results obtained form the cost-focused facility location model (table 4.2), will serve as benchmark for the performance of the social facility model.
The purpose of the model is to find a balance between the conflicting goals and incorporate all aspects in the decision making process.
4.2.1 Weights
The first step in obtaining the optimal result is determining of the weight factors for the goals.
As mentioned in section 3.2, this prioritization of importance should be done by experts, which could be the users of the model, and it should focus on the preferences and goals of the users.
With a MCDM-model, the weights related to the constraints or goals are of great importance.
Within certain limits, that are preferably set by the experts mentioned above, it could possible to vary the importance of the goals marginally. This variation may result in a (significantly) lower total negative deviation. Therefore, a sensitivity analysis will be performed on the different weight scores to see what combination of weights, within some set limits, results in the lowest relative total negative deviation. A selection of criteria will be used to simulate different company prefer- ences. The resulting weight combinations will be applied on all scenarios to get a broad overview of the applicability of the model.
For the sensitivity analysis of the weights, a total of 10 points are divided over the 5 weights.
All values are integer and non-zero. This leaves a total of 126 possible combinations. The total negative deviation is calculated for all combinations. A comparison will be made between repre- sentative combinations based on a company’s preferences. There are five combinations of weights that will be calculated, next to the combination where all weights are equal: cost and demand focused, cost and emission focused, environmental focused, quality of life focused and water impact focused.
1https://sweden.se/society/energy-use-in-sweden/
