Master’s thesis
Msc Technology & Operations Management
“Including Corporate Social Responsibility in the Facility Location problem”
Joost Meester S2359758
1st supervisor: Dr. X. Zhu
2nd supervisor: Prof. Dr. J. Riezebos
Abstract
Recently, the focus on corporate social responsibility (CSR) has gained improved attention within literature. While traditionally the facility location decision was merely based on the costs, nowadays the environmental and social impact must also be taken in account. This research investigates economic, environmental and social factors that will influence the facility location decision. A profit based objective formula, including the environmental and social parameters, will be modelled in order to investigate the optimal location decision. This will lead to an optimal facility location, calculated in a real-life example setting in the
1 Preface
This master’s thesis is the final step in obtaining my master degree in the field of Technology and Operations management. Finishing this thesis would not be possible without the help of several people. I would like to thank dr. X. Zhu for his advices throughout the whole part of the thesis project. Furthermore, I would like to thank dr. X. Tong for the support he provided during the thesis. Lastly, I would like to thank my family for their support during my study.
1. Introduction
The facility location, also known as the facility location problem, is the field of research concerned with finding the optimal location for a companies’ to-be-opened facility. The correct facility location decision can be a major determinant in attracting customers and making profit (Yu et al. 2017). The facility location is a long-term, strategic decision, due to the relative large time scale and high costs associated with the facility location decision (Anvari & Turkay, 2017). The role of the facility location is becoming more important with the increasing need for more comprehensive models that capture many aspects relevant to real-life problems simultaneously (Melo et al. 2009).
The private sector traditionally focuses on minimising costs when estimating a new facility location (Dou & Sarkis, 2010). However Anvari & Turkay (2017) states that “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.” Over the last decades,
humanity has become more aware of the need for sustainable development (Hutchins & Sutherland, 2008). Regarding Mota et al. (2015), sustainability (fulfilling current needs without harming future generations) is more important than ever. This thesis is showing the importance of environmental and social (influence on the local community) factors, which have rarely been introduced into objective functions as of yet.
In line with this, different stakeholders are putting pressure on firms to adopt environmentally friendly or social practices (Delmas & Toffel, 2004). Besides pressure from outside, improvement to the firm’s reputation drives companies to invest in Corporate Social Responsibility (Aguinis & Glavas, 2012). Companies are challenged to investigate consequences for the local community and
2 considered the three pillars of sustainability” (Anvari & Turkay, 2017). In recent years, several
companies have faced issues when not correctly adopting CSR-practices. Volkswagen is one of the better-known companies that suffered a lot of damage as a result of concealing the environmental damage Volkswagen cars are expelling. The Washington Post reported in 2017 that this scandal resulted in a $4.3 billion fine for the company.
The novel contribution of this research is to create a model that can be used to investigate the optimal facility location which does not harm the environment, and furthermore brings value to society. To address this issue, the following research question has been formulated:
Research Question: Regarding corporate social responsibility, what is the optimal facility location? While previous work in this field is mostly focused on minimizing the cost or maximizing the profit associated with the location decision, this thesis tries to include all possible decision making criteria, based on the ideas of corporate social responsibility. First, all possible decision making criteria will be identified. Second, the appropriate decision making criteria will be translated into parameters that can be used in a mathematical model. Finally, the model will be created and solved in order to find the optimal facility location. When the optimal facility location is established, a sensitivity analysis with respect to the key parameters will be performed, to understand what influence certain parameters had on the decision variables. This sensitivity analysis should give answer to the first sub question:
- How do changes in key parameters affect the capacity optimum and the location choice?
By answering this question we are able to understand what effects changes in parameters such as a government subsidy level would have on the location choice and optimal capacity level. The other sub question is related to finding the optimal production quantity at a location:
- What is the capacity optimum per facility?
3 2. Literature review
This research is combining two main research areas. The first one is corporate social responsibility, the second one the facility location problem. This literature review starts with exploring the main ideas behind corporate social responsibility. Afterwards, the facility location problem including its objectives, variations and methodologies are identified. In the last part of the literature review, a list of decision making criteria is provided.
2.1. Corporate social responsibility
Historically, companies tried mainly to maximize their profit. However, companies began to realize that profit maximization would not lead to long term survival. This way of sustainable thinking has led to the current concept of Corporate Social Responsibility (CSR) (Mir & Shah, 2018)), in a review, based on 588 journal articles and 102 books, Aguinis & Glavas (2012) defined corporate social responsibility as: “context-specific organizational actions and policies that take into account stakeholders’ expectations and the triple bottom line of economic, social, and environmental performance.”
While in the past, social responsibility and sustainability was oriented towards the environmental aspect, in recent years its scope now also includes the economic and social aspects (Mota et al. 2015). Recently, companies are trying to implement more corporate social responsibility practices. On the one hand, they are forced by government regulations (Delmas & Toffel, 2004). While on the other hand, customers are nowadays more socially conscious.Wu et al. (2016) stated that 88 percent of consumers think companies should try to achieve their business goals while not harming the environment or society. Additionally, Delmas & Toffel (2004) enumerate different stakeholders that can leverage the adoption of environmental practices, including governments, regulators,
customers, competitors, community and environmental interest groups and industry associations.
On individual level, CSR practices mainly consist of someone making an ethically correct decision. On business level, these practices are of a larger context, like product safety or fair labour practices (Ferrell et al., 2013). Different managerial systems exist to help ensure things like product quality (ISO 9000). These systems also exist for environmental (ISO 14000) and social responsibility (social accountability 8000). The adoption of CSR practices can lead to different competitive advantages. Porter & Kramer (2006) report that the advantages will mainly consist of an increase in the
4 product can expect higher sales. However, the production of a “green” product will lead to higher production costs. Mir & Shah (2018) found a positive association between CSR adoption and the long term profitability while studying the consumer goods industry of India. Kleindorfer (2005) implicates that social and environmental practices can, besides profitability, also lead to an improvement in internal processes.
A negative trend since the 2000’s in the communication related to CSR-practices is described in Jaworska (2018). Jaworska studied 294 CSR reports from companies in the oil sector. In the mid 2000’s, these companies agreed on the idea that oil companies were co-responsible for climate change and other negative consequences of their work, and should adopt CSR-practices to prevent harm to the environment. In recent years the oil-companies explained changes in climate as something inevitable, not caused by the oil industry. Jaworska concludes that oil-companies do not really care about the CSR-practices they actually adopt, but more about the way they report their CSR-practices to the public in order to gain good-will.
2.1.1 Environment & Co2 emission
One of the components of the Triple Bottom Line is the environment. Environmental sustainability implies economic growth without environmental deterioration (Isil & Hernke, 2017). Economic & technical development in the past centuries has led to global problems regarding the environment, as Banerjee (2003) describes: global warming, ozone depletion, loss of biodiversity, soil erosion, air and water pollution are irreversible effects of human development. Global warming (also referred to as the “Greenhouse effect”) is observed as a more long-term problem, as global warming will not result in large disasters in the upcoming decades. However, Wang & Choi (2015) predict boosted sea levels and the increased likelihood of extreme storms if the current Carbon dioxide dioxide (Co2) concentration does not drastically change. Sathiendrakumar (2003) supports this idea with the statement: “Estimates suggest that a 50 cm rise in sea level by 2100, would place approximately 92 million people worldwide at risk of being flooded “. Co2 is the main gas responsible for the
Greenhouse effect, as it accounts for sixty percent of the greenhouse effect caused by mankind (Sathiendrakumar, 2003).
5 2.1.2 Social parameters
Besides environmental sustainability, CSR practices within companies are focused on the social utility, resulting in welfare for the community. It is related to fair operating practices, solving problems correctly with consumers and community involvement & development (Anvari, 2017). Gauthier (2005) divides the social factors into two categories: internal and external. The internal factors are based on the business policies, integrated into the core values of the company. These internal factors will not differ between possible facility locations as business policies will not be changed at different facility locations. External factors are different among the stakeholders of the company. Employees benefit from safety, access to medical care & education, as listed by
Kleindorfer (2005), Jorgensen (2008) and Hutchins (2008). The main incentive for customers is demand satisfaction, as unfulfilled demand may be of harm to the customer (Anvari, 2017, Neumüller et al, 2015).
Where transportation cost, labour cost or even environmental cost (usually measured in costs for cleaning contaminated area or removing polluting gasses) can be expressed in money, measuring the social value might be somewhat problematic. Anvari (2017) lists all identified social parameters (access to education, job equity etc.), and ranks the values for each parameter. This results in a social utility value for each potential facility location. Badri (1999) uses an analytical hierarchy process to make it possible to give values to the arbitrary social parameters.
Clarke & Islam (2003) used a more macro-economic way of estimating social utility resulting in social welfare. They calculate the expected change in the Gross Domestic Product (GDP) to estimate the increase (or decrease) in social welfare. Cohen et al. (2016) use the suppliers profit plus the
consumer surplus minus the government expenditures as components for measuring social welfare. 2.2. Facility location problems
The facility location decision is a costly decision to companies, and the decision will have a long-term impact. The decision is, because of the impact, hard to reverse (Snyder, 2006). Owen (1998)
specified the facility location decision as a “critical aspect of strategic planning for a broad spectrum of public and private firms.”
6 important early work regarding the facility location problem theory (Tellier & Vertefeuille, 1995). Weber identified three factors that would be the most important for the location decision: transportation cost, labour cost and agglomeration forces. Weber tried to minimize the costs associated with those factors.
Melo et al. (2009) described the general facility location problem as a set of customers in a specific area, and a related set of possible facility locations to serve the demands of those specific
customers. The company tries to minimize the distance, time or cost between customers and facilities. This makes it possible for the company to select the facility or facilities that should be opened to serve the customers.
In addition to optimizing the general facility location mentioned above, maximizing profit is the second-most used objective. Melo et al. (2009), mentioned that some companies make use of multiple performance measures when estimating a new facility location. Farahani et al. (2010) suggests some possibilities when using multiple performance measures, such as minimizing the number of located facilities, maximizing responsiveness or maximizing the service level.
2.2.1. Facility location variants
7 Most of the Facility Location Problems assume a single product, or single commodity (Nezhad et al. 2012). However, it is also possible to make use of multiple products in the Facility location problem. Canel & Khumawala (2001) describes that this is rarely used.
Another dissimilarity that can be observed within the Facility Location Problem is the difference in stochastic and deterministic models. Snyder (2006) appraises the use of stochastic models that include uncertainties in the forecast of demand or costs. Stochastic models include randomness for certain parameters, and make the scenario more realistic.
2.2.2. Facility location methodologies
When searching for the optimal facility location, different methodologies for estimating this optimal location can be used. Farahani et al. (2010) describe the two main options as exact and heuristic approaches. Heuristic approaches should be applied when an exact method would be too time consuming to calculate. Heurististic approaches try to approach the optimal solution in complex models, making use of somewhat educated guesses. Within these two main approaches, a large variety exists in estimating the optimal location. Jia et al. (2007b) argues that exact methods should only be applied in relative small or medium sized models.. Farahani et al. (2010) give multiple examples of variants within the heuristic approaches. Some papers are using weighted-average or fuzzy-set theory rankings to compare the best alternative with the second best in order to find a global optimum.
2.3. Decision making criteria
Different criteria can be used to establish the facility location decision. Each company can possibly use different criteria, regarding the business situation. Literature has identified multiple criteria that can be used to estimate the facility location. These criteria can be translated into parameters, used for a mathematical model.
Regarding the literature, several parameters can be identified that are used in the facility location problem. The parameters are divided among the parts of the Triple Bottom Line. For each
8 Economic parameters Identified in literature by: Explanation
Transportation costs
Melo (2009), MacCarthy (2003), Anvari (2017)
Availability of transport facilities, costs for transporting final goods
Labour costs
Kinkel (2012), MacCarthy (2003),
Anvari (2017) Wage rates, availability of skilled labour Tax costs Hoffmann (1994), Kinkel (2012) Tax costs associated with the local legislation Interest costs Hoffmann (1994), Kinkel (2012) Interest costs observed at the location Energy costs MacCarthy (2003), Anvari (2017) Energy costs (fuel, electricity etc.)
Acquisition costs Anvari (2017), MacCarthy (2003), Costs associated with the set-up of the location Proximity to customers
Melo (2009), Kinkel (2012), MacCarthy (2003), Mota (2015)
Distance to (possible) customers of the company
Customers wealth Kinkel (2012), MacCarthy (2003),
Average wealth and spending habits of customers
Proximity to suppliers
Melo (2009), Kinkel (2012),
MacCarthy (2003), Mota (2015) Distance to (possible) suppliers of the company Quality of suppliers Kinkel (2012), MacCarthy (2003),
Quality of products or services from (possible) suppliers
Proximity to current
facility locations Mota (2015), Kinkel (2012)
Distance to current facility locations of the company
Environmental
parameters Identified in literature by: Explanation CO2 emission Cohen (2016), Hutchins (2008)
Carbon dioxide emission expected at the facility location
Quality of environment MacCarthy (2003) Current quality of environment observed Electric Vehicle
Adoptation Avci (2014), Cohen (2016) Use of electric transport Pollution to area Kleindorfer (2005), Hutchins (2008)
Toxic pollution (due to the facility) expected at the location.
Solid waste output Kleindorfer (2005), Hutchins (2008)
Output of solid waste (unwanted or unusable materials).
Social Parameters Identified in literature by: Explanation
Human rights level Jorgensen (2008)
Human rights level, which indicates whether child labour, compulsory labour etc. exists in the country
Access to education
Hoffmann (1994), Anvari (2017), MacCarthy (2003), Hutchins (2008)
Opportunities to attend schools, universities etc.
Access to medical care
Hoffmann (1994), Anvari (2017), MacCarthy (2003), Hutchins (2008),
Jorgensen (2008) Level of medical care observed at the location Employees social
security
Jorgensen (2008), MacCarthy (2003), Anvari (2017)
Psychological safety of employees, including minimum wages and employment protection Equity level MacCarthy (2003), Hutchins (2008) Men/women equity, poverty levels
Employees physical safety
Kleindorfer (2005), Jorgensen
(2008), Hutchins (2008) Workers’ safety at the facility location Crime rate Hoffmann (1994), MacCarthy (2003) Crime rate observed at the area
Philanthropy Hutchins (2008), Jorgensen (2008)
Companies’ efforts to improve the social welfare in the area, including development of schools, hospitals or charity donations.
9 Table 1 provides us with a concise overview of relevant parameters that are used in literature when measuring CSR-related factors. The information from table 1 is important since we introduce novel CSR-related factors into the model description in the next chapter. Table 1 can be used as a guideline in estimating parameters for a to-be-created model. The literature review also pointed out the CSR-practices currently adopted by firms. Furthermore, the literature review provides an overview of the methodologies, objectives and variants within the literature in the field of the facility location problem. Differences observed in literature regarding the facility location problem can be summarized as follows:
Discrete versus Continuous facility location problems
Capacitated (CFLP) versus Uncapacitated (UFLP) facility location problems Stochastic versus Deterministic models
10 3. Model description
As the literature review describes, there is a large variety in the models existing in the facility location problem. The models range from single to commodity models, single to multi-objective, and differ between deterministic and stochastic models. This model will be based on a single commodity model, as we will only use one product. The objective will be a single objective, based on maximizing the profit. Because we won’t include randomisationin the model, the model will be a deterministic one. For finding the optimal solution, Excel’s solver gives us the possibility to find an exact optimum. This section describes the assumptions that come with the model.
Furthermore, the parameters and decision variables are formulated. The last part of this section formulates the final objective function.
3.1. Assumptions
- Facility location options are specified beforehand. - Energy is sufficiently available.
- Demand is always fulfilling, so that the demand for a product equals the production quantity. In other words: demand and supply is always at equilibrium.
- Transportation will be done with trucks only. - Trucks will always be driving a full truckload. 3.2. Parameters
For the parameters listed below, refers to the possible facility locations with and refers to the customers with .
- Economical costs (€) - Environmental costs (€) - Social surplus (€)
- Distance to customer j (km)
- Cost of transporting one product one kilometre (€) - Demand from customer j (units)
- Labour costs (€)
- Fixed energy usage (MWh)
11 - Average holding cost per unit (€)
- Warehouse fixed carbon dioxide emission output (kg)
- Warehouse variable carbon dioxide emission output per unit (kg per unit) - Carbon dioxide emission rate per kilometre for a truck (kg per km) - Amount of units fitting in one truckload
- Carbon dioxide emission rate per MWh (kg) - Carbon dioxide disposal costs per kg (€) - Marginal unit cost (€)
- Government subsidy level per product (€)
- Price elasticity factor for demand (€ decrease per production quantity increase) - Effective price paid by consumers (€)
- Government expenditures (€) - Suppliers profit (€)
- Consumers surplus (€) - Selling price (€) 3.3. Decision variables
- Production quantity (units)
- Facility location to be opened or not (dummy) 3.4. Objective function
3.4.1. Facility location ( )
For a pre-specified amount of facility locations , the model tries to observe which facility location to open and which location to close. The possible facility locations are specified beforehand. The facility location will take a value of 1 if it will be opened, and a value of 0 if it remains closed, so that: { } 1 if facility i is opened, 0 otherwise
For each facility location, the yearly total profit will be calculated. The model tries to maximize the profit for every facility location .
3.4.2. Triple Bottom Line
12 way of modelling is also used by Anvari et al. (2017), which differs from in the paper of Anvari, social welfare is calculated according to a ranked-weight scale. In this model, the costs are split into economical costs and environmental costs. Furthermore, social welfare (or social surplus) is included. More explanation about the distribution of the total costs is given hereafter.
A standard, yearly, profit function is made up of the production quantity ( ) times the selling price ( ), minus the total yearly costs ( ). This is leading to the objective function of:
(1)
{ } 1 if facility i is opened, 0 otherwise
The yearly total costs roughly consist of three parts, as described in the theoretical background: 1. The traditional (economic) costs like transportation costs, setup costs and labour costs.
2. The environmental costs associated with the facility location.
3. The social surplus the location brings to the local community. In other words: the increase in welfare caused by the facility location.
The yearly total costs ( ) can be divided among the three parts of the triple bottom line, are the traditional (economic) costs. i the environmental costs and is the social surplus (the increase in welfare).
(2)
3.4.3. Economic costs ( )
13 ∑
(3)
Note that for both the set up costs ( ) and the labour costs ( ) a fixed value will be used. While set up costs are usually measured as a one-time cost for the location, it is possible to measure these costs on a yearly base by including depreciation. Because the variables are fixed, they do not depend on the decision variable . The energy usage is made up from the fixed energy usage (the usage that yields zero production quantity) and the variable energy usage per produced unit . When the energy usage in MWh is computed, we can multiply the energy usage with the price of one MWh of energy ( ) to finally get the total costs for energy.
3.4.4. Environmental cost ( )
As stated in the theoretical background of this thesis, carbon dioxide (CO2) emission is the main
source of environmental costs. The carbon dioxide emission is caused by truck emission due to transportation, emission from the facility itself and the emission due to energy usage.
Hua et al. (2011) made up an estimation of the carbon dioxide emission related to holding products at the facility location. It is based on the fixed carbon dioxide emission ( ) for an empty warehouse plus the variable carbon dioxide emission factor based on the average inventory ( )
Tsao et al. (2018) formulated a way of computing the carbon dioxide emission due to transporting products to customers using trucks. Combined with the formula from Tompkins et al. (2010), the carbon dioxide emission from transport can be measured by ∑ . is the amount of products that fits within one truck, is the carbon dioxide emission rate per kilometre for a truck.
is an element in the computation of the carbon dioxide emission output from transport. Because represents the amount of units fitting within one truckload, dividing with gives the number of instances a truck has to drive to a single customer. Multiplying with will eventually give the total number of kilometres a truck will drive to a certain customer. The in front of the formula ∑ ) is necessary because the truck also have to drive back from the customer to the facility.
14 .
To calculate the total costs related to carbon dioxide emission, some federal agencies use estimates of the disposal costs per kg, which can be used in measurement. These are the disposal costs, denoted as .
The total environmental cost is given by the formula:
(∑ ) (4) 3.4.5. Social Parameters ( )
Cohen et al. (2016) tried to measure the social welfare in a somewhat macro-economic way. In this case we are making use of a general deterministic function. The government sets the subsidy level, while the company determines the price and the production quantity for a product. Determining
in a system can be explained by:
(5)
is the consumer surplus, the government expenditures, and the expected supplier’s profit. The suppliers profit will be equal to:
(6)
The price ( is calculated by multiplying the price elasticity factor of the product times the production quantity ( ), and subtract it from the price that yields zero demand (
(7)
In words: the profit will be selling price ( ) times the production quantity ( minus the marginal
unit cost ( ) times the production quantity ( ).
The government expenditures ( ) will be based on the production quantity times the subsidy level per product:
15 The Consumer Surplus is the difference between the price that consumers are willing to pay ( ), and the price they are actually paying ( ).
(9)
In case of a linear demand curve (which, according to formula (7) is the case), The consumer surplus can be identified as the area beneath the demand curve above the market price, and can be
calculated by multiplying ½ times the production quantity times the difference between the actual effective price paid by consumers and the price that equals zero demand (Buts & Jegers (2013)). The formula used in Cohen et al. (2016) considers a demand function depending on the effective price paid by consumers ( ). The effective price paid by consumers ( ) can be calculated as follows:
(10)
Whereas is the subsidy level per product, and the price.
3.4.6. Final objective function.
Recall from equation 1 that the original objective function was formulated as
. After all variables used in the model are determined, it is possible to substitute those variables into equation 1, resulting in the final objective function of:
16 3.5. Constraints
To give a clear overview, the constraints are divided among the constraints for assumptions, decision variables and dependent variables. Below each assumption, a clarification of the assumption is given between brackets.
Constraints for the assumptions:
- ∑ (12)
(Energy is sufficiently available) - ∑ (13)
(Demand is always fulfilling) Constraints on the decision variables: - (14)
(Nonnegative production quantity) - , (15)
- , , , , , , , , , , , (16)
- , (17)
(Constraints 15, 16 and 17: Non-negativity for input variables) Constraints on the dependent variables (obtained by using the independent variables in (1)-(10)): - (18)
- (19)
- (20)
- (21)
17 (Nonnegative effective price paid by consumers, resulting in a selling price that should be larger than the subsidy level)
- (23) (Nonnegative supplier’s profit, resulting in a selling price that should be larger than the marginal costs)
- (24)
(Nonnegative selling price, that requires the selling price to be larger than the price elasticity factor times the production quantity)
- (25)
(Nonnegative government expenditures)
- ( ) ( ) (26)
(Nonnegative Consumer Surplus requires the maximum willingness to pay to be larger than the effective price paid by consumers)
18 4. Data description
4.1. Hypothetical case description
This thesis attempts to find the optimal facility location to place a new facility that should serve the existing customers. To find this optimal location, a hypothetical dataset will be created that makes it possible to solve the formulated model from the previous section. First, some assumptions will be made for the pre-specified possible facility locations and the customers that will be served from those facility locations. The hypothetical setting that is created to solve the model is a hypothetical setting within the Netherlands. There will be five possible facility locations (all of them located within the Netherlands). These locations are divided across the country. The possible facility locations are given in the table below:
Facility location #1 Groningen
Facility location #2 Deventer
Facility location #3 Amsterdam
Facility location #4 Rotterdam
Facility location #5 Eindhoven
Table 2: overview of the pre-specified possible facility locations.
Besides the facility locations, the model needs customers that should be served from one of those facility locations. For the customer’s locations, we also use cities within the Netherlands. In the created setting, we will use ten customers that should be served. As the factories are distributed across the country, this will be done in the same way with the customers.
Customer #1 Hoorn Customer #2 Leiden Customer #3 Breda Customer #4 Middelburg Customer #5 Lelystad Customer #6 Roermond Customer #7 Zwolle Customer #8 Nijmegen Customer #9 Emmen Customer #10 Leeuwarden
Table 3: overview of the customers locations
Because the model only uses trucks for transportation, Google Maps will be used to calculate
19 indicates a possible location to place the facility.
indicates the location of a customer.
20 Each facility location has a given distance to each customer. The city centre is used when measuring distances between cities. Furthermore we take the shortest distance between city centres instead of the shortest travel time between city centres. The distance table containing the calculated distances between each customer and location can be found in the appendix.
The first decision variable in the model is the facility location to be opened or not ( ). The other decision variable is the production quantity ( ). As mentioned in the previous section, the model assumes that the demand of the customers will always be equal to the production quantity.
However, the demand should obviously be divided among the customers. The distribution key of the production quantity over the customers can be done in different ways. The production quantity could be randomly distributed among the customers, or a predetermined percentage of the
production quantity could go to each customer. In this case, when using 10 customers in the setting, we will equally divide the production quantity (and thus the demand) among the customers. So each customer is demanding ten percent of the production quantity. The reason to distribute the demand equally among the customers is to prevent randomness affecting the results. When a large customer is location very close to a specific facility location, the optimal location will be biased towards that specific location, only because we randomly assigned a large proportion of the demand to that customer.
4.2. Setting of parameters
Besides the distances between possible facility locations and customers, some other values for the used parameters should be established. The value of these parameters will be established in this section. Whenever it’s possible, the values will be based on real-life examples, to make the model as realistic as possible.
Both the set-up and labour costs (respectively and ) are fixed and therefore they can take any value. For the setup costs we estimate a value of €3.500.000 and for labour costs we use the value of €6.000.000. For the holding rate ( ), used to compute the holding costs, we use €0,20 per product. The price of one MWh of energy ( ) usage in the Netherlands (for companies using large amounts of energy on a yearly base) is around €70 per MWh. Furthermore we assume the fixed energy usage ( ) to be 170MWh, and the variable energy usage per produced unit ( ) to be 0,006 MWh per product. The selling price of the product is equal to . For we use €10. This implies that when the production quantity ( ) is zero, the selling price will be equal to €10. The price elasticity factor will be set to 0,0001. This means that for every 10.000 production increase of
21 product. The marginal unit cost ( ) will be equal to 70 percent of the selling price (so for is zero,
will be €7).
For the amount of units fitting in one truckload ( ) we assume we will make use of a standard truck size that can fit a maximum of 300 products in its truck. We assume a truck will cost €2,12 per kilometre. This is based on a report published by the Canadian government (see references), estimating the per kilometre cost of $2,47 (equal to €2,12) per kilometre. The cost of transporting one product one kilometre ( ) will therefore be equal to €2,12 divided by 300 is €0,007. For the costs and emission rates related to carbon dioxide, information is widely available due to
government’s efforts to reduce the carbon dioxide emission. Cohen et al. (2016) estimates (based on the findings of Arar (2010)) the carbon dioxide emission rate per MWh of energy usage ( at 755kg of carbon dioxide emission per MWh. The carbon dioxide emission costs are estimated to be around €35 per ton. This is equal to 0,035€ per kg. The carbon dioxide emission rate per kilometre for a truck is equal to 0,5kg per kilometre. For the estimation of the carbon dioxide emission due to the warehouse, we use the estimations as they are in Hua et al. (2009). In the paper of Hua et al., the warehouse fixed carbon dioxide emission output ) is equal to zero, while the warehouse
variable carbon dioxide emission output per unit ( ) will be one kg per unit. A concise overview of the used setting is given in appendix B.
4.3. Scenarios
In the described setting (with five possible facility locations and ten customers), two different scenario’s will be examined. Recall that total cost consists of three components:
In Scenario 1, the environmental costs and the social welfare will be neglected, so that the objective function is only to minimize the economic costs related to the facility location.
In Scenario 2, the environmental costs and the social welfare will be included in the model.
After collecting the results, it is possible to compare both scenarios. After comparing we are able to understand whether companies will make a different choice in their facility location when we exclude (scenario 1) or include (scenario 2) practices related to corporate social responsibility. For the production quantity ( ), we will study its effect on the total yearly profit by using values that range between 5.000 and 70.000 for production quantity . (70.000 is the quantity where
23 5. Results and discussion
Scenario 1 is the scenario where the environmental costs and the social welfare will be neglected, and therefore only the economic costs will be taken into account. The results are visualized in figure 2. The graph shows the five cities where the facility could be places, with a different color for each city. The Y-axis represents the total profit; the X-axis represents the production quantity.
Figure 2: Overview of total profit per facility location in scenario 1
For scenario 1, the graphs indicate that Amsterdam will be the optimal location for placing the facility. The difference in the profit per location can be fully explained on the basis of the transport costs, being a part of the total cost. This can be explained by Amsterdam being located at the shortest distance to its customers, the transport cost for Amsterdam will always be lower compared to other cities. With its isolated location within the Netherlands, Groningen has the greatest distance to the customers. Increasing the production quantity will enlarge the gap in total profit between cities. This is due to the fact that, when increasing the production quantity, the transport cost will rise with a higher factor in Groningen than it will in Amsterdam, while the revenues for both cities will remain at the same level. The foundation of this lies in the assumption that demand is equally divided among customers. Due to this assumption, Groningen will never be able to close the gap in transport costs with Amsterdam. A Random distribution of customers’ demand might change this result. When, for instance, a large customer is located close to Groningen (which at the same time implies that this large customer is located at a large distance to most other cities), results would be more in favour of Groningen.
24
Figure 3: Overview of total profit per facility location in scenario 2
For Scenario 2, the results are the same when looking at the best possible facility location; these can be observed in Figure 3. Amsterdam remains the best location, while Groningen is the worst location to place the facility. A difference between Figure 2 and Figure 3 is the magnitude of the graphs. While in Figure 2, the graphs are closer to each other than they are in Figure 3. This implies that the best location of Scenario 1 (Amsterdam) becomes even better in Scenario 2, while the worst location of Scenario 1 (Groningen) becomes relatively worse in Scenario 2. The differences in magnitudes of the graphs between scenario 1 and scenario 2 can be explained by the carbon dioxide emission costs that are added in scenario 2. Groningen is the location that has the longest distance to customers. When adding carbon dioxide emission costs on trucks to the scenario, Groningen (which has already the largest transport costs) will be penalised even more for its location in the country. These extra costs are resulting in relatively large cost for carbon dioxide emission, increasing the total cost for the location.
A notable but not very surprising observation is that Amsterdam, for every value of the production quantity , will be the best location for the facility placement. The reason for this is that apart from the distance to customers and the corresponding transport costs and carbon dioxide emission costs, the values for the other parameters were the same. This is the reason that Amsterdam, no matter what production quantity we will be producing, will always be the best location. Factors in the model that could be different between cities are energy prices, wage rates or local subsidies. The exact
25 optimal production quantity for a given location can be established with the use of Excel’s Solver. Solver is an add-in that will help you find a minimum or a maximum for a given cell, by changing other variable cells of your choice. The optimal levels of production quantity for all five possible locations can be found in table 4. The cities in the table are ranked from most optimal to least optimal location.
Scenario 1 Scenario 2
Amsterdam (#1) 43.389 units 53.052 units
Deventer (#2) 43.088 units 52.670 units
Rotterdam (#3) 42.969 units 52.518 units
Eindhoven (#4) 42.510 units 51.934 units
Groningen (#5) 40.942 units 49.943 units
Table 4: Capacity optimum for every single facility location in scenario 1 and 2.
Table 4 indicates that (for both scenario 1 and 2) cities with a relative high value for the total profit (and thus a high ranking in table 4) will have a larger optimal capacity than cities with a relative low value for the total profit (and thus a low ranking in table). For the current optimal location
26 made that show the total profit for each of the scenario’s (Figure 3).
Figure 3: Overview of total profit between scenario 1 and scenario 2 (Location: Amsterdam).
Figure 3 indicates that for lower levels of the production quantity, scenario 1 yields a higher total profit. On the contrary, for higher levels of the production quantity, scenario 2 yields a higher total profit. The indifference point between both scenarios is at a production quantity of 20453. This indicates that below the production quantity value of 20453, excluding the CSR-related factors when estimating the total profit would leave companies with the highest profit. Above the production quantity value of 20453, including the CSR-related factors when estimating the total profit will leave companies with the highest profit. For lower production quantities in scenario 2, costs arise related to carbon dioxide emission due to the fixed energy usage. As these costs do not appear in scenario 1, this scenario will be more profitable at lower levels of production. When production increases, scenario 2 becomes more profitable due to an increase in the social welfare. This increase in social welfare outgrows the increase in carbon dioxide emission costs related to a rise in capacity.
In the next section, the effect of changes in key parameters on the total yearly profit will be studied, and used to compare both scenario’s for the current optimal location (Amsterdam). First, the key parameters is identified. Second, a sensitivity analysis is performed to study the effects on the optimal production quantity when changing the value of the key parameters.
27 The most important parameters affecting the total yearly profit are the government subsidy level ( ), and the parameters related to carbon dioxide emission. For the carbon dioxide emission, the emission rates related to trucks, energy and warehouse are standardized factors. In other words; we are not able to change the emission rates on trucks, as they will always stay at the same level for a single truck. Therefore we will study the effect of changes in the carbon dioxide disposal costs per kg ( To study the effect of changes in the government subsidy level, we should first add a small addition to the model. In the current model, the subsidy level is only affecting the government expenditures ( ). When is increasing, so is . A higher value for the government
expenditures will result in a lower social welfare level ( .), which will finally result in higher total costs and a lower total profit for the location. However, in a more realistic situation, a change in subsidy level would influence the selling price of a product. If the subsidy level would increase, a company can increase the selling price of the product with the same amount, because the effective price paid by consumers ( ) would remain the same. If the government is increasing the subsidy level, the most common scenario is that both the consumer and the supplier would make a profit out of it. In our case, we will assume that for every €1 increase in the subsidy level, 30 percent of the subsidy would go to the supplier. This will result in a €0,30 price increase, the effective price paid by consumers ( ), on the other hand, will drop with €0,70. The values for all independent variables will remain the same as described in section 4.2.
28 Gap
carbon dioxide emission costs per
kg total average profit (€) Gap
- 0.023 151398 0,661% 13,0% 0.026 150404 0,665% 11,5% 0.029 149410 0,670% 10,3% 0.032 148416 0,674% 9,38% 0.035 147422 0,679% 8,57% 0.038 146428 0,683% 7,89% 0.041 145434 0,688% 7,32% 0.044 144440 0,693% 6,82% 0.047 143446 -
Table 4: sensitivity analysis on the carbon dioxide emission costs per kg
Table 5 represents the sensitivity analysis on the subsidy level. For this instance, a new optimal capacity of 56410, based on the Amsterdam location has been used. The results appear to be somewhat paradoxical. An increase in the subsidy level results in a lower total profit. However, when we analyse the formula . When we increase the subsidy level , it will result in a 1:1 increase in the government expenditures . On the other hand does not increase with a 1:1 ratio. In our case, 30 percent of the subsidy goes to the supplier, and is reflected in the increase in selling price , which affects . 70 percent of the subsidy goes to the customer, reflected in a lower effective price paid by consumers . Because
and (with ), a €1 increase in subsidy level will increase with a value less than €1. Therefore the total profit will decrease when the subsidy level increases. Lower values for the marginal unit cost will level the total profit upwards. Cohen (2016) confirms the idea that consumer subsidies coordinate the supply chain in terms of price and
quantities, which, in our hypothetical setting played a big role. However, a significant difference with the article from Cohen (2016) is that an increase in government subsidies would boost the local community, which is not the case in this thesis.
Gap subsidy level (€) total profit (€) Gap
- 2 392624 2,39% 12,5% 2.25 383457 2,45% 11,1% 2.5 374290 2,51% 10,0% 2.75 365124 2,58% 9,09% 3 355957 2,64% 8,33% 3.25 346791 2,72% 7,69% 3.5 337624 2,79% 7,14% 3.75 328457 2,87% 6,66% 4 319291 -
29 6. Conclusion & Limitations
This thesis has provided a method to include Corporate Social Responsibility in the facility location decision. A hypothetical setting has been created that gives a numerical example for a real life application of the formulated model. This thesis proves the hypothesised benefit of including environmental and social factors. This study introduced new methods for combining traditionally less quantifiable factors into mathematical models of facility locations problem and showed positive results, creating a stepping stone for introducing less quantifiable factors into other mathematically solved problems in business.
The objective function (formula 1) maximizes the total profit. In general it can be said that taking into account CSR-related factors will more profitable than using the classical method if the value for the out scales the value for the , which in our example was the case. For lower levels of production quantity , excluding CSR-related factors will lead to a higher profit. Locations with an unfavourable location to customers are disadvantaged twice when the carbon dioxide emission costs are taken into account. An addition in the model could lie in the assumption that transport is only executed by trucks. Other, less polluting transport methods like electric vehicles or trains could be added in order to study the effect on the carbon dioxide emission. The hypothetical case with facility locations and customers within the Netherlands might result in an underestimation of the transport costs and corresponding carbon dioxide emissions when applying it in other countries. While the Netherlands is a relative small and highly populated country, other countries in Europe are certainly not as dense, which might result in higher transport & carbon dioxide emission costs. Additional research with data from other countries should be used to verify the correctness of the model.
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34 8. Appendix
Appendix A: Distance metrics for customers to supplier.
35 Eindhoven - Hoorn 167 km Eindhoven - Leiden 134 km Eindhoven - Breda 61 km Eindhoven - Middelburg 160 km Eindhoven - Lelystad 150 km Eindhoven - Roermond 51 km Eindhoven - Zwolle 147 km Eindhoven - Nijmegen 66 km Eindhoven - Emmen 222 km Eindhoven - Leeuwarden 239 km
Appendix B: overview of parameter settings used in the scenario comparison
