Green Facility Location

Abstract

Transportation is one of the main contributing factors of global carbon emissions, and thus, when dealing with facility location models in a distribution context, transportation emissions may be substantially higher than the emissions due to production or storage. Because facility location models define the configuration of deliveries, green location models become an important alternative to reduce CO2 emissions in logistics.

This chapter presents a variety of green location models that include the estimation of carbon emissions. It also provides basic guidelines in understanding these models in comparison with cost minimization models.

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1 Introduction

Transportation emissions comprise a large share of the world’s overall emissions, and freight transport is responsible for a relatively large share of these emissions. Transportation emissions can be reduced by making different choices in logistics, such as in changing the mode of transport or changing routing or loading of the vehicles in the network (see Chap. 7 by Blanco and Sheffi (2017) for more on green logistics). These logistics choices are influenced significantly by the inventory policies that have been deployed in a company (see Chap. 8 by Marklund and Berling (2017) for more on green inventory management). For instance, allowing for a more carbon-friendly slow mode of transportation would typically require increasing or repositioning the inventory in the supply network.

Apart from logistics choices and inventory policies, the transportation performance in terms of costs and emissions is strongly determined by the design of the network. In distribution networks, this refers in particular to the location of distribution centers or other transport hubs such as factories or cross-docks. In this chapter, we will address the issue of locating such a transport hub .

The logistics problem that determines the configuration of a company’s delivery of goods is the facility location problem. The facility location problem is to locate a set of facilities (e.g., factories, cross-docks, distribution centers) in a physical space, such that all the demands of the customers are assigned to at least one facility and the total transport cost is minimized. While the literature of facility location is well-established and large in size, in this chapter, we focus on a variant of this problem that specifically includes the transport carbon emissions in the formulation. We refer to location problems that aim at minimizing transportation CO₂ emissions as Green Facility Location problems.

By limiting the scope to emissions from mobile sources (i.e., transport), we obviously do not consider emissions from stationary sources that could be influenced by the location decision. Without being exhaustive, these may include:

• Emissions at the distribution center . These relate to the energy usage of the distribution center. In most cases this would be electricity for light and/or automation, and for refrigeration. Potentially economies of scale could exist that would be related to the design of the network. Industry data suggest that in most distribution networks, the emissions at the distribution center are less than 10 % of the total logistics-related emissions

• Availability of local energy sources . In particular for energy-intensive operations, the availability of renewable local energy may significantly impact the supply chain emissions. For instance, locating an aluminum plant in an area where geothermal electricity is available could reduce a supply chain’s overall carbon emissions while still increasing its transport emissions.

Excluding the emissions from stationary sources from the models discussed in this chapter implies that effectively we are limiting ourselves to distribution networks and the location choice of distribution centers and cross-docks. However, in our discussion we use the more general term “facility.”

Usually companies designing their distribution channels select the locations of warehouses and distribution centers with the objective to serve the demand of the customers while minimizing distance (or transport costs). In this chapter, we review some models that include the transportation CO₂ emissions in the uncapacitated facility location. We then discuss the solutions we may obtain when the number of facilities to be located is fixed by using the p-Median problem. We present discussions and managerial implications for the green facility location. We are interested in learning whether location decisions obtained by cost minimization are different from those obtained by the green facility location model.

1.1 Facility Location and Carbon Emissions

Typically, facility location decisions are made by considering the associated costs that include transportation (from the facilities to the customers) and the operation of the facility (production and storage). As discussed above, we may split the main sources of CO₂ emissions associated to the location of facilities in a similar way: emissions from mobile sources (transportation) and emissions from stationary sources (production, storage, and handling). Having more facilities reduce the CO₂ emissions from mobile sources due to the fact that the distance from the facility to the customer destinations decreases. Obviously, this increases emissions from stationary sources due to their larger number. Therefore, the challenge in green facility location is to define the proper number and position of the facilities that will serve a set of customers while minimizing the overall CO₂ emissions.

Many studies show that transportation and production may substantially contribute to CO₂ emissions. For example, the three main contributing sectors to emissions in the developed world are electricity production, energy-intensive manufacturing, and transportation (European Commission 2011). While production of electricity and energy-intensive manufacturing are considered within Scope 1 and 2 of the GHG inventory, transportation by service providers is considered within the Scope 3 emissions (see Chap. 3 by Boukherroub et al. (2017) for further detail). Scope 3 emissions often represent the largest source of GHG emissions and in some cases can account for up to 90 % of the total carbon impact (Carbon Trust 2013). In addition, when the facility location problem consists of locating distribution centers instead of manufacturing plants, typically the CO₂ emissions from mobile sources are much higher those of the stationary sources, as the latter then only include the emission at the distribution center. Storage and handling emissions are substantially smaller than transportation emissions, by a factor of 10 for some products (Cholette and Venkat 2009). Therefore, in this chapter, we will focus on studying the location of distribution centers with main emphasis on transportation carbon emissions.

Many practices exist in industry to reduce carbon emissions by implementing more efficient and sustainable practices into their logistics operations (e.g., Heineken Sustainability Report (2013), Groupe Danone (2014), MIT-EDF (2013)) However, very few have considered the location of distribution centers as an relevant alternative to reduce transportation CO₂ emissions. One of the exceptions may be Unilever, which increased the number of regional hubs and located these hubs closer to the customers (Unilever Press Release (2013)).

The location of facilities is critical to the efficient and effective operation of a supply chain; poorly placed plants can result in excessive costs and low service level no matter how well tactical decisions (e.g., vehicle routing, inventory management) are optimized (Daskin et al. 2005). In this chapter we demonstrate that facility location choice may significantly impact mobile CO₂ emissions in the supply chain. Note that the main drivers of transportation carbon emissions are distance, truck load (Greenhouse Gas Protocol Standard 2011), and the number of trips required to deliver demand to each customer. Changing the number and location of the facilities in the distribution network impacts all of these drivers.

1.2 Trade-Off Between Cost and Carbon Emissions in the Facility Location

Transportation costs (TC) in facility location problems typically take demand (w) and distance (d) into account. These costs are usually modeled as an objective function using the demand-weighted total distance ($\mathrm{T}\mathrm{C} = \alpha wd$), and assuming an α constant cost per distance per unit (Revelle et al. 2008). Notice that this formulation finds optimal solutions where the facilities are closer to regions with high demand. However, for minimizing transportation CO₂ emissions, good solutions may require a different analysis.

Transportation CO₂ emissions are affected by a variety of conditions related to the type of vehicle (e.g., engine power, torque, fuel type, aerodynamic drag coefficient) and the characteristics of the delivery operation (e.g., road, slope, vehicle speed, load) (Akçelik and Besley 2003). Due to the lack of detailed information about the delivery operation (specific slopes, speed, aerodynamics, etc.) during the decision-making process, companies typically use more aggregate activity-based methods to estimate CO₂ emissions (see Chap. 3 by Boukherroub et al. (2017) for more background on carbon footprinting). Two of the most common activity-based methods are the GHG Protocol and the methodology developed by the Network for Transport and Environment (NTM). Because the GHG Protocol methodology typically uses an emission factor that is independent of the type of vehicle or type of road (United States Environmental Protection Agency 2011) (GHG Protocol Calculation Tools 2011), a facility location model minimizing CO₂ emission based on the GHG protocol would provide optimal locations that are identical to cost-minimization model solutions, i.e., optimal locations tend to be closer to regions with high demand. However, this does not hold necessary when a more detailed approach like the NTM methodology is used.

The NTM methodology requires more detailed parameters: fuel consumption, distance travelled, and weight per shipment (NTM Road 2010). The fuel consumption is a function of the type of truck, the load factor, and the type of road. NTM uses the European Assessment and Reliability of Transport Emission Models and Inventory Systems’ database which developed a detailed emission model for all transport modes to provide consistent emission estimates at the national, international, and regional level (TRL 2010). The NTM estimation model is:

$E=l\left[d\left({f}^e+\left({f}^f-{f}^e\right)\frac{w}{W}\right)\right]$,

where

E total emissions in grams of CO₂

l constant emission factor (2621 g of CO₂/L)

f ^e fuel consumption of the empty vehicle (L/km)

f ^f fuel consumption of the fully loaded vehicle (L/km)

W truck capacity

Comparing transport cost and CO₂ emissions, notice that the effect of distance is linear in both expressions. However, demand and truck capacity drive the transport cost in a different way from driving the CO₂ emissions. Figure 9.1 shows the comparison of transport costs and CO₂ emissions for different demand levels. For the example we use a 14-t truck for urban road type and we set 100 demand units equivalent to 1 t.

Fig. 9.1

Transport costs and CO₂ emissions over different demand levels

Note that the growth in demand does not translate into a linear increase in CO₂ emissions, as it is in cost. For example, a demand of 20,000 units increases the cost up to 20 % while the increase in CO₂ is approximately of 5 %. The chart also shows that an increase in demand has an impact on CO₂ emissions mainly when this growth implies more trips.

Because of these differences in the transport cost and CO₂ emission structures, intuitively we may conclude that facility location models with one or the other objective function may have different optimal solutions. While cost-minimization models find optimal locations closer to high-demand nodes, CO₂ minimization models may also consider optimal locations closer to demand nodes where a larger number of trips are required to serve the customer’s demand. This characteristic of CO₂ minimization models may be observed in both the high-demand nodes and for restricted truck accessibility constraint in the nodes. Therefore, in facility location problems, solutions obtained by minimizing transportation cost are not necessarily equivalent to solutions obtained by minimizing transportation CO₂ emissions.

2 Green Facility Location Models

In this section we present some general facility location models that are commonly studied in the logistics literature, including both continuous and discrete models. We later discuss some extensions of these models that study CO₂ emissions in location decisions.

2.1 Traditional Facility Location Models

The facility location problem has a very long history. It was first introduced by Weber (1909) and a large number of extensions and applications can be found in the literature. For a basic explanation of the facility location problems we refer to (Daskin 2008) (Daskin et al. 2005) and for recent reviews we refer to (Melo et al. 2009) (Revelle et al. 2008). Typically, facility location problems are classified based on their solution space as continuous if the candidate locations can be located anywhere within the area or discrete if the candidate facilities are restricted to a finite set of locations (Daskin 2008). In addition, when continuous models assume that demands are distributed continuously across a service region, this approach is known as analytical location model .

The continuous and analytical approaches provide a general overview of the optimal locations, and are commonly used for researchers to provide guidelines or insights (Geofrion 1976). A variety of applications can be found in the literature related to extensions of location models, such as hub location problem (Saberi and Mahmassani 2013), freight transport network (Campbell 2013), and hub-and-spoke network design (Carlsson and Jia 2013). For analytical models, solution methods are derived by using mathematical analysis, while for continuous location models that are not analytically solveable, iterative numerical procedures ensure its convergence to optimal solutions, for example the Weiszfeld algorithm (Weiszfeld 1936) for the Weber problem.

For practical applications, discrete formulations are more realistic to provide feasible and optimal locations, but are more difficult to solve. For this type of models, candidate locations are pre-screened based on complementary information such as supplier’s proximity, labor proximity, local regulations, and available physical space, among others. The basic model that locates the optimal facility among a set of candidate locations in a discrete space is known as the p-Median problem. The p-Median problem is defined as follows (Revelle and Swain 1970):

Let I be a set of demand nodes and J be a set of candidate locations.

Parameters:

h _i  demand at node $i\in I$

d _ij  distance between candidate facility site $j\in J$ and customer location $i\in I$

Decision variables:

X _j  1 if we locate at site $j\in J,$ 0 otherwise.

Y _ij  fraction of demand at customer location $i\in I$ that is served by facility at site $j\in J.$

The p-Median problem is then formulated as follows (P1):

$$ \mathrm{M}\mathrm{i}\mathrm{n}\to {\displaystyle \sum}_{j\in J}{\displaystyle \sum}_{i\in I}{h}_i{d}_{ij}{Y}_{ij} $$

Subject to

$$ \begin{array}{cc}{\displaystyle \sum}_{j\in J}{Y}_{ij}=1& \forall i\in I\end{array} $$

(9.1)

$$ {\displaystyle \sum}_{j\in J}{X}_j=p $$

(9.2)

$$ \begin{array}{cc}{Y}_{ij}-{X}_j\le 0& \forall i\in I\ \forall j\in J\end{array} $$

(9.3)

$$ \begin{array}{cc}{X}_j\in \left\{0,1\right\}& \forall j\in J\end{array} $$

(9.4)

$$ \begin{array}{cc}{Y}_{ij}\ge 0& \forall i\in I,\ \forall j\in J\end{array} $$

(9.5)

The objective function minimizes the demand-weighted total distance. Constraint (1) states that each demand node is covered. Constraint (2) establishes that p facilities are located. Constraint (3) states that the facility is opened when a demand node is assigned. Constraints (4) are the integrality constraints and (5) are the non-negative constraints. When applied to a general network, the p-Median problem can be difficult to solve. However, since the single sourcing condition holds in this formulation (i.e., Y _ij will naturally take values of zero or one), the property limits the potential facility locations to the network nodes, and therefore it reduces the number of possible location configurations to $n!/\left(n-p\right)!p!$, where n is the number of nodes (Owen and Daskin 1998). However, a total enumeration of all possible solutions may be computationally prohibited. Kariv and Hakimi (1979) showed that the p-Median problem is NP-hard.

The p-Median problem has been the basis of multiple extensions such as the fixed charge facility location problem, both uncapacitated and capacitated, and in other problems such as multi-item and multi-echelon (Geoffrion and Graves 1974) (Pirkul and Jayaraman 1996). It also has multiple real-world applications such as plant location-allocation (Daskin and Dean 2005), network design (Kalpakis et al. 2001), (Ruffolo et al. 2007), (Stephens et al. 1994), sensor deployment (Greco et al. 2010), and data mining (Christou 2011). Other applications are presented in ReVelle et al. (2008). The p-Median problem has also attracted much research attention in combinatorial optimization and many solution methods have been proposed to solve the problem. For instance, variable neighborhood search (Hansen and Mladenovi 1997), genetic algorithm (Hosage and Goodchild 1986), tabu search (Rolland et al. 1997), scatter search (García-López et al. 2003), ant colony optimization (Kochetov et al. 2005), and simulated annealing (Murray and Church 1996). Pullan (2008) finally presents a population-based hybrid search that was tested again in multiple instances from literature and the results show that the algorithm finds the optimal solutions for many problems, and for others it was capable of finding improvements on the best known solutions from literature.

A natural extension of the p-Median problem is to relax the number of facilities to be opened p and include a fixed location cost f _j . This problem is called the fixed charge facility location problem (P2) (Balinski 1965):

$$ \mathrm{M}\mathrm{i}\mathrm{n}\to {\displaystyle \sum}_{j\in J}{\displaystyle \sum}_{i\in I}\ {f}_j{X}_j+\alpha {\displaystyle \sum}_{j\in J}{\displaystyle \sum}_{i\in I}\ {h}_i{d}_{ij}{Y}_{ij} $$

Subject to

(1)–(5)

When we also include a constraint (6) ${\displaystyle \sum}_{i\in I}{h}_i{Y}_{ij}-{b}_j{X}_j\le 0,$ $\forall j\in J,$ that limits the assigned demand at facility $j\in J$ to a maximum of b _j , the resulting model (P3) is known as the capacitated facility location problem. Similar to the p-Median problem, the fixed charge facility location is also NP-hard. Previous approaches used to solve the p-Median problem may also be applicable in this case. Other solution heuristics methods are tabu search (Glover 1989; Glover and Laguna 1997) and the dual ascendant algorithm (Erlenkotter 1978), among others.

2.2 Carbon Emissions in Facility Location Models

We now discuss some models that include the estimation of CO₂ emissions in the facility location problem. As mentioned in Sect. 9.1, transportation CO₂ emissions in facility location models should be considered carefully, specifically because cost and CO₂ emissions structures do not typically share the same structures. However, some studies show that even when this is the case, still solutions obtained by minimizing transport cost are not necessarily equivalent to solutions obtained by minimizing CO₂ emissions.

2.2.1 Analytical and Continuous Models

We start by discussing the study of Bouchery and Fransoo (2015) on intermodal hinterland network design. The authors present an analytical model that aims at finding the optimal location of one facility (in their example an inland container terminal) with respect to cost, carbon emissions, and modal shift objectives. The demand is assumed to be uniform over a rectangle region representing the hinterland of the port under consideration. The density of the demand is equal to ρ containers per square kilometer and the origin of the flows (the port) is located at coordinates (0, 0).

The model assumes that transport cost and carbon emissions have the same structure, and considers two transport mode options: direct shipment (shipment via truck directly from the origin to the customer) and intermodal transportation (shipment via rail to an intermodal terminal and subsequently from the terminal via truck to the customer). The cost and CO₂ emissions of serving a demand region i of size A _i by using direct shipment are expressed as follows: ${Z}_{0,i}^{\mathrm{DS}}={\delta}_{0,i}\rho {A}_i{Z}_1$ and ${E}_{0,i}^{\mathrm{DS}}={\delta}_{0,i}\rho {A}_i{E}_1$, respectively, where:

δ _o,i  distance from the port to the gravity center of demand zone i (km)

Z ₁ truck transportation cost per container-kilometer

E ₁ carbon emissions from truck transportation (kg of CO₂ per container-km)

The cost and CO₂ emissions when using intermodal transportation are expressed as follows: ${Z}_{0,j}^{\mathrm{IT}}={\delta}_{0,T}\left({\mathrm{ZF}}_2+\rho {A}_i{Z}_2\right)+{\delta}_{T,i}\rho {A}_i{Z}_1$ and ${E}_{0,i}^{\mathrm{IT}}={\delta}_{o,T}\left({\mathrm{EF}}_2+\rho {A}_i{E}_2\right)+$, where:

δ _0,T  distance from the port to the inland terminal (km)

δ _T,i  distance from the terminal to the gravity center of demand zone i (km)

ZF₂ fixed train transportation cost per km

Z ₂ linear train transportation cost per container-km

EF₂ fixed emissions associated to train transportation (kg of CO₂ per km)

E ₂ linear train transportation emissions (kg of CO₂ per container-km)

The authors identify optimal solutions based on European data.

Their results show that the terminal is located closer to the port when optimizing cost and is located further away from the port when optimizing carbon emissions. This result shows that even when cost and CO₂ emissions have the same structure, there are significant differences in the optimal solutions for both formulations. This effect is clearly explained by the differences in the fixed train parameters, which is also consistent to the fact that train transportation under high utilization is more efficient from the emissions perspective than truck, but it is more expensive in terms of cost. For more details we refer to the full study (Bouchery and Fransoo 2015).

Although some other articles on continuous green facility location models can be found in the literature, the area is still very scarce. Buyuksaatci and Esnaf (2014) present a carbon emission-based facility location problem that considers the minimization of CO₂ emissions by using the gravitational center method. The study uses a formulation based on the GHG protocol, but it does not discuss any managerial insight or implication derived from the proposed formulation.

2.2.2 Discrete Models

We now discuss the studies on green facility location models with discrete formulations. Diabat and Simchi-Levi (2010) present a two-level multi-commodity facility location problem with a carbon constraint. Their problem is to decide the optimal location of plants and distribution centers and the assignment, in such a way that the total costs are minimized and the carbon emissions do not exceed a specific carbon cap. The model assumes carbon emissions from distributions by using a distance emission factor (tons of CO₂ per km), and thus neglecting the impact of the load on CO₂ emissions (see Chap. 7 Blanco and Sheffi (2017), that explains how transportation emissions are also affected by the load of the vehicles in the network). Despite this rather coarse assumption, the general conclusion seems in line with intuition: if carbon emission allowance decreases, supply chain cost increases

Elhedhli and Merrick (2012) study a supply chain network design problem that takes CO₂ emissions into account. The objective of the study is to simultaneously minimize logistics costs and the environmental costs of CO₂ emissions by strategically locating warehouses within the distribution network. This model considers the GHG protocol estimation of CO₂ emissions and uses a scaling parameter to convert the CO₂ into cost. This approach allows inclusion of the cost of carbon emissions into supply chain network design. The experimental results show that the addition of carbon costs drives solutions with more distribution centers be opened to decrease CO₂ emissions in transportation.

Although the study provides interesting managerial insights, the model uses the most aggregate approaches to estimate CO₂ emissions in transportation (i.e., the GHG protocol with EPA emission factors). Velázquez-Martínez et al. (2014a) address the effects of using different aggregation levels to measure transport carbon emissions, and they show that errors associated with aggregation could be substantial and systematic. This suggests that increasing the level of detail in the facility location problem is necessary.

Cost may not necessarily be the only driver to reduce CO₂ emissions in transportation. For example, companies may be subject to a cap-and-trade system, or may use carbon emission reductions as a driver for brand management, product differentiation, or employee motivation (CDP 2011a, b). This suggests that a practical formulation of green facility location models should potentially take simultaneously cost and CO₂ objectives into account.

A possible alternative to consider both objectives (cost and CO₂ emissions) is to model the green facility location problem using a multi-objective setting. Most real-world problems naturally involve multiple objectives (minimizing cost, maximizing service level, minimizing CO₂ emissions, etc.) A Multi-objective approach allows to define a set of efficient solutions (or a Pareto frontier) which are defined as the set of solutions such that there is no other solution that dominates them, i.e., each solution of the set is strictly better than the rest of the solutions in at least one objective and is not worse than the rest of the solutions in all objectives (Coello 2009). These efficient solutions are often preferred to single solutions because they can be practical when considering real-life problems since the final solution of the decision maker is always a trade-off (Konak et al. 2006).

In line with this stream of research, Harris et al. (2014) present a formulation of the fixed charge facility location model (P3) with two objective functions: costs and CO₂ emissions. Their facility location model considers individual depots with capacities b _j , where each customer is served directly by a single depot, and thus, forcing the “single sourcing condition” to be held in the model. Therefore, it is possible to build a solution algorithm that first determines which facilities to open, and then to allocate the customers to the open facilities. The study proposes an expression to estimate transportation CO₂ emissions based on the GHG protocol, i.e., transportation CO₂ emissions are linearly dependent on the distance travelled and demand.

The study discusses a multi-objective optimization solution method for the cost and CO₂ facility location model, in which a decision maker can explore trade-off solutions for customer allocation based on the pre-selected facility location. Figure 9.2 (Harris et al. 2014) shows the different solutions of the location decision, and for each decision, the potential allocation assignment.

Fig. 9.2

Trade-off solutions for customer location—allocation decisions. Adapted from Harris et al. (2014)

The article focuses on the solution methods and provides a framework to analyze trade-offs between cost and CO₂ emissions for location models.

Because we notice that all previous studies conclude that the increase in the number of open facilities implies a reduction on CO₂ emissions (and typically more facilities also imply higher costs), we may argue that a practical approach to analyze the trade-off between cost and CO₂ emissions in facility locations, is to simplify the formulation by not including the fixed emission per open facility. Therefore, we are interested in studying the effect of transportation cost versus transportation CO₂ emissions with a fixed amount of facilities previously defined (i.e., p-Median problem).

Vélazquez-Martínez et al. (2014b) study the trade-off between cost and CO₂ emissions by using a multi-objective approach for the facility location problem. The model corresponds to the p-Median problem with cost and CO₂ objective functions. The general assumptions of the p-Median problem are applicable to this model; that is, deterministic demand and the candidate locations are known in advance. In addition, the model also assumes that the company may manage multiple trucks with different capacities and the trucks are assigned according to demand node constraints (or company policy). These assumptions allow the model to include the possibility that certain customers are reachable only by certain types of trucks, with distinct cost structures.

To formulate the carbon emissions objective function, the authors include theNTM methodology in the objective function (Vélazquez-Martínez et al. 2014b).Note that $\left[\frac{h_i}{W_i}\right]$ represents the number of trips that are required to serve customer$i\in I$, and thus, affects the total distance travelled.

$$ l{\displaystyle \sum}_{j\in J}{\displaystyle \sum}_{i\in I}{d}_{ij}\left[{f_i}^e+\left({f_i}^f-{f_i}^e\right)\frac{h_i}{W_i}\right]\left[\frac{h_i}{W_i}\right]{Y}_{ij} $$

This formulation enables us to understand in more detail the trade-off between distance (d _ij ) and utilization (h _i /W _i ) while deciding the location-allocation decisions. For example, when serving customers with a homogeneous fleet (i.e., ${W}_i=W$ for all $i\in I$), the location solutions are the same as those that are obtained by P1, i.e., facilities are located closer to customers with the highest demand, and thus minimizing transport cost is equivalent to minimizing CO₂ emissions. However, when serving customers with a non-homogeneous fleet (e.g., caused by truck constraints due to regulations or transport infrastructure), facilities may be located closer to customers served by small trucks. This may be explained due to the fact that multiple trips are required and thus more distance is travelled to serve these customers.

3 Practical Implications of the Green Location Models

Transportation is one of the main contributing factors of global carbon emissions, and thus, when dealing with facility location models in a distribution context, transportation emissions may be substantially higher than the emissions due to production or storage. In addition, because facility location models define the configuration of deliveries, green location models become an important alternative to reduce CO₂ emissions in logistics. Because transportation usually is included in Scope 3 of the GHG inventory, and usually represents the highest source of emissions in a supply chain, companies may start focusing more on increasing the number of distribution centers while increasing the reachability to customers.

While cost-minimization solutions tend to locate facilities closer to high-demand customers, CO₂ emissions minimization solutions tend to locate facilities closer to customers that have truck accessibility constraints. This is explained because truck constraints drive the number of trips required to serve customers, and this factor is larger than the increase in demand and/or utilization. This may be particularly important for companies managing non-homogeneous vehicle fleet, or for policy makers in large dense areas where demand is high (based on the high density of inhabitants and small stores), but heavy-duty vehicles are not allowed. New regulations may be needed to balance the accessibility of big trucks in certain periods to increase logistics efficiency and to also reduce the number of small vehicle in those regions.

For some logistics problems , even when aggregate approaches are used to estimate transportation CO₂ emissions and thus this formulation shares the same structure with transportation cost, the location solutions may be substantially different. For companies that are interested in increasing modal shift or using more intermodal transport, these strategies may result in increase in CO₂ emissions. Particularly when different modes are used like in intermodal networks, the difference in parameters for transportation cost and CO₂ emissions can lead to a completely different set of solutions for both objective functions.

A multi-objective setting for the green facility location models may provide decision makers with a framework to analyze the trade-off between cost and CO₂ emissions. This approach may bring a new tool for companies to define better strategies to reduce CO₂ emissions. Because decision makers likely seek alternatives that reduce emissions but keep costs low, multi-objective modeling provides a set of trade-off solutions that were previously unknown in single objective modeling. This may imply that new solutions may appear with good offset of cost and CO₂ emissions. For example, locations where small increases in cost may imply high reductions of CO₂ emissions.

4 Directions for Future Work

The area of green facility location is still small in research. Because transportation cost and CO₂ emissions do not have the same structure, a specific formulation for CO₂ emissions minimization model for facility location should be considered. Unfortunately few studies consider the detailed expression to estimate transportation CO₂ emissions in location models, and most of them use GHG protocol, and thus, the complete effect has not been studied and understood.

In addition, only a few companies have implemented strategies using facility locations to reduce their environmental impact. Thus, more applications of the models in practical cases are needed so more understanding of the models and trade-off can be achieved and validated in practice. In addition, a few articles from prior literature include in their formulations the emissions generated by the facilities, and usually only the production of electricity. The models are mainly focus on the emissions causes by transportation, and specifically for the last-mile delivery. However, no research has been conducted to analyze the impact of transportation of raw materials in facility locations, and thus, more model formulations are needed to address this gap.

In addition, considering the different sources of energy for the facilities (wind, fuels, etc.) and to include them in the future green facility location models to understand the impact of energy source on plan locations, is a fruitful research avenue. Furthermore, including other type of pollutants —such as noise, particulate matter, CO, and NO_x—as possible objective functions in the green facility location models is a worthwhile research direction. For this problem, researchers may need to develop new heuristics strategies to accommodate the complexities.

In this chapter, we have limited our discussion on the impact of emissions from mobile sources, within which carbon and other pollutants are the most impactful. Inclusion of environmental effects of stationary sources has not yet been studied in the facility location problem. As discussed above, this could also relate to carbon emission, for instance due to local presence of renewable energy sources. However, also other effects could then be taken into account, such as the effect of the location choice on the water footprint.