a multi-objective optimization model for sustainable logistics facility location

4
A multi-objective optimization model for sustainable logistics facility location Tang Xifeng a,, Zhang Ji b , Xu Peng a a School of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China b Department of Civil, Architectural and Environmental Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA article info Keywords: Sustainable facility location Service reliability Carbon dioxide emissions abstract This paper offers an exploratory study of sustainable facility location. The methodology, based on the classical uncapacitated facility location problem, provides decision makers with a multi-objective optimization model to determine the trade-off among economic, service and environmental considerations. Our results indicate that it may be desirable to open more facilities than optimal from a narrow economic perspective to reduce the car- bon dioxide emissions of transport and to improve service reliability. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Road freight transport has been a rapidly growing contributor to carbon dioxide (CO 2 ) emissions (European Commission, 2010). Logistics system design models have traditionally focused on minimizing economic cost or maximizing customer ser- vice level without taking CO 2 emissions into account. Recent studies, however, started to address the challenging require- ments of sustainable facility location. This paper develops a multi-objective uncapacitated facility location problem (UFLP) with an environmental objective in the context of sustainable development. The model is to simultaneously minimize economic cost, CO 2 emissions, and max- imize service reliability by strategically locating facilities within a logistics network. 1 2. Model formulation and solution algorithms 2.1. Formulation of the model The UFLP is a classical facility location problem and forms the basis of many location models that have been used in logis- tics network design. Its finds the best location of facilities and the allocation of customers that minimizes transportation and fixed costs (Daskin et al., 2003). To be competitive, logistics service providers need to offer suitable levels of service to customers, and this is often related to facility location layouts, distances from customers to facilities, time requirements for delivering goods, the capability of facilities to supporting customer’ demands, and the connectivity of transportation routes. Here, customer service reliability is defined as the probability of one facility providing the required goods to customers within a given time given a set of constraints. One of the constraints considered is the need to limit CO 2 emissions. While there are a number of factors affecting emissions levels, we only consider the amount of goods being transported and the 1361-9209/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.trd.2013.03.003 Corresponding author. Tel.: +86 13851962244. E-mail address: [email protected] (T. Xifeng). 1 For recent work in this field see, Chaabane et al. (2011) and Elhedhli and Merrick (2012). Transportation Research Part D 22 (2013) 45–48 Contents lists available at SciVerse ScienceDirect Transportation Research Part D journal homepage: www.elsevier.com/locate/trd

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Transportation Research Part D 22 (2013) 45–48

Contents lists available at SciVerse ScienceDirect

Transportation Research Part D

journal homepage: www.elsevier .com/ locate/ t rd

A multi-objective optimization model for sustainable logisticsfacility location

1361-9209/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.trd.2013.03.003

⇑ Corresponding author. Tel.: +86 13851962244.E-mail address: [email protected] (T. Xifeng).

1 For recent work in this field see, Chaabane et al. (2011) and Elhedhli and Merrick (2012).

Tang Xifeng a,⇑, Zhang Ji b, Xu Peng a

a School of Civil and Transportation Engineering, Hohai University, Nanjing 210098, Chinab Department of Civil, Architectural and Environmental Engineering, Illinois Institute of Technology, Chicago, IL 60616, USA

a r t i c l e i n f o

Keywords:Sustainable facility locationService reliabilityCarbon dioxide emissions

a b s t r a c t

This paper offers an exploratory study of sustainable facility location. The methodology,based on the classical uncapacitated facility location problem, provides decision makerswith a multi-objective optimization model to determine the trade-off among economic,service and environmental considerations. Our results indicate that it may be desirableto open more facilities than optimal from a narrow economic perspective to reduce the car-bon dioxide emissions of transport and to improve service reliability.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Road freight transport has been a rapidly growing contributor to carbon dioxide (CO2) emissions (European Commission,2010). Logistics system design models have traditionally focused on minimizing economic cost or maximizing customer ser-vice level without taking CO2 emissions into account. Recent studies, however, started to address the challenging require-ments of sustainable facility location.

This paper develops a multi-objective uncapacitated facility location problem (UFLP) with an environmental objective inthe context of sustainable development. The model is to simultaneously minimize economic cost, CO2 emissions, and max-imize service reliability by strategically locating facilities within a logistics network.1

2. Model formulation and solution algorithms

2.1. Formulation of the model

The UFLP is a classical facility location problem and forms the basis of many location models that have been used in logis-tics network design. Its finds the best location of facilities and the allocation of customers that minimizes transportation andfixed costs (Daskin et al., 2003).

To be competitive, logistics service providers need to offer suitable levels of service to customers, and this is often relatedto facility location layouts, distances from customers to facilities, time requirements for delivering goods, the capability offacilities to supporting customer’ demands, and the connectivity of transportation routes.

Here, customer service reliability is defined as the probability of one facility providing the required goods to customerswithin a given time given a set of constraints. One of the constraints considered is the need to limit CO2 emissions. Whilethere are a number of factors affecting emissions levels, we only consider the amount of goods being transported and the

46 T. Xifeng et al. / Transportation Research Part D 22 (2013) 45–48

distance travelled assuming, road vehicles are identical, that average speed is known, and the gradient of a road is not afactor.

Based on the UFLP, the problem is formulated as a mixture of three mathematical programming formulations: minimumeconomic cost, maximum customer service reliability and minimum CO2 emissions. We define the indices i = 1, 2,. . ., I andj = 1, 2,. . ., J as corresponding to customers and candidate facilities; each customer having a demand hi. A logistics facility atlocation j has a fixed cost fj. The unit cost of shipping from a facility at location j to customer i is cij. The distance between afacility at j and customer i is dij. The speed of trucks shipping from facilities to surrounding customers is modeled as a ran-dom variable v with a distribution function Fv(�). Ti is the time deadline of customer i; evf is the CO2 emissions of a fully loadedvehicle; eve is the CO2 emissions of an empty vehicle, and w is the weight limit for a vehicle. Two binary location variables areintroduced; Xj taking the value one if a facility is open at candidate location j and zero otherwise; Yij takes a value of one ifcustomer i is assigned to facility j and zero if not. The model can be formulated as:

Table 1The dem

Cust

Dem

MinXJ

j¼1

fjXj þXJ

j¼1

XI

i¼1

cijhidijYij ð1Þ

Max Minfð1� Fvðdij=TiÞÞYijg ð2Þ

MinXJ

j¼1

XI

i¼1

dij½ðevf � eveÞhi=wþ evedhi=we�Yij ð3Þ

S:t:XJ

j¼1

Yij ¼ 1 8i ð4Þ

Yij 6 Xj 8i; j ð5Þ

Xj 2 f0;1g 8j ð6Þ

Yij 2 f0;1g 8i; j ð7Þ

The objective function (1) minimizes the sum of fixed location and transportation costs. The objective function (2) maxi-mizes minimum service reliability and function (3) minimizes CO2 emissions from transportation. Constraints (4) guaranteethat each customer is assigned to exactly one logistics facility, and constraints (5) state that a customer cannot be assigned toa facility unless it is open. Constraints (6) and (7) are standard integrality constraints.

2.2. The hybrid algorithm

A classical technique is utilized to solve the multi-objective optimization problem, which applies the e-constraint meth-od. From the perspective of sustainable development, the environmental impact is considered as the priority, with the eco-nomic and the service objectives formulated as constraints. After transforming the multiple objectives into one, the greedyheuristic is used to construct a feasible solution by greedily dropping facilities from the solution until no further improve-ment can be obtained. In detail, the procedure is:

Step 1: let the current number of facility locations k = J, that is, exists facilities at all candidate sites.Step 2: allocate each customer to the nearest facility among k facility locations, and compute the CO2 emissions and thecost and the service reliability to each customer.Step 3: if the economic cost is lower than the decision maker’s expectation, and the service reliability is higher than thespecified limit, stop and return the last results; otherwise, go to Step 4.Step 4: select one facility and ensure that the increase in CO2 emissions is smaller than if its customers are reallocated toother nearby facilities, while guaranteeing that the economic cost and service reliability satisfy the decision makers.Step 5: drop the facility from the solution and let k = k � 1, then go to Step 2.

and of each customer location.

omer location C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25

and (ton) 166 156 88 59 163 191 79 141 99 170 159 50 176 199 113 180 126 48 56 93 155 169 162 77 116

Table 2The fixed location cost of each candidate facility.

Facility location F1 F2 F3 F4 F5 F6 F7 F8 F9 F10

Location cost ($) 78,500 46,900 92,200 58,700 89,800 46,300 85,400 67,100 76,000 85,300

Table 3The distance between each customer location and each candidate facility location.

Distance (km) C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20 C21 C22 C23 C24 C25

F1 85 241 297 111 269 252 114 123 204 141 66 183 219 234 171 42 153 135 147 42 218 11 176 292 237F2 47 276 147 222 155 112 294 213 168 77 157 163 161 151 267 128 257 177 69 119 183 266 201 10 240F3 100 42 209 158 164 249 120 44 256 130 131 49 76 128 253 103 116 264 26 295 177 75 195 251 15F4 86 152 124 242 182 53 133 262 168 211 223 27 276 184 270 163 209 141 21 194 131 32 131 251 85F5 166 122 11 246 229 39 98 139 271 121 60 232 228 257 282 278 189 132 267 269 74 245 42 15 197F6 262 53 88 57 257 264 48 25 126 55 255 230 267 202 245 90 136 224 70 145 129 43 226 164 147F7 13 173 241 38 115 14 95 10 108 257 204 127 210 158 61 102 143 111 259 55 48 264 73 283 292F8 272 182 104 247 26 207 269 226 147 176 41 18 56 90 101 258 285 259 214 187 183 29 196 97 225F9 40 65 25 192 221 212 75 211 77 113 258 176 222 212 27 103 26 140 262 70 288 106 258 242 171F10 251 156 154 75 100 132 94 65 279 67 22 53 21 115 79 37 84 150 282 159 29 179 26 181 90

Table 4Best solution to the sustainable facility location problem.

Facility location Allocation of customers Total cost ($) Service reliability CO2 emissions (Kg)

F1 C20, C22

F2 C24

F3 C19, C25

F4 C2, C7, C10

F5 C1, C4, C6, C8, C18 658,752 0.9929 5.3137 � 103

F6 C5, C12, C14

F7 C3, C9, C15, C17

F8 C11, C13, C16, C21, C23

Fig. 1. Impact of the number of facilities on economic cost and CO2 emissions.

T. Xifeng et al. / Transportation Research Part D 22 (2013) 45–48 47

3. Computational experiments

We assume there are 25 customers, Cj (j = 1,2, . . .,25), the demand of each customer hi as shown in Table 1. There are 10candidate facility locations designated as Fj (j = 1,2, . . .,10) with the fixed location cost of each shown in Table 2. Table 3 liststhe distances between each customer and candidate facility location, dij. The shipment cost per ton-kilometer is cij= $1. Thetruck considered is fully loaded with 25 tons, the CO2 emissions of a fully loaded vehicle is evf = 1.096 kg/km, the CO2 emis-sions of an empty vehicle is eve = 0.772 kg/km; and the truck’s speed is normally distributed with a mean of 80 km/h and

Fig. 2. Impact of the number of facilities on economic cost and service reliability.

48 T. Xifeng et al. / Transportation Research Part D 22 (2013) 45–48

variance 102. Customers have the same time deadline of 2 h. The limits of service reliability and costs are Rij =0.9, andTC = $700,000.

The computations are solved by coding in MATLAB Version 7.13 (R2011b), and executing the computational program, theresults are shown in Table 4.

4. Sensitivity analysis

The solution provides a reasonable compromise solution. When relevant parameters are kept unchanged, and the modelonly includes the economic objective, the optimum locations of facilities are at F2, F6 and F10, and the minimum cost is$380,725. The poorest service reliability is 0.691, and the CO2 emissions are 9.377 � 103 kg. When the model includes boththe economic and the service objectives, but assuming the latter has priority, the optimum locations of facilities are F2, F4, F6,F7, F8, F9 and F10, the maximum service reliability is 0.993, while the cost is $584,503, and CO2 emissions are 5.506 � 103 kg.

Focusing on CO2 emissions, service reliability and the number of open facilities, Fig. 1 shows how emissions fall with morefacilities, and Fig. 2 how reliability increases with more facilities. As seen in the figures, costs fall with decreasing numbers offacilities in the earlier phases, and is minimized when there are three facilities, they then begin to rise because of the savingin locating facilities is fully absorbed into transport costs. For longer distances, the number of facilities decreases, and CO2

emissions rise, while service reliability decreases. As the environmental impact of transport increases disproportionatelywith the cost of operating facilities, the environmentally friendly solution requires more open facilities than does economiccost effectiveness.

5. Conclusions

The paper has offered an extension of the classical UFLP, in which the economic objective, service objective and environ-mental objective are considered simultaneously as part of the sustainable facility location design. The computational testsdemonstrate that the optimum solution obtained is a reasonable trade-off of the three component objectives, and suggestthat more logistics facilities be opened to decrease CO2 emissions and improve service level.

Acknowledgements

The authors gratefully acknowledge the editor-in-chief and anonymous reviewers for their valuable comments and sug-gestions that will significantly improve the paper. This research is partially supported by the Fundamental Research Fund forthe Central Universities (No. B12020025), PRC.

References

Chaabane, A., Ramudhin, A., Paquet, M., 2011. Designing supply chains with sustainability considerations. Production Planning & Control 22, 727–741.Daskin, M.S., Snyder, L.V., Berger, R.T., 2003. Facility Location in Supply Chain Design. Working Paper. Northwestern University.Elhedhli, S., Merrick, R., 2012. Green supply chain network design to reduce carbon emissions. Transportation Research Part D 17, 370–379.European Commission, 2010. Energy and Transport in Figures. European Commission, Brussels.