A Recourse Stochastic Goal Programming Approach for the Multi-objective Stochastic Vehicle Routing Problem
This paper addresses a multi‐objective stochastic vehicle routing problem where several conflicting objectives such as the travel time, the number of vehicles in use and the probability of an accident are simultaneously minimized. We suppose that demands and travel durations are of a stochastic natu...
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| Vydané v: | Journal of multi-criteria decision analysis Ročník 23; číslo 1-2; s. 3 - 14 |
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| Jazyk: | English |
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Chichester
Blackwell Publishing Ltd
01.01.2016
Wiley Periodicals Inc |
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| ISSN: | 1057-9214, 1099-1360 |
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| Abstract | This paper addresses a multi‐objective stochastic vehicle routing problem where several conflicting objectives such as the travel time, the number of vehicles in use and the probability of an accident are simultaneously minimized. We suppose that demands and travel durations are of a stochastic nature. In order to build a certainty equivalent program to the multi‐objective stochastic vehicle routing problem, we propose a solution strategy based on a recourse approach, a chance‐constrained approach and a goal‐programming approach. The resulting certainty equivalent program is solved to optimality using CPLEX. Copyright © 2016 John Wiley & Sons, Ltd. |
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| AbstractList | This paper addresses a multi-objective stochastic vehicle routing problem where several conflicting objectives such as the travel time, the number of vehicles in use and the probability of an accident are simultaneously minimized. We suppose that demands and travel durations are of a stochastic nature. In order to build a certainty equivalent program to the multi-objective stochastic vehicle routing problem, we propose a solution strategy based on a recourse approach, a chance-constrained approach and a goal-programming approach. The resulting certainty equivalent program is solved to optimality using CPLEX. This paper addresses a multi‐objective stochastic vehicle routing problem where several conflicting objectives such as the travel time, the number of vehicles in use and the probability of an accident are simultaneously minimized. We suppose that demands and travel durations are of a stochastic nature. In order to build a certainty equivalent program to the multi‐objective stochastic vehicle routing problem, we propose a solution strategy based on a recourse approach, a chance‐constrained approach and a goal‐programming approach. The resulting certainty equivalent program is solved to optimality using CPLEX. Copyright © 2016 John Wiley & Sons, Ltd. |
| Author | Alaya, Houda Masri, Hatem Ben Abdelaziz, Fouad |
| Author_xml | – sequence: 1 givenname: Hatem surname: Masri fullname: Masri, Hatem email: Correspondence to: College of Business Administration, University of Bahrain, PO Box 32038, Sakhir, Bahrain. , hmasri@uob.edu.bh organization: College of Business Administration, University of Bahrain, Sakhir, Bahrain – sequence: 2 givenname: Fouad surname: Ben Abdelaziz fullname: Ben Abdelaziz, Fouad organization: NEOMA Business School, Mont-Saint-Aignan, France – sequence: 3 givenname: Houda surname: Alaya fullname: Alaya, Houda organization: Institut Supérieur de Gestion, University of Tunis, Le Bardo, Tunisia |
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| References | Ben Abdelaziz F, Masri H. 2010. A compromise solution for the multiobjective stochastic linear programming under partial uncertainty. European Journal of Operational Research 202(1): 55-59. Ghoseiri K, Ghannadopour SF. 2010. Multi-objective vehicle routing problem with time windows using goal programming and genetic algorithm. Applied Soft Computing 10: 1096-1107. Fölsz F, Mészáros C, Rapcsák T. 1995. Distribution of gas cylinders. European Journal of Operational Research 87(3): 613-623. Zhao Y, Li C, Zhang J, Ren X, Ren W. 2011. Research on vehicle routing problem with stochastic demand based on multi-objective methodICIC 1. Lecture Notes in Computer Science 6838: 153-161, Springer. Laporte G, Louveaux FV. 1993. The integer L-shaped method for stochastic integer programs with complete recourse. Operations Research Letters 13: 133-142. Laporte G, Louveaux FV, Van Hamme L. 1994. Exact solution of a stochastic location problem by an integer L-shaped algorithm. Transportation Science 28: 95-103. Laporte G, Louveaux F, Mercure H. 1989. Models and exact solutions for a class of stochastic location-routing problems. European Journal of Operational Research 39(1): 71-78. Tan KC, Cheong CY, Goh CK. 2007. Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation. European Journal of Operational Research 117: 813-839. Walkup DW, Wets RJ-B. 1967. Stochastic programs with recourse. SIAM Journal on Applied Mathematics 15(5): 1299-1314. Laporte G, Louveaux FV, Mercure H. 1992. The vehicle routing problem with stochastic travel times. Transportation Science 26: 161-170. Bertsimas DJ. 1992. A vehicle routing problem with stochastic demand. Operations Research 40: 574-585. Ben Abdelaziz F. 2012. Solution approaches for the multiobjective stochastic programming. European Journal of Operational Research 216(1): 1-16. Ben Abdelaziz F, Aouni B, El Fayedh R. 2007. Multi-objective stochastic programming for portfolio selection. European Journal of Operational Research 177: 1811-1823. Mendoza JE, Villegas JG. 2013. A multi-space sampling heuristic for the vehicle routing problem with stochastic demands. Optimization Letters 7(7): 1503-1516. Thompson P, Psaraftis H. 1993. Cyclic transfer algorithms for multi-vehicle routing and scheduling problems. Operations Research 41(5): 935-946. Gendreau M, Laporte G, Seguin R. 1995. An exact algorithm for the vehicle routing problem with stochastic demands and customers. Transportation Science 29(2): 143-155. Jozefowiez N, Semet F, Talbi E-G. 2008. Multi-objective vehicle routing problems. European Journal of Operational Research 189(2): 293-309. Aouni B, Ben Abdelaziz F, La Torre D. 2012. The stochastic goal programming model: theory and applications. Journal of Multi-Criteria Decision Analysis 19(5-6): 185-200. Stewart WR, Golden BL. 1983. Stochastic vehicle routing: a comprehensive approach. European Journal of Operational Research 14: 371-385. Gass S, Saaty T. 1955. The computational algorithm for the parametric objective function. Naval Research Logistics Quarterly 2: 39-45. Lambert V, Laporte G, Louveaux F. 1993. Designing collection routes through bank branches. Computers & Operations Research 20(7): 783-791. Park YB, Koelling CP. 1986. A solution of vehicle routing problems in a multiple objective environment. Engineering Costs and Production Economics 10: 121-32. Calavete HI, Galé C, Oliveros M, Sànchez-Valverde B. 2007. A goal programming approach to vehicle routing problems with soft time windows. European Journal of Operational Research 177: 1720-1733. Christiansen C, Lysgaard J. 2007. A branch-and-price algorithm for the capacitated vehicle routing problem with stochastic demands. Operations Research Letters 35(6): 773-781. Goodson JC, Ohlmann JW, Thomas BW. 2012. Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand. European Journal of Operational Research 227(2): 312-323. Masmoudi M, Ben Abdelaziz F. 2012. A recourse goal programming approach for the portfolio selection problem. INFOR: Information Systems and Operational Research 50(3): 134-139. Miller C, Tucker A, Zemlin RA. 1960. Integer programming formulation of traveling salesman problems. ACM 7(4): 326-329. Ando N, Taniguchi E. 2006. Travel time reliability in vehicle routing and scheduling with time windows. Networks and Spatial Economics 6: 293-311. Guitouni A, Masri H. 2014. An orienteering model for the search and rescue problem. Computational Management Science 11(4): 459-473. Charnes A, Cooper WW. 1971. Chance-constrained programming. Management Science 5: 73-79. Tas D, Dellaert N, van Woensel T, de Kok T. 2013. Vehicle routing problem with stochastic travel times including soft time windows and service costs. Computers and Operations Research 40(1): 214-224. Li X, Tian P, Leung SC. 2010. Vehicle routing problems with time windows and stochastic travel and service times: models and algorithm. International Journal of Production Economics 125: 137-145. 2010; 10 1986; 10 2010; 202 2010; 125 2013; 40 1993; 20 1993; 41 2012; 19 2006; 6 1960; 7 1994; 28 2008; 189 2013; 7 2015; 8 2012; 227 2007; 35 1955; 2 1983; 14 2012; 50 1993; 13 2007; 117 2011; 6838 2007; 177 1995; 87 1992; 26 1967; 15 1995; 29 2012; 216 1971; 5 2014; 11 1992; 40 1989; 39 |
| References_xml | – reference: Aouni B, Ben Abdelaziz F, La Torre D. 2012. The stochastic goal programming model: theory and applications. Journal of Multi-Criteria Decision Analysis 19(5-6): 185-200. – reference: Laporte G, Louveaux F, Mercure H. 1989. Models and exact solutions for a class of stochastic location-routing problems. European Journal of Operational Research 39(1): 71-78. – reference: Ben Abdelaziz F, Aouni B, El Fayedh R. 2007. Multi-objective stochastic programming for portfolio selection. European Journal of Operational Research 177: 1811-1823. – reference: Stewart WR, Golden BL. 1983. Stochastic vehicle routing: a comprehensive approach. European Journal of Operational Research 14: 371-385. – reference: Ben Abdelaziz F, Masri H. 2010. A compromise solution for the multiobjective stochastic linear programming under partial uncertainty. European Journal of Operational Research 202(1): 55-59. – reference: Ando N, Taniguchi E. 2006. Travel time reliability in vehicle routing and scheduling with time windows. Networks and Spatial Economics 6: 293-311. – reference: Guitouni A, Masri H. 2014. An orienteering model for the search and rescue problem. Computational Management Science 11(4): 459-473. – reference: Goodson JC, Ohlmann JW, Thomas BW. 2012. Cyclic-order neighborhoods with application to the vehicle routing problem with stochastic demand. European Journal of Operational Research 227(2): 312-323. – reference: Laporte G, Louveaux FV, Van Hamme L. 1994. Exact solution of a stochastic location problem by an integer L-shaped algorithm. Transportation Science 28: 95-103. – reference: Mendoza JE, Villegas JG. 2013. A multi-space sampling heuristic for the vehicle routing problem with stochastic demands. Optimization Letters 7(7): 1503-1516. – reference: Walkup DW, Wets RJ-B. 1967. Stochastic programs with recourse. SIAM Journal on Applied Mathematics 15(5): 1299-1314. – reference: Charnes A, Cooper WW. 1971. Chance-constrained programming. Management Science 5: 73-79. – reference: Thompson P, Psaraftis H. 1993. Cyclic transfer algorithms for multi-vehicle routing and scheduling problems. Operations Research 41(5): 935-946. – reference: Tas D, Dellaert N, van Woensel T, de Kok T. 2013. Vehicle routing problem with stochastic travel times including soft time windows and service costs. Computers and Operations Research 40(1): 214-224. – reference: Calavete HI, Galé C, Oliveros M, Sànchez-Valverde B. 2007. A goal programming approach to vehicle routing problems with soft time windows. European Journal of Operational Research 177: 1720-1733. – reference: Laporte G, Louveaux FV. 1993. The integer L-shaped method for stochastic integer programs with complete recourse. Operations Research Letters 13: 133-142. – reference: Laporte G, Louveaux FV, Mercure H. 1992. The vehicle routing problem with stochastic travel times. Transportation Science 26: 161-170. – reference: Masmoudi M, Ben Abdelaziz F. 2012. A recourse goal programming approach for the portfolio selection problem. INFOR: Information Systems and Operational Research 50(3): 134-139. – reference: Zhao Y, Li C, Zhang J, Ren X, Ren W. 2011. Research on vehicle routing problem with stochastic demand based on multi-objective methodICIC 1. Lecture Notes in Computer Science 6838: 153-161, Springer. – reference: Park YB, Koelling CP. 1986. A solution of vehicle routing problems in a multiple objective environment. Engineering Costs and Production Economics 10: 121-32. – reference: Ben Abdelaziz F. 2012. Solution approaches for the multiobjective stochastic programming. European Journal of Operational Research 216(1): 1-16. – reference: Ghoseiri K, Ghannadopour SF. 2010. Multi-objective vehicle routing problem with time windows using goal programming and genetic algorithm. Applied Soft Computing 10: 1096-1107. – reference: Christiansen C, Lysgaard J. 2007. A branch-and-price algorithm for the capacitated vehicle routing problem with stochastic demands. Operations Research Letters 35(6): 773-781. – reference: Lambert V, Laporte G, Louveaux F. 1993. Designing collection routes through bank branches. Computers & Operations Research 20(7): 783-791. – reference: Gendreau M, Laporte G, Seguin R. 1995. An exact algorithm for the vehicle routing problem with stochastic demands and customers. Transportation Science 29(2): 143-155. – reference: Fölsz F, Mészáros C, Rapcsák T. 1995. Distribution of gas cylinders. European Journal of Operational Research 87(3): 613-623. – reference: Miller C, Tucker A, Zemlin RA. 1960. Integer programming formulation of traveling salesman problems. ACM 7(4): 326-329. – reference: Bertsimas DJ. 1992. A vehicle routing problem with stochastic demand. Operations Research 40: 574-585. – reference: Tan KC, Cheong CY, Goh CK. 2007. Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation. European Journal of Operational Research 117: 813-839. – reference: Li X, Tian P, Leung SC. 2010. Vehicle routing problems with time windows and stochastic travel and service times: models and algorithm. International Journal of Production Economics 125: 137-145. – reference: Gass S, Saaty T. 1955. The computational algorithm for the parametric objective function. Naval Research Logistics Quarterly 2: 39-45. – reference: Jozefowiez N, Semet F, Talbi E-G. 2008. Multi-objective vehicle routing problems. European Journal of Operational Research 189(2): 293-309. – volume: 87 start-page: 613 issue: 3 year: 1995 end-page: 623 article-title: Distribution of gas cylinders publication-title: European Journal of Operational Research – volume: 189 start-page: 293 issue: 2 year: 2008 end-page: 309 article-title: Multi‐objective vehicle routing problems publication-title: European Journal of Operational Research – volume: 7 start-page: 326 issue: 4 year: 1960 end-page: 329 article-title: Integer programming formulation of traveling salesman problems publication-title: ACM – volume: 117 start-page: 813 year: 2007 end-page: 839 article-title: Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation publication-title: European Journal of Operational Research – volume: 216 start-page: 1 issue: 1 year: 2012 end-page: 16 article-title: Solution approaches for the multiobjective stochastic programming publication-title: European Journal of Operational Research – volume: 227 start-page: 312 issue: 2 year: 2012 end-page: 323 article-title: Cyclic‐order neighborhoods with application to the vehicle routing problem with stochastic demand publication-title: European Journal of Operational Research – volume: 177 start-page: 1720 year: 2007 end-page: 1733 article-title: A goal programming approach to vehicle routing problems with soft time windows publication-title: European Journal of Operational Research – volume: 39 start-page: 71 issue: 1 year: 1989 end-page: 78 article-title: Models and exact solutions for a class of stochastic location‐routing problems publication-title: European Journal of Operational Research – volume: 41 start-page: 935 issue: 5 year: 1993 end-page: 946 article-title: Cyclic transfer algorithms for multi‐vehicle routing and scheduling problems publication-title: Operations Research – volume: 19 start-page: 185 issue: 5–6 year: 2012 end-page: 200 article-title: The stochastic goal programming model: theory and applications publication-title: Journal of Multi‐Criteria Decision Analysis – volume: 20 start-page: 783 issue: 7 year: 1993 end-page: 791 article-title: Designing collection routes through bank branches publication-title: Computers & Operations Research – volume: 5 start-page: 73 year: 1971 end-page: 79 article-title: Chance‐constrained programming publication-title: Management Science – volume: 7 start-page: 1503 issue: 7 year: 2013 end-page: 1516 article-title: A multi‐space sampling heuristic for the vehicle routing problem with stochastic demands publication-title: Optimization Letters – volume: 50 start-page: 134 issue: 3 year: 2012 end-page: 139 article-title: A recourse goal programming approach for the portfolio selection problem publication-title: INFOR: Information Systems and Operational Research – volume: 8 start-page: 85 issue: 1 year: 2015 end-page: 109 – volume: 40 start-page: 574 year: 1992 end-page: 585 article-title: A vehicle routing problem with stochastic demand publication-title: Operations Research – volume: 29 start-page: 143 issue: 2 year: 1995 end-page: 155 article-title: An exact algorithm for the vehicle routing problem with stochastic demands and customers publication-title: Transportation Science – volume: 10 start-page: 1096 year: 2010 end-page: 1107 article-title: Multi‐objective vehicle routing problem with time windows using goal programming and genetic algorithm publication-title: Applied Soft Computing – volume: 125 start-page: 137 year: 2010 end-page: 145 article-title: Vehicle routing problems with time windows and stochastic travel and service times: models and algorithm publication-title: International Journal of Production Economics – volume: 202 start-page: 55 issue: 1 year: 2010 end-page: 59 article-title: A compromise solution for the multiobjective stochastic linear programming under partial uncertainty publication-title: European Journal of Operational Research – volume: 177 start-page: 1811 year: 2007 end-page: 1823 article-title: Multi‐objective stochastic programming for portfolio selection publication-title: European Journal of Operational Research – volume: 14 start-page: 371 year: 1983 end-page: 385 article-title: Stochastic vehicle routing: a comprehensive approach publication-title: European Journal of Operational Research – volume: 28 start-page: 95 year: 1994 end-page: 103 article-title: Exact solution of a stochastic location problem by an integer L‐shaped algorithm publication-title: Transportation Science – volume: 13 start-page: 133 year: 1993 end-page: 142 article-title: The integer L‐shaped method for stochastic integer programs with complete recourse publication-title: Operations Research Letters – volume: 6 start-page: 293 year: 2006 end-page: 311 article-title: Travel time reliability in vehicle routing and scheduling with time windows publication-title: Networks and Spatial Economics – volume: 11 start-page: 459 issue: 4 year: 2014 end-page: 473 article-title: An orienteering model for the search and rescue problem publication-title: Computational Management Science – volume: 15 start-page: 1299 issue: 5 year: 1967 end-page: 1314 article-title: Stochastic programs with recourse publication-title: SIAM Journal on Applied Mathematics – volume: 40 start-page: 214 issue: 1 year: 2013 end-page: 224 article-title: Vehicle routing problem with stochastic travel times including soft time windows and service costs publication-title: Computers and Operations Research – volume: 2 start-page: 39 year: 1955 end-page: 45 article-title: The computational algorithm for the parametric objective function publication-title: Naval Research Logistics Quarterly – volume: 6838 start-page: 153 year: 2011 end-page: 161 article-title: Research on vehicle routing problem with stochastic demand based on multi‐objective method publication-title: Lecture Notes in Computer Science – volume: 35 start-page: 773 issue: 6 year: 2007 end-page: 781 article-title: A branch‐and‐price algorithm for the capacitated vehicle routing problem with stochastic demands publication-title: Operations Research Letters – volume: 26 start-page: 161 year: 1992 end-page: 170 article-title: The vehicle routing problem with stochastic travel times publication-title: Transportation Science – volume: 10 start-page: 121 year: 1986 end-page: 32 article-title: A solution of vehicle routing problems in a multiple objective environment publication-title: Engineering Costs and Production Economics |
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| SubjectTerms | Goal programming multi-objective programming Route choice Stochastic models stochastic programming Studies Transportation problem (Operations research) vehicle routing problem Vehicles |
| Title | A Recourse Stochastic Goal Programming Approach for the Multi-objective Stochastic Vehicle Routing Problem |
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