Abstract
The capacitated vehicle routing problem with stochastic demands can be modelled using either the chance-constrained approach or the recourse approach. In previous works, we extended the former approach to address the case where uncertainty on customer demands is represented by belief functions, that is where customers have so-called evidential demands. In this paper, we propose an extension of the recourse approach for this latter case. We also provide a technique that makes computations tractable for realistic situations. The feasibility of our approach is then shown by solving instances of this difficult problem using a metaheuristic algorithm.
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Notes
- 1.
The problem can also presented in terms of delivery, rather than collection, of goods.
References
Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer, New York (1997)
Bodin, L.D., Golden, B.L., Assad, A.A., Ball, M.O.: Routing and scheduling of vehicles and crews: the state of the art. Comput. Oper. Res. 10(2), 63–212 (1983)
Denoeux, T.: Analysis of evidence-theoretic decision rules for pattern classification. Pattern Recogn. 30(7), 1095–1107 (1997)
Dror, M., Laporte, G., Trudeau, P.: Vehicle routing with stochastic demands: properties and solution frameworks. Transport. Sci. 23(3), 166–176 (1989)
Gauvin, C., Desaulniers, G., Gendreau, M.: A branch-cut-and-price algorithm for vehicule routing problem with stochastic demands. Comput. Oper. Res. 50, 141–153 (2014)
Harmanani, H., Azar, D., Helal, N., Keirouz, W.: A simulated annealing algorithm for the capacitated vehicle routing problem. In: 26th International Conference on Computers and Their Applications, New Orleans, USA (2011)
Helal, N., Pichon, F., Porumbel, D., Mercier, D., Lefèvre, É.: The capacitated vehicle routing problem with evidential demands: a belief-constrained programming approach. In: Vejnarová, J., Kratochvíl, V. (eds.) BELIEF 2016. LNCS, vol. 9861, pp. 212–221. Springer, Cham (2016). doi:10.1007/978-3-319-45559-4_22
Masri, H., Ben Abdelaziz, F.: Belief linear programming. Int. J. Approx. Reason. 51, 973–983 (2010)
Mourelatos, Z.P., Zhou, J.: A design optimization method using evidence theory. J. Mech. Design 128, 901–908 (2006)
Vehicle Routing Data sets. http://www.coin-or.org/SYMPHONY/branchandcut/VRP/data/index.htm. Accessed 20 Mar 2016
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Srivastava, R.K., Deb, K., Tulshyan, R.: An evolutionary algorithm based approach to design optimization using evidence theory. J. Mech. Design 135(8), 081003-12 (2013)
Sungur, I., Ordónez, F., Dessouky, M.: A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty. IIE Trans. 40, 509–523 (2008)
Stewart Jr., W.R., Golden, B.L.: Stochastic vehicle routing: a comprehensive approach. Eur. J. Oper. Res. 14(4), 371–385 (1983)
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Helal, N., Pichon, F., Porumbel, D., Mercier, D., Lefèvre, É. (2017). A Recourse Approach for the Capacitated Vehicle Routing Problem with Evidential Demands. In: Antonucci, A., Cholvy, L., Papini, O. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2017. Lecture Notes in Computer Science(), vol 10369. Springer, Cham. https://doi.org/10.1007/978-3-319-61581-3_18
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