Branch-Price-and-Cut Algorithms for the Vehicle Routing Problem with Stochastic and Correlated Travel Times

被引:9
|
作者
Rostami, Borzou [1 ,2 ]
Desaulniers, Guy [3 ,4 ]
Errico, Fausto [4 ,5 ,6 ]
Lodi, Andrea [2 ,4 ]
机构
[1] Wilfrid Laurier Univ, Lazaridis Sch Business & Econ, Waterloo, ON N2L 3C5, Canada
[2] Polytech Montreal, Canada Excellence Res Chair CERC Data Sci Real Ti, Montreal, PQ H3C 3A7, Canada
[3] Polytech Montreal, Dept Math & Ind Engn, Montreal, PQ H3C 3A7, Canada
[4] Grp Res Decis Anal GERAD, Montreal, PQ H3T 1J4, Canada
[5] Ecole Technol Super Montreal, Dept Civil Engn, Montreal, PQ H3C 1K3, Canada
[6] Interuniv Res Ctr Enterprise Networks Logist & Tr, Montreal, PQ H3T 1J4, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
vehicle routing; uncertain travel times; correlation; convex quadratic programming; branch-price-and-cut;
D O I
10.1287/opre.2020.2037
中图分类号
C93 [管理学];
学科分类号
12 ; 1201 ; 1202 ; 120202 ;
摘要
In this paper, we consider a version of the capacitated vehicle routing problem (CVRP) where travel times are assumed to be uncertain and statistically correlated (CVRP-SCT). In particular, we suppose that travel times follow a multivariate probability distribution whose first and second moments are known. The main purpose of the CVRP-CST is to plan vehicle routes whose travel times are reliable, in the sense that observed travel times are not excessively dispersed with respect to their expected value. To this scope we adopt a mean-variance approach, where routes with high travel time variability are penalized. This leads to a parametric binary quadratic program for which we propose two alternative set partitioning reformulations and show how to exploit the structure of the correlation matrix when there is correlation only between adjacent links. For each model, we develop an exact branch-price-and-cut algorithm, where the quadratic component is dealt with either in the column generation master problem or in its subproblem. We tested our algorithms on a rich collection of instances derived from well-known data sets. Computational results show that our algorithms can efficiently solve problem instances with up to 75 customers. Furthermore, the obtained solutions significantly reduce the time variability when compared with standard CVRP solutions.
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页码:436 / 455
页数:20
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