TY - JOUR

T1 - Solving the Single Vehicle Routing Problem with Variable Capacity

AU - Louveaux, Francois V.

AU - Salazar-Gonzalez, Juan-Jose

PY - 2016/5

Y1 - 2016/5

N2 - This paper considers the classical vehicle routing problem (VRP) where the vehicle capacity is not fixed. Indeed, at the moment of acquiring (or renting) the vehicle that will serve all customers, there is some freedom of choice. A larger vehicle capacity implies a lower total distance travelled but larger operating costs. The reverse is true for a smaller vehicle. This paper gives an approach to select the best capacity and the best route to minimize a function of the acquisition cost and travelled distance.We first consider an enumerative approach, which consists of solving a sequence of VRPs, starting from the one having the largest capacity. The number of VRPs to solve using this approach is unknown. Based on computational experiments, this number is mostly large in our benchmark instances. We then proceed to a direct approach based on the two-index formulation of the VRP. We introduce several valid inequalities that allow us to have an integer linear programming formulation of the VRP with fixed vehicle capacity. We describe separation procedures for these inequalities. We conclude with computational results that confirm the utility of these inequalities when solving benchmark VRP instances.

AB - This paper considers the classical vehicle routing problem (VRP) where the vehicle capacity is not fixed. Indeed, at the moment of acquiring (or renting) the vehicle that will serve all customers, there is some freedom of choice. A larger vehicle capacity implies a lower total distance travelled but larger operating costs. The reverse is true for a smaller vehicle. This paper gives an approach to select the best capacity and the best route to minimize a function of the acquisition cost and travelled distance.We first consider an enumerative approach, which consists of solving a sequence of VRPs, starting from the one having the largest capacity. The number of VRPs to solve using this approach is unknown. Based on computational experiments, this number is mostly large in our benchmark instances. We then proceed to a direct approach based on the two-index formulation of the VRP. We introduce several valid inequalities that allow us to have an integer linear programming formulation of the VRP with fixed vehicle capacity. We describe separation procedures for these inequalities. We conclude with computational results that confirm the utility of these inequalities when solving benchmark VRP instances.

KW - vehicle routing problem

KW - unknown vehicle capacity

KW - branch-and-cut algorithm

KW - ALGORITHMS

U2 - 10.1287/trsc.2014.0556

DO - 10.1287/trsc.2014.0556

M3 - Journal article

VL - 50

SP - 708

EP - 719

JO - Transportation Science

JF - Transportation Science

SN - 0041-1655

IS - 2

ER -