An exact algorithm to solve the vehicle routing problem with stochastic demands under an optimal restocking policy

•We present an exact method to solve vehicle routing problem with stochastic demands.•We lower approximate the optimal restocking policy to bound recourse function.•We enhance the Integer L-shaped method by redefining lower bounding functionals.•We can solve problems with 100 customers having arbitr...

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Bibliographic Details
Published in:European journal of operational research Vol. 273; no. 1; pp. 175 - 189
Main Authors: Salavati-Khoshghalb, Majid, Gendreau, Michel, Jabali, Ola, Rei, Walter
Format: Journal Article
Language:English
Published: Elsevier B.V 16.02.2019
Subjects:
Integer L-shaped algorithm
Lower bounding functionals
Optimal restocking policy
Routing
Stochastic demands
Routing
Lower bounding functionals
Optimal restocking policy
Integer L-shaped algorithm
Stochastic demands
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•We present an exact method to solve vehicle routing problem with stochastic demands.•We lower approximate the optimal restocking policy to bound recourse function.•We enhance the Integer L-shaped method by redefining lower bounding functionals.•We can solve problems with 100 customers having arbitrary discrete demands. This paper examines the Vehicle Routing Problem with Stochastic Demands (VRPSD), in which the actual demand of customers can only be realized upon arriving at the customer location. Under demand uncertainty, a planned route may fail at a specific customer when the observed demand exceeds the residual capacity. There are two ways to face such failure events, a vehicle can either execute a return trip to the depot at the failure location and refill the capacity and complete the split service, or in anticipation of potential failures perform a preventive return to the depot whenever the residual capacity falls below a threshold; overall, these return trips are called recourse actions. In the context of VRPSD, a recourse policy which schedules various recourse actions based on the visits planned beforehand on the route must be designed. An optimal recourse policy prescribes the cost-effective returns based on a set of optimal customer-specific thresholds. We propose an exact solution method to solve the multi-VRPSD under an optimal restocking policy. The Integer L-shaped algorithm is adapted to solve the VRPSD in a branch-and-cut framework. To enhance the efficiency of the presented algorithm, several lower bounding schemes are developed to approximate the expected recourse cost.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2018.07.039