An Integer L-shaped algorithm for vehicle routing problem with simultaneous delivery and stochastic pickup

Abstract

This paper addresses an exact algorithm for vehicle routing problem with simultaneous pickup and delivery in which customer demands to be collected are stochastic. The problem is modeled as a two-stage stochastic programming problem with recourse, in which routing decisions are made based on known delivery demand and deterministic expected pickup demand in the first stage and recourse actions are made in the second stage when stochastic pickup quantities have been revealed. However, failures happen when the load of the vehicle is insufficient to meet the observed pickup demand of a customer. Three recourse policies are proposed to help deal with the failures to proceed with the routing decisions in the first stage. The Integer L-shaped algorithmic framework is used to solve this two-stage stochastic programming problems with recourse. Furthermore, effective lower bounding of the expected recourse cost of partial routes is designed for the three recourse policies, respectively. Computational experiments on the newly generated instances compare the performance of the Integer L-shaped algorithm under the three recourse policies, and the conclusion is validated via numerous simulations. The effectiveness of the proposed lower bounding functionals is confirmed through reduced optimality gaps and lower computing times.