Heuristic algorithm for the Split-Demand One-Commodity Pickup-and-Delivery Travelling Salesman Problem

This article addresses the problem of designing routes of minimum cost for a capacitated vehicle moving a commodity between a set of customers, allowing two characteristics uncommon in the pickup-and-delivery literature. One characteristic is that a customer may be visited several times. The other characteristic is that a customer may be used as intermediate location to temporarily collect and deliver product. The article describes a matheuristic algorithm that iteratively applies a constructive procedure and a refinement procedure. The constructive procedure represents each customer by a set of nodes each one associated with a potential visit|, decomposes each customer demand into partial demands associated with its nodes, and solves a one-commodity pickup-and-delivery Travelling Salesman Problem with a variable neighbourhood search. The refinement procedure is a branch-and-cut algorithm to optimize some pieces of a given solution. Exhaustive computational results on benchmark instances demonstrate the good performance of the algorithm when solving instances with up to 500 customers.