The One-Commodity Pickup-and-Delivery Travelling Salesman Problem

This article deals with a new generalization of the well-known "Travelling Salesman Problem" (TSP) in which cities correspond to customers providing or requiring known amounts of a product, and the vehicle has a given capacity and is located in a special city called depot. Each customer and the depot must be visited exactly once by the vehicle serving the demands while minimizing the total travel distance. It is assumed that the product collected from pickup customers can be delivered to delivery customers. The new problem is called "onecommodity Pickup-and-Delivery TSP" (1-PDTSP). We introduce a 0-1 Integer Linear Programming model for the 1-PDTSP and describe a simple branch-and-cut procedure for finding an optimal solution. The proposal can be easily adapted for the classical "TSP with Pickup-and-Delivery" (PDTSP). To our knowledge, this is the first work on an exact method to solve the classical PDTSP. Preliminary computational experiments on a test-bed PDTSP instance from the literature show the good performances of our proposal.