Mixed-Integer Linear Programming Models for One-Commodity Pickup and Delivery Traveling Salesman Problems

Abstract

This article addresses two different pickup and delivery routing problems. In the first one, called the one-commodity pickup and delivery traveling salesman problem, a known amount of a single product is supplied or demanded by a set of two different types of locations (pickup or delivery nodes). Therefore, a capacitated vehicle must visit each location once at a minimum cost. We also deal with the relaxed case where locations can be visited several times. In the last problem, the pickup or delivery operation can be split into several smaller pickups or deliveries, and also locations can be used as temporal storage points with the aim of reducing the cost of the route. To solve these problems, we present two mixed-integer linear programming models and we solve them via commercial solver. We analyze how several visits to a single location may improve solution quality and we also show that our simple strategy has a good performance for instances with up to 60 locations.