Heuristics for the traveling salesman problem with pickup and delivery

Abstract

We consider the Traveling Salesman Problem with Pickup and Delivery (TSPPD), an extension of the well-known Traveling Salesman Problem where each customer to be served is associated with two quantities of goods to be collected and delivered, respectively. A vehicle with given capacity starts at a depot and must visit each customer exactly once. The vehicle capacity must not be exceeded and the total length of the tour must be minimized. We describe new heuristics for TSPPD, the first based on the exact solution of a special case and the second based on tabu search, and we analyze their average performance through extensive computational experiments. Scope and purpose In several industries vehicles must routinely visit customers and make at each visit a pickup and a delivery. Clearly this must be accomplished without ever violating the vehicle capacity. A common example arises in beer or soft drinks delivery where full bottles must be delivered and empty bottles must be collected. We study this problem for the case of a single vehicle. Since the problem is extremely hard to solve to optimality, we have developed a number of heuristics and tested them on a large number of instances exhibiting different characteristics.