This paper deals with a generalisation of the well-known traveling salesman problem (TSP) in which cities correspond to customers providing or requiring known amounts of a product, and the vehicle has a given upper limit capacity. Each customer must be visited exactly once by the vehicle serving the demands while minimising the total travel distance. It is assumed that any unit of product collected from a pickup customer can be delivered to any delivery customer. This problem is called one-commodity pickup-and-delivery TSP (1-PDTSP). We propose two heuristic approaches for the problem: (1) is based on a greedy algorithm and improved with a k-optimality criterion and (2) is based on a branch-and-cut procedure for finding an optimal local solution. The proposal can easily be used to solve the classical “TSP with pickup-and-delivery,” a version studied in literature and involving two commodities. The approaches have been applied to solve hard instances with up to 500 customers.
This article concerns the "One-commodity Pickup-andDelivery Traveling Salesman Problem" (1-PDTSP), in which a single vehicle of fixed capacity must either pick up or deliver known amounts of a single commodity to a given list of customers. It is assumed that the product collected from the pickup customers can be supplied to the delivery customers, and that the initial load of the vehicle leaving the depot can be any quantity. The problem is to find a minimum-cost sequence of the customers in such a way that the vehicle's capacity is never exceeded. This article points out a close connection between the 1-PDTSP and the classical "Capacitated Vehicle Routing Problem" (CVRP), and it presents new inequalities for the 1-PDTSP adapted from recent inequalities for the CVRP.
This paper treats of a generalization of the Traveling Salesman Problem (TSP) called Multi-commodity one-to-one Pickup-and-Delivery Traveling Salesman Problem (m-PDTSP) in which cities corresponds to customers providing or requiring known amounts of m different objects, and the vehicle has a given upper-limit capacity. Each object has exactly one origin and one destination, and the vehicle must visit each customer exactly once. This justifies the words "one-to-one" and "traveling salesman problem" in the name of the problem, respectively. We introduce a Mixer Integer Linear Programming model for the m-PDTSP, discuss decomposition techniques and describe some strategies to solve the problem based on a branchand-cut procedure. Preliminary computational experiments on randomly generated euclidian instances are shown.
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