The single-vehicle two-echelon one-commodity pickup and delivery problem

We present in this paper a generalization of the one-commodity pickup and delivery traveling salesman problem where each customer supplies or demands a given amount of a certain product. The objective is to design a minimum cost two-echelon transportation network. The first echelon is the route of a capacitated vehicle that visits some customers, and the second echelon consists in the allocation of the non-visited customers to visited ones. The customers that must be visited by the vehicle and the ones that must be allocated to others are not predefined. We present three mathematical models for the problem, design an exact branch-and-cut algorithm to solve it, and show extensive computational results on benchmark instances. (C) 2020 Elsevier Ltd. All rights reserved.