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The multi-commodity pickup-and-delivery traveling salesman problem



The “multi-commodity Pickup-and-Delivery Traveling Salesman Problem” (m-PDTSP) is a generalization of the well-known “Traveling Salesman Problem” in which cities correspond to customers providing or requiring known amounts of m different products, and the vehicle has a known capacity. Each customer must be visited exactly once by the vehicle serving the demands of the different products while minimizing the total travel distance. It is assumed that a unit of a product collected from a customer can be supplied to any other customer that requires this product. We introduce a mixed integer linear programming model for the m-PDTSP, discuss a classical decomposition technique, describe valid inequalities to strengthen the linear programming relaxation of the model, and detail separation procedures to develop a branch-and-cut procedure. Computational experiments on randomly generated instances with up to 30 customers, three products, and small vehicle capacities are analyzed. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 63(1), 46–59 2014