A hybrid GRASP/VND heuristic for the one-commodity pickup-and-delivery traveling salesman problem
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This paper deals with a generalisation of the well-knowntraveling 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 calledone-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 ak-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.