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The Multiple Travelling Salesman Problem with a Multiple Number of Paths per Route
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This paper gives a formulation of a routing problem that we believe covers a vast number of real-life situations. The problem consists in designing routes for vehicles and salesmen that, starting from a single depot, will supply n-l customers, with given quantities of a certain commodity. For each vehicle, certain salesmen are selected to leave the depot inside the vehicle. At each stop along the route of each vehicle, the salesmen assigned to it can leave the vehicle and start a walking route, serving the customers along this route and returning to the vehicle at the node where this walking route had started. The goal in designing routes is to minimize the total distribution time. Constraints concerning load capacity and maximum distances to be covered by each vehicle and each salesmen are considered. We also assume that each costumer is served once and only once by a single vehicle or a single salesman and that the time period from departure to arrival back at the depot for each vehicle, is bounded above by some value. We call this problem the multiple travelling salesmen problem with a multiple number of paths per route. A combinatorial formulation of this problem is first presented, based on which a 0,1 formulation is established.
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Cerdeira, J. O. and Coelho, J. D., The Multiple Travelling Salesman Problem with a Multiple Number of Paths per Route (January, 1983). FEUNL Working Paper Series No. 3