Cooperation of Customers in Traveling Salesman Problems with Profits

5 Pages Posted: 25 Nov 2019

See all articles by Ondrej Osicka

Ondrej Osicka

Norwegian School of Economics (NHH) - Department of Business and Management Science

Mario Guajardo

Norwegian School of Economics (NHH) - Department of Business and Management Science

Kurt Jornsten

Norwegian School of Economics (NHH) - Department of Business and Management Science

Date Written: November 22, 2019

Abstract

The traveling salesman problem and its variants are among the most studied problems in the literature on transportation and logistics. In one of these variants known as the profitable tour problem [2], a profit-maximizing carrier decides whether to visit a particular customer with respect to the prize the customer offers for being visited and traveling cost associated with the visit, all in the context of other customers. The purpose of this paper is to define the profitable tour game, a cooperative version of the profitable tour problem, and to derive its properties. We are particularly interested in prize allocations that create incentives for the carrier to visit all relevant customers.

Applications of the profitable tour game might include for example situations in shipping where a carrier is able to serve demands of several customers with a single vehicle. Whether it comes to delivery or pickup of goods, the customers might need to induce the carrier to visit them by offering sufficient rewards. Subsequently, negotiation with other customers in the same position could lead to better prizes while the carrier's visit would remain guaranteed. This knowledge could also be utilized by the carrier by offering specifically tailored discounts on multiple orders from the same area or by evaluating and pricing of new customers.

Keywords: Traveling salesman problem, Profitable tour problem, Prize-collecting TSP, Logistics, Cooperative game theory, Prize allocation

JEL Classification: C00, C71

Suggested Citation

Osička, Ondřej and Guajardo, Mario and Jornsten, Kurt, Cooperation of Customers in Traveling Salesman Problems with Profits (November 22, 2019). NHH Dept. of Business and Management Science Discussion Paper No. 2019/17, Available at SSRN: https://ssrn.com/abstract=3491771

Ondřej Osička (Contact Author)

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

Mario Guajardo

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

Kurt Jornsten

Norwegian School of Economics (NHH) - Department of Business and Management Science ( email )

Helleveien 30
Bergen, NO-5045
Norway

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