In this paper, we study a cost-allocation problem that arises in a distribution-planning situation at the Logistics Department at Norsk Hydro Olje AB, Stockholm, Sweden. We consider the routes from one depot during one day. The total distribution cost for these routes is to be divided among the customers that are visited. This cost-allocation problem is formulated as a vehicle-routing game (VRG), allowing the use of vehicles with different capacities. Cost-allocation methods based on different concepts from cooperative game theory, such as the core and the nucleolus, are discussed. A procedure that can be used to investigate whether the core is empty or not is presented, as well as a procedure to compute the nucleolus. Computational results for the Norsk Hydro case are presented and discussed.

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In memory of Åsa HallefjordIn this article, a cost allocation problem that arises in a distribution planning situation at the Logistics Department at Norsk Hydro Olje AB is studied. A specific tour is considered, for which the total distribution cost is to be divided among the customers that are visited. This problem is formulated as a traveling salesman game, and cost allocation methods based on different concepts from cooperative game theory, such as the nucleolus, the Shapley value and the τ-value, are discussed. Additionally, a new concept is introduced: the demand nucleolus. Computational results for the Norsk Hydro case are presented and discussed.

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