This thesis concerns cost allocation problems in distribution planning. The cost allocation problems we study are illustrated using the distribution planning situation at the Logistics department of Norsk Hydro Olje AB. The planning situation is modeled as a Traveling Salesman Problem and a Vehicle Routing Problem with an inhomogeneous fleet. The cost allocation problems are the problems of how to divide the transportation costs among the customers served in each problem. The cost allocation problems are formulated as cooperative games, in characteristic function form, where the customers are defined to be the players. The games contain five and 21 players respectively. Game theoretical solution concepts such as the core, the nucleolus, the Shapley value and the (tau)-value are discussed. From the empirical results we can, among other things, conclude that the core of the Traveling Salesman Game is large, and that the core of the Vehicle Routing Game is empty. In the accounting of Norsk Hydro the cost per m(sup 3) can be found for each tour. We conclude that for a certain definition of the characteristic function, a cost allocation according to this principle will not be included in the core of the Traveling Salesman Game. The models and methods presented in this thesis can be applied to transportation problems similar to that of Norsk Hydro, independent of the type of products that are delivered. 96 refs, 11 figs, 26 tabs
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