Cost allocation on vehicle routing problem

Co-operative logistics is important to solve several logistics problems, such as a shortage of tracks and drivers, inefficient loading, NO_x pollution and so on. While, current evolvement of computer networks makes it possible to provide various information for common use through networks. And further development of information infrastructure is under way. Under these circumstances, co-operative logistics is socially desired in order to solve logistics problems. However, cost allocation method for co-operative logistics has not been clearly stated so far, and that becomes obstacle for implementating co-operative logistics. This is the paper which gives a solution about how to allocate the transportation costs out of logistics costs. We do not adopt the traditional solutions of co-operative game theory (i.e. Shapley values, core, nucleus, etc.). Instead, we use the expantion solution of Fishburn and Pollark on the Traveling Salesman Game. That is because the number of NP hard problems i.e. Vehicle Routing Problems for getting traditional solutions increases exponentially as the number of customers increases. Furthermore, this paper shows that participants of co-operative logistics should be able to choose their own costs allocation method based on their policies for rental costs and road costs, and also on allocation of saving costs by cooperation. We propose two axioms for cost allocation functions, and some saving functions as well. The furture themes of this problem are how to allocate logistics costs on various conditions (ex. time windows).