Stable cooperation in dynamic vehicle routing problems

This paper explores transportation cost minimization in the vehicle routing problem under carriers’ cooperation on large‐scale transport networks. The underlying model is a dynamic cooperative game with transferable utility (TU) functions. We propose a heuristic iterative algorithm for constructing the subadditive characteristic function of the corresponding static game. The algorithm is modified in order to construct the characteristic function of the dynamic routing game. The Shapley value and the subcore concept serve to form the optimal solutions. And finally, we describe a cost distribution procedure in the dynamic game, which guarantees the strong time consistency of the subcore and the dynamic stability of the cooperation agreement.