Stable cooperation in dynamic VRP

In the paper the problem of carriers transportation cost in the cooperative vehicle routing problem (VRP) on large-scale networks is treated. A heuristic method for calculation subadditive characteristic function in the TU-cooperative dynamic VRP game is proposed. The algorithm is updated for the dynamic cooperative VRP game. Shapley value and the subcore concept is used to form an optimal solution. A cost distribution procedure which provides strong time consistency of the subcore and the dynamic stability of cooperation agreement is developed and demonstrated.