To study collaboration in cargo routing we address the following key questions related to collaborative logistics:
How does one evaluate the maximum potential benefit from collaborating? In many cases, it can be done by finding the centralized system optimal solution. However, to obtain such a solution is not easy because the underlying computational problem is NP hard.
How should a membership mechanism be formed to be consistent during sufficiently long period of time, and what are the desired properties that such a mechanism should possess? This issue is closely connected with the time consistency of cooperative game solutions.
How should the benefits achieved by collaborating be allocated among the members in a "fair" way? In the cargo transportation routing setting we investigate what does a "fair" allocation mean and how such an allocation may be achieved in the context of day-to-day operations to be time consistent during transportation process.
To answer these questions we will discuss in the talk a cooperative game theory approach to model collaboration in cargo transportation on large-scale networks. The problem of assessment of carriers transportation cost in the cooperative vehicle routing problem (VRP) is treated. A heuristic method for calculation subadditive characteristic function in the static and dynamic TU-cooperative VRP game is proposed. Shapley value and the Subcore concept are used to form an optimal solution in the game. A cost sharing procedure which provides strong time consistency of the Subcore and the dynamic stability of collaboration agreement is described and demonstrated on sample examples.