Group for Research in Decision Analysis

Time Consistent Collaboration in Cargo Transportation

Victor V. Zakharov Saint Petersburg State University, Russia

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.