A collaborative approach based on Shapley value for carriers in the supply chain distribution

This paper addresses the problem of horizontal collaboration between carriers at the tactical planning level of the supply chain distribution. The study focuses on the relationship between a shipper and many carriers used to serve the transport requests of several geographically distributed customers. A profit sharing mechanism based on game theory is proposed in order to implement win-win collaboration between the carriers. The Shapley value is used to fairly share the profit of the grand coalition between the carriers. The collaboration is supported by mixed-integer linear programming model for the transport planning of all possible coalitions consisted by the carriers. The transport plans and the profit of each carrier can be generated by model simulation. The validity of the collaboration is checked by the super-additivity property of the game in each experiment. According to the subcontracting is allowed or not, the experimentations are carried out in two different contexts with realistic data sets. The experimental results show that each carrier's profit improvement is significant for all experiments, and that the collaboration also improves the customer service rate.