Optimized Shapley value cost allocation model for carriers’ collaboration in road haulage transportation

Abstract

Transportation carriers can achieve significant profit or cost savings if they collaborate rather than engage in wasteful competition among themselves. However, the challenge in cooperative game theory is finding the optimal cost allocation methods to support pecuniary expectations of coalition members. In this paper, we determine cost allocation model that supports horizontal collaboration among transportation carriers involved in downstream distribution of packaged cement from shipper’s processing plant to customer locations in selected states in Nigeria. The study focuses on the relationship between the shipper and haulage carriers that service the transport needs of its geographically distributed customers. A cost allocation mechanism based on game theory is proposed to implement win-win collaboration among the carriers. We applied a Shapley value cost allocation model to fairly distribute the cost savings from operation of five grand coalitions (S) formed by the carriers. The Shapely values were then optimized with mixed integer programming model to realize optimal cost savings from the coalition. The result revealed that the coalitions: S3 (N165,173,700.00) and S4 (N27,200,960.00) contributed significantly to the optimal savings apart from their initial contributions. The path that corresponds to S3 (X3) is the coalition providing service from Calabar to Jos while the path that corresponds to S4 (X4) is the coalition providing service from Calabar to Owerri and the optimal savings is N48,286,760,000.00. Based on these results, we therefore encourage horizontal collaboration among haulage transport providers in their overall interest, that of the shipper and hence ensure supply or distribution chain cost efficiency.

Keywords

• Shapley value
• mixed-integer programming
• haulage transportation carriers
• transport distribution chain
• cost allocation