Nucleolus based cost allocation methods for a class of constrained lane covering games

In truckload transportation procurement networks, shippers purchasing the services of truckload carriers seek to form multi-company tours which consist of regularly scheduled shipments with minimal empty truck movements with the aim of getting better rates from the carriers in return. Identifying the minimum cost collaborative solution and sharing the costs in a fair manner are two interrelated and critical tasks for the success of such networks. The restrictions on the tours which can be formed make both of these tasks very challenging. In this paper, we take a cooperative game theory approach and study the resulting constrained lane covering game. We first show the set of conditions which must be satisfied for the game to have a non-empty core. We propose nucleolus based cost allocation methods. We also develop column and row generation methods for solving these mathematical models. We compare our proposed cost allocation models with alternative cost allocation methods and each other using a set of core stability metrics through computational experiments on randomly generated instances from the literature.