Fair cost allocation for collaborative hub networks

Collaboration in logistics is an effective tool not only for cost savings but also for reducing the carbon footprint. Hub networks take advantage of scale economies by bundling flows. Merging hub networks through horizontal collaboration unlocks further economic and environmental advantages. We consider the problem of designing a collaborative hub network as a cooperative game and show that the core of the game might be empty, meaning that an efficient and stable cost allocation does not exist. Our key novelty lies in formulating this design problem as a cooperative game and demonstrating the potential absence of a fair and stable solution. Various game theoretical approaches are used for the allocation of joint costs due to the collaboration. Each approach is also tested through extensive numerical experiments to gain insight into the features and behavior of the corresponding cost allocation game. These experiments are conducted on both randomly generated and also real-world hub location instances. Achieving a stable and also fair cost allocation among collaborators is critical for the future of the organization. Finally, we compare the performance of the nucleolus, the Shapley value and the least core cost allocation methods based on different fairness measures such as relative savings, stability concepts and coalition satisfaction. This work ultimately paves the way for more efficient and sustainable logistics operations by measuring the value of collaboration in hub network design and minimizing the operating costs and also environmental footprint of the logistics industry.