Sharing orders or vehicles? Multi-carrier robust service network design problem

The substantial increase in order volume has resulted in a highly competitive freight market, which requires horizontal collaboration among carriers to guarantee cost-effective and timely delivery in transportation. In this case, the collaborative methods implemented by the carriers obviously impact the freight capacities. Hence, to our best knowledge, this paper investigates the collaborative service network design problem under the frameworks of order sharing and vehicle sharing for the first time. Meanwhile, in response to fluctuations in customer demand, we develop a novel two-stage robust optimization model based on the budget uncertainty set for each collaborative framework. Given the NP-hard nature of solving these formulas, an innovative smart-downscale-scenario column-and-constraint generation algorithm is designed to solve the proposed models efficiently, which embeds a linear classifier that identifies scenarios beneficial for convergence. A comparative analysis with the column-and-constraint generation algorithm shows the advantages of our proposed method, which achieves a 25% improvement in solution speed with only a minimal loss in accuracy. In addition, a qualitative analysis of the solution structures is conducted in various collaborative frameworks to demonstrate their flexibility in managing uncertain demand. Based on generated small-scale instances, the results suggest that when the unit outsourcing cost is high, the order sharing framework is more effective for scenarios characterized by low demand volatility; conversely, the vehicle sharing framework is deemed more appropriate for contexts with high demand volatility. Finally, we explore the grand coalition stability through the cooperative game core allocation method.