Core-based cost allocation for collaborative multi-stop truckload shipping problem

Abstract

With the recently emerged digital platforms in logistics, shippers can easily collaborate by bundling their heavy less-than-truckload orders via multi-stop truckload shipping to reduce transportation cost. The platform has responsibility for planning the shipping routes, for bundling the orders and fairly allocating the cost to shippers. To address this challenging problem in practice, we propose a new cooperative game based on a variant of a pickup and delivery model with soft time windows for shipper collaboration. The centralized optimization model is NP-hard and the core of the game may be empty. We adopt the least-core concept and simplify the core stability constraints as route-wise conditions. Based on theoretical results, we propose an innovative route-generation joint searching algorithm that iteratively solves the centralized optimization and least-core allocation problems at the same time, where the route-generation subproblem is solved by a customized multi-start local search subroutine. Extensive computational experiments on a real-world case demonstrate that the proposed algorithm can quickly generate a near-optimal solution with minor optimality gap and a least-core allocation with small stability deviation. With our algorithm, the shippers also receive substantial cost savings from collaboration.

Keywords:

• Multi-stop truckload shipping
• collaborative logistics
• cooperative game
• least-core
• column-and-row-generation

Data availability statement

The authors confirm that the data supporting the findings of this study are available at https://github.com/laimhx/BundleShipping/tree/main/.

Acknowledgments

The authors appreciate valuable comments by the Editor-in-Chief, Department Editor, Associate Editor, and the two anonymous referees that helped improve the paper.

Additional information

Funding

The authors acknowledge the generous support from the National Natural Science Foundation of China (Nos. 71971057, 72231002, 72371070) and the Fundamental Research Funds for the Central Universities (No. 2242022R 40021).

Notes on contributors

Minghui Lai

Minghui Lai is an associate professor in the School of Economics and Management, Southeast University, Nanjing. He received his PhD from the Chinese University of Hong Kong, Hong Kong. His research interest lies in the design and operations of digital platforms, including logistics, transportation, and energy. He has published dozens of papers in leading logistics and transportation journals, including Transportation Science, Transportation Research Part C and E, European Journal of Operational Research, etc.

Yating Wu

Yating Wu is a PhD candidate in the School of Economics and Management, Southeast University, Nanjing. Her current research interests are in the operations of logistics and transportation digital platforms.

Xiaoqiang Cai

Xiaoqiang Cai is a Presidential Chair Professor in The Chinese University of Hong Kong-Shenzhen. He received his PhD from Qinghua University and conducted postdoctoral researches at the University of Cambridge and the Queen’s University of Belfast, UK. His research interest are mainly in industrial and systems engineering, operations research, and logistics and supply chain management science.