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

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.