Core stable coalition selection in collaborative truckload transportation procurement

We study the problem of forming a core stable coalition that minimizes system-wide cost, given a set of candidate full truckload shipment lanes, which we model as players, and a characteristic function that corresponds to solving an NP-Hard cost minimizing lane covering problem. Since not every coalition has a non-empty core in this setting, we formulate a mixed integer linear program that can identify a core stable coalition with minimal system-wide cost along with a cost allocation in the core. We propose a solution method that embeds row generation, column generation, and an upper bounding heuristic into branch-and-bound, which can be considered as a form of branch-and-cut-and-price. We evaluate the performance of our solution method through extensive numerical experiments on randomly generated problem instances.