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.

我们研究了形成一个核心稳定联盟的问题，该联盟最小化系统范围的成本，给定一组候选的整车装运车道，我们将其建模为参与者，以及对应于解决 NP-Hard 成本最小化车道覆盖问题的特征函数. 由于在此设置中并非每个联盟都具有非空核心，因此我们制定了一个混合整数线性程序，该程序可以识别具有最小系统范围成本的核心稳定联盟以及核心中的成本分配。我们提出了一种将行生成、列生成和上限启发式嵌入到分支定界中的解决方法，可以将其视为分支和切割价格的一种形式。我们通过对随机生成的问题实例进行广泛的数值实验来评估我们的解决方案方法的性能。