具有外包决策的多商品流问题
The Multi-Commodity Flow Problem with Outsourcing Decisions
AI总结：
本文研究含枢纽与非枢纽节点网络中的多商品路由及外包决策，构建 Stackelberg 博弈，证明费用可离散化与问题 NP 困难，并提出多种 MIP 表述及计算分析。
摘要：
我们研究了一个新的奖品收集问题，即在给定的包含枢纽节点和非枢纽节点的网络中安排商品路径，其中非枢纽节点的服务将外包给第三方承运商。该问题被建模为一个 Stackelberg 博弈：存在一家主导企业（领导者），由其决定服务商品的一个子集。领导者的目标是通过向每个非枢纽节点分配至多一个承运商，将运输服务的第一段和第三段外包给较小的承运商（作为跟随者）。承运商努力最大化自身利润，而其利润受领导者报价的影响。领导者的目标是确定最优外包费用以及向非枢纽节点分配承运商的方案，从而使已安排路径商品的利润最大化。必须考虑跟随者的最优反应，因为如果某些运输段的利润为负或不能最大化其利润，跟随者可能拒绝服务这些运输段。我们还研究了两种替代设定：一种是外包费用固定，另一种是只要所得利润非负，承运商就接受任何报价。我们证明可能的外包费用集合可以离散化，并将该问题表述为一个单层混合整数非线性规划。对于所考虑的所有问题变体，我们证明了其 NP 困难性，并提出若干 MIP 表述且进行了计算研究。我们研究了这些 MIP 表述的计算可扩展性，并分析通过改变承运商保留价格所获得的解。最后，通过比较所引入的问题变体，我们得出了一些有趣的管理洞见。
英文摘要：
We address a new prize-collecting problem of routing commodities in a given network with hub and non-hub nodes, in which the service of the non-hub nodes will be outsourced to third-party carriers. The problem is modeled as a Stackelberg game: there is a major firm (leader) that decides to serve a subset of commodities. The leader aims to outsource first and third legs of transportation services to smaller carriers (who act as followers) by allocating at most one carrier to each non-hub node. The carriers try to maximize their own profits, which are influenced by the leader's offers. The goal of the leader is to determine the optimal outsourcing fees, along with the allocation of carriers to the non-hub nodes, so that the profit from the routed commodities is maximized. The optimal response of the followers must be taken into account, as the followers might refuse to serve some legs in case they are negative or do not maximize their profit. We also study two alternative settings: one in which the outsourcing fees are fixed, and the other one in which the carriers accept any offer, as long as the resulting profit is non-negative. We prove that the set of possible outsourcing fees can be discretized and formulate the problem as a single-level mixed-integer nonlinear program. For all considered problem variants, we prove NP-hardness and propose and computationally investigate several MIP formulations. We study the computational scalability of these MIP formulations and analyze solutions obtained by varying the reservation prices of the carriers. Finally, by comparing the introduced problem variants, we derive some interesting managerial insights.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
