异质成本批量订购问题中的合作：合并周期的影响
Cooperation in lot-sizing problems with heterogeneous costs: the effect of consolidated periods
AI总结：
针对异质成本经济批量订购合作博弈，证明了存在公平稳定的成本分配方式，提出参数化成本分配族及稳定充分条件，并分析了合并周期对分配稳定性的影响。
摘要：
我们研究了有限时间跨度下由异质成本经济批量订购问题定义的合作博弈，其中每个企业在每个周期都面临单一产品的需求，联盟可以集中订单。合作模式如下：联盟成员共享订购渠道、库存持有技术和缺货积压技术。这意味着每个企业都使用联盟参与方提供的最优订购渠道和库存持有技术，即它们以联盟成员的最低成本进行采购、持有库存、支付缺货需求成本和下达订单。因此，企业的目标是以最低运营成本满足规划周期内的需求。我们的贡献在于证明了企业间存在整体运营成本的公平分配方式，使得任何代理群体都无法通过退出联盟获利。随后，我们提出了一个参数化的成本分配族，并给出了该分配族能抵御企业联盟背叛的充分条件。最后，我们聚焦于时间跨度内被合并的周期，分析了它们对成本分配稳定性的影响。
英文摘要：
We consider a cooperative game defined by an economic lot-sizing problem with heterogeneous costs over a finite time horizon, in which each firm faces demand for a single product in each period and coalitions can pool orders. The model of cooperation works as follows: ordering channels and holding and backlogging technologies are shared among the members of the coalitions. This implies that each firm uses the best ordering channel and holding technology provided by the participants in the consortium. That is, they purchase, hold inventory, pay backlogged demand and make orders at the minimum cost of the coalition members. Thus, firms aim at satisfying their demand over the planing horizon with minimal operation cost. Our contribution is to show that there exist fair allocations of the overall operation cost among the firms so that no group of agents profit from leaving the consortium. Then we propose a parametric family of cost allocations and provide sufficient conditions for this to be a stable family against coalitional defections of firms. Finally, we focus on those periods of the time horizon that are consolidated and we analyze their effect on the stability of cost allocations.
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