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.
翻译:我们考虑一种合作游戏,其定义是经济大宗化问题,在有限的时间范围内,费用不一,每个公司在每一时期都面临单一产品的需求,联盟可以集合订单。合作模式的运作方式如下:联盟成员分享订购渠道、持有和回击技术,这意味着每个公司使用联营集团参与者提供的最佳订购渠道和持有技术,即购买、持有库存、支付积压需求并以联盟成员的最低成本来支付订单。因此,公司的目标是在规划地平线上以最低运营成本满足其需求。我们的贡献是表明,各公司之间对总运营成本有公平的分配,以便没有一批代理商从离开联营集团中获利。然后,我们提出一个成本分配的参数组合,并提供充分的条件,使这一组合成为一个稳定的组合,防止公司联合倒闭。最后,我们集中关注那些时间跨度的时期,我们分析其对成本分配稳定性的影响。