Cooperative lot-sizing models with backlogging and heterogeneous costs are studied in Guardiola et al. (2020). In this model several firms participate in a consortium aiming at satisfying their demand over the planing horizon with minimal operation cost. Each firm uses the best ordering channel and holding technology provided by the participants in the consortium. The authors show that there are always fair allocations of the overall operation cost among the firms so that no group of agents profit from leaving the consortium. This paper revisits those cooperative lot-sizing models and presents a new family of cost allocations, the unitary Owen points. This family is an extension of the Owen set which enjoys very good properties in production-inventory proble, introduced by Guardiola et al. (2008). Necessary and sufficient conditions are provided for the unitary Owen points to be fair allocations. In addition, we provide empirical evidence, throughout simulation, showing that the above condition is fulfilled in most cases. Additionally, a relationship between lot-sizing games and a certain family of production-inventory games, through Owen's points of the latter, is described. This interesting relationship enables to easily construct a variety of fair allocations for cooperative lot-sizing models.

翻译：在Guardiola等人(2020)的研究中，探讨了带有缺货和异质成本的联合批量订购模型。在该模型中，多家企业组成联盟，旨在以最低运营成本满足计划期内的需求。每家企业在联盟成员的订购渠道和持有技术中选择最优方案。研究表明，总运营成本总能实现企业间的公平分摊，使得任何子群体均无脱离联盟的动机。本文重新审视这些联合批量订购模型，并提出一类新的成本分摊方案——酉奥温点。该方案是奥温集的扩展，后者由Guardiola等人(2008)提出并具备生产-库存问题中的优良性质。本文给出了酉奥温点作为公平分摊方案的充要条件。此外，通过仿真实验提供的实证证据表明，该条件在多数情况下成立。进一步地，本文描述了批量订购博弈与特定生产-库存博弈家族之间的关系，后者通过奥温点建立关联。这一有趣的关系使得构建联合批量订购模型中的多种公平分摊方案变得简便易行。