This paper takes a game theoretical approach to open shop scheduling problems to minimize the sum of completion times. We assume that there is an initial schedule to process the jobs (consisting of a number of operations) on the machines and that each job is owned by a different player. Thus, we can associate a cooperative TU-game to any open shop scheduling problem, assigning to each coalition the maximal cost savings it can obtain through admissible rearrangements of jobs’ operations. A number of different approaches to admissible schedules for a coalition are introduced and, in the main result of the paper, a core allocation rule is provided for games arising from unit (execution times and weights) open shop scheduling problems for the most of these approaches. To sharpen the bounds of the set of open shop scheduling problems that result in games that are balanced, we provide two counterexamples: one for general open shop problems and another for further relaxations of the definition of admissible rearrangements for a coalition.

本文采用博弈论方法来解决开店调度问题，以最小化完成时间的总和。我们假设有一个初始计划来处理机器上的作业（由多个操作组成），并且每个作业由不同的玩家拥有。因此，我们可以将合作 TU 游戏与任何开放式车间调度问题相关联，为每个联盟分配通过可允许的作业操作重新安排可以获得的最大成本节约。介绍了许多不同的联盟可接受时间表的方法，并且在本文的主要结果中，为大多数这些方法的单元（执行时间和权重）开放车间调度问题提供了一个核心分配规则.