The open shop is a classical scheduling problem known since 1976, which can be described as follows. A number of jobs have to be processed by a given set of machines, each machine should perform an operation on every job, and the processing times of all the operations are given. One has to construct a schedule to perform all the operations to minimize finish time also known as the makespan. The open shop problem is known to be NP-hard for three and more machines, while is polynomially solvable in the case of two machines. We consider the routing open shop problem, being a generalization of both the open shop problem and the metric traveling salesman problem. In this setting, jobs are located at nodes of a transportation network and have to be processed by mobile machines, initially located at a predefined depot. Machines have to process all the jobs and return to the depot to minimize makespan. A feasible schedule is referred to as normal if its makespan coincides with the standard lower bound. We introduce the Irreducible Bin Packing decision problem, use it to describe new sufficient conditions of normality for the two machine problem, and discuss the possibility to extend these results on the problem with three and more machines. To that end, we present two new computer-aided optima localization results.

开放式车间是 1976 年以来已知的经典调度问题，可以描述如下。许多作业必须由一组给定的机器处理，每台机器应对每个作业执行一个操作，并且所有操作的处理时间都是给定的。必须制定一个时间表来执行所有操作，以最大限度地减少完成时间，也称为完工时间。众所周知，开放车间问题对于三台或更多台机器是 NP 难的，而在两台机器的情况下是多项式可解的。我们考虑路由开放商店问题，它是开放商店问题和度量旅行商问题的推广。在这种情况下，作业位于交通网络的节点，必须由最初位于预定义仓库的移动机器处理。机器必须处理所有工作并返回仓库以最大限度地减少制造时间。如果一个可行的进度表的完工时间与标准下限一致，则它被称为正常进度表。我们介绍了不可约装箱决策问题，用它来描述两台机器问题的新的正态性的充分条件，并讨论将这些结果扩展到三台或更多机器的问题上的可能性。为此，我们提出了两个新的计算机辅助优化定位结果。并讨论将这些结果扩展到三台或更多机器的问题上的可能性。为此，我们提出了两个新的计算机辅助优化定位结果。并讨论将这些结果扩展到三台或更多机器的问题上的可能性。为此，我们提出了两个新的计算机辅助优化定位结果。