The two-machine open shop problem was proved to be solvable in linear time by Teofilo Gonzalez and Sartaj Sahni in 1976. Several algorithms for solving that problem have been proposed since that time. We introduce another optimal algorithm for that classical problem with an interesting property: it allows to process jobs in almost arbitrary order, unlike the Gohzalez–Sahni algorithm where jobs have to be partitioned into two specific subsets. This new algorithm in turn helps us to solve a much more general problem: the easy-TSP version of the routing open shop with a variable depot, in which unmovable jobs are located in the nodes of a transportation network (with optimal route known), and mobile machines have to travel between the nodes to process jobs in the open shop environment. The common initial location of the machines is not fixed but has to be chosen, and all machines have to return to that location—the depot—to minimize finish time. We also consider the generalization of this problem in which travel times are individual for each machine. This contributes to the discussion on the differences between different scheduling models with transportation delays: classic transportation delays (in our terms, with no depot at all), with a variable depot, and with a fixed depot. It turns out that the depot makes the difference and makes the problem harder to solve.

1976 年，Teofilo Gonzalez 和 Sartaj Sahni 证明了两机开店问题可以在线性时间内解决。从那时起，已经提出了几种解决该问题的算法。我们为该经典问题引入了另一种具有有趣特性的最优算法：它允许以几乎任意的顺序处理作业，这与 Gohzalez-Sahni 算法不同，后者的作业必须划分为两个特定的子集。这种新算法反过来帮助我们解决了一个更普遍的问题：带有可变仓库的路由开放商店的easy-TSP版本，其中不可移动的工作位于运输网络的节点中（具有已知的最佳路线），移动机器必须在节点之间穿行才能在开放式商店环境中处理作业。机器的共同初始位置不是固定的，而是必须选择的，并且所有机器都必须返回该位置——仓库——以最小化完成时间。我们还考虑了这个问题的推广，其中每台机器的旅行时间都是独立的。这有助于讨论具有运输延迟的不同调度模型之间的差异：经典运输延迟（用我们的术语来说，根本没有站点）、可变站点和固定站点。事实证明，仓库发挥了作用，并使问题更难解决。这有助于讨论具有运输延迟的不同调度模型之间的差异：经典运输延迟（用我们的术语来说，根本没有站点）、可变站点和固定站点。事实证明，仓库发挥了作用，并使问题更难解决。这有助于讨论具有运输延迟的不同调度模型之间的差异：经典运输延迟（用我们的术语来说，根本没有站点）、可变站点和固定站点。事实证明，仓库发挥了作用，并使问题更难解决。