The scheduling of gantry cranes with respect to mutual interference has received considerable attention in recent years. We consider a subproblem which arises when each crane has a sequence of tasks to be assigned. The problem is concerned with resolving the interference between two cranes by determining which crane avoids the other in order to let it complete its next task first. We provide a fairly general problem framework accounting for different crane systems and various side constraints. We assume a cost function for each task that determines the cost of completing the task at a specific point in time. We then distinguish between the objectives to minimize both the total cost and the maximum cost among tasks. A general dynamic programming framework is provided which allows us to solve all problem versions in pseudo-polynomial time. Furthermore, we show that while the general problem aiming for minimum total cost is binary NP-hard, the general problem aiming for minimum maximum cost can be solved in polynomial time. Finally, we address two important special cases of the former, and we show that they can be solved in polynomial time as well.

近年来，关于相互干扰的龙门起重机调度受到了相当多的关注。我们考虑一个子问题，当每台起重机有一系列要分配的任务时，就会出现这个子问题。该问题涉及通过确定哪台起重机避开另一台起重机以使其先完成下一个任务来解决两台起重机之间的干扰。我们为不同的起重机系统和各种侧面约束提供了一个相当通用的问题框架。我们假设每个任务都有一个成本函数，它决定了在特定时间点完成任务的成本。然后我们区分目标以最小化任务之间的总成本和最大成本。提供了一个通用的动态编程框架，它允许我们在伪多项式时间内解决所有问题版本。此外，我们表明，虽然以最小总成本为目标的一般问题是二元 NP-hard，但以最小最大成本为目标的一般问题可以在多项式时间内解决。最后，我们解决了前者的两个重要特殊情况，并证明它们也可以在多项式时间内求解。