Following a recent interest in sustainable scheduling under operational costs that vary over time, we study scheduling problems on a single machine under time-of-use electricity tariffs. We consider two main variants of the problem: cost minimization and profit maximization. In the cost minimization problem, the set of jobs to be processed is given, and the goal is to schedule all jobs within a planning horizon so as to minimize the total cost, while in the profit maximization problem, one needs to select a set of jobs to be processed such that the total profit is maximized. The general cases of the cost minimization and profit maximization problems in which preemptions are forbidden are strongly NP-hard. In this paper, we show that some special cases with identical processing times can be solved by efficient algorithms. In addition, we consider several extensions of the problems, including release times, due dates, and variable energy consumption.

中文翻译：

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分时电价下最小成本和最大利润调度的复杂性和算法

随着最近对运营成本随时间变化的可持续调度的兴趣，我们研究了按使用时间电价在单台机器上的调度问题。我们考虑该问题的两个主要变体：成本最小化和利润最大化。在成本最小化问题中，要处理的作业集合是给定的，目标是在一个计划范围内调度所有作业以最小化总成本，而在利润最大化问题中，需要选择一组要处理的工作以使总利润最大化。禁止抢占的成本最小化和利润最大化问题的一般情况是强 NP 难的。在本文中，我们展示了一些具有相同处理时间的特殊情况可以通过有效的算法来解决。此外，