Complexity and algorithms for min cost and max profit scheduling under time-of-use electricity tariffs

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.