Single‐machine common flow allowance scheduling with aging effect, resource allocation, and a rate‐modifying activity

In this paper, we consider scheduling of deteriorating jobs on a single machine with slack (SLK) due date assignment, resource allocation, and a rate‐modifying activity. The rate‐modifying activity can change jobs’ processing rates such that the actual processing time of a job depends on whether the job is processed before or after the rate‐modifying activity. In addition, the actual processing time of a job also depends on its position in a processing sequence (i.e., the aging effect) and the amount of resource allocated to it. The objective is to determine the optimal sequence, optimal common flow allowance, optimal resource allocation, and optimal location of the rate‐modifying activity to minimize a total penalty function comprising the earliness, tardiness, common flow allowance, and resource allocation costs. We consider two variants of the problem associated with two different processing time functions and provide a polynomial‐time algorithm to solve each variant.