Bicriteria Common Flow Allowance Scheduling with Aging Effect, Convex Resource Allocation, and a Rate-Modifying Activity on a Single Machine

We consider a single machine scheduling problem with slack due date assignment in which the actual processing time of a job is determined by its position in a sequence, its resource allocation function, and a rate-modifying activity simultaneously. The problem is to determine the optimal job sequence, the optimal common flow allowance, the optimal amount of the resource allocation, and the position of the rate-modifying activity such that the two constrained optimization objective cost functions are minimized. One is minimizing the total penalty cost containing the earliness, tardiness, common flow allowance subject to an upper bound on the total resource cost, the other is minimizing the total resource cost subject to an upper bound on the total penalty cost. For two optimization problems, we show that they can be solved in optimal time, respectively.