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Scheduling problems with variable processing times and past-sequence-dependent delivery times are considered on a single-machine. The delivery times of jobs depend on their waiting times of processing. A job’s actual processing time depends on its position in a sequence, its starting time and its allocation of non-renewable resources. Under the linear resource consumption function, the goal (version) is to determine the optimal sequence and optimal resource allocation such that the sum of scheduling cost and total resource consumption cost is minimized. Under the convex resource consumption function, three versions of the scheduling cost and total resource consumption cost are discussed. We prove that these four versions can be solved in polynomial time, respectively. Some applications are also given by using the scheduling cost, which involve the makespan, total completion time, total absolute differences in completion times (TADC), and total absolute differences in waiting times (TADW).

This paper studies the slack due-window assignment scheduling problem with deterioration effects and a deterioration maintenance activity on a single-machine. The machine deteriorates during the machining process, and at a certain moment performs a deterioration maintenance activity, that is, the duration time of the maintenance activity is a linear function of the maintenance starting time. It is needed to make a decision on when to schedule the deteriorating maintenance activity, the optimal common flow allowances and the sequence of jobs to minimize the weighted penalties for the sum of earliness and tardiness, weighted number of early and delayed, and weighted due-window starting time and size. This paper proposes a polynomial time algorithm to solve this problem.