Single-machine Slack Due-Window Assignment and Scheduling with Past-Sequence-dependent Delivery Times and Controllable Job Processing Times

In this paper, we study single-machine scheduling that considers slack (SLK) due-window assignment, past-sequence-dependent delivery times and controllable job processing times simultaneously. We assume that the actual processing time of a job is a function of the learning effect on the job and resource allocation to the job and the job delivery time is proportional to its waiting time. The objective is to find jointly the optimal job sequence, optimal flow allowance value (i.e., optimal common waiting time) and optimal resource allocation to minimise a total cost comprising the earliness, tardiness, due-window-related and resource consumption costs. We consider two models of the job processing time function and provide polynomial-time solution algorithms for the corresponding problems. We also provide a more efficient solution algorithm for a special case of the problem.