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This paper addresses single-machine scheduling problems with past-sequence-dependent (denoted by Formula: see text) delivery times, due-window assignments and deteriorating jobs simultaneously. The Formula: see text delivery time of a job is proportional to the job’s waiting time, and the deteriorating jobs mean that the processing time of a job is a proportional increasing function of its starting time. For common, slack and different due-window assignments, the goal is to minimize the weighted sum of earliness, tardiness, due-window starting time and size. Some optimal propositions of the problems are given, and by these propositions, polynomial time algorithms are proposed to optimally solve the above problems.
Lu et al. (Thu,) studied this question.