Sequencing with earliness and tardiness penalties: a review
Operations Research
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
Computers & Mathematics with Applications
Analysis of computer job control under uncertainty
Journal of Computer and Systems Sciences International
Computers and Operations Research
Competitive analysis for make-to-order scheduling with reliable lead time quotation
Journal of Combinatorial Optimization
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A set of n jobs with statistically independent random processing times has to be processed on a single machine without idling between jobs and without preemption. It is required to set due dates and promise them to customers. During the production stage, earliness and tardiness against the promised due dates will be penalized. The goal is to minimize the total expected penalties. We consider two due date setting procedures with optimum customer service level, and an O(nlogn) time complexity. We show that one is asymptotically optimal but the other is not. Both heuristics include safety time and the sequence remains the same regardless of disruptions, so the result is robust. For the normal distribution we provide sufficient optimality conditions, precedence relationships that the optimal sequence must obey, and tight bounds.