Due‐date assignment and machine scheduling in a low machine‐rate situation with stochastic processing times

Due date assignment combined with shop floor scheduling has attracted enormous amount of research, in recent years. In many make‐to‐order situations, the processing times are not known exactly in advance. Further, machine rates are not constant at different times. We assume the case where the machine rate is low at the beginning of the scheduling horizon. However, it can be brought back to normal rate by performing a maintenance activity. The problem includes assigning due‐dates and scheduling the jobs and maintenance activity on a single machine where the processing times are stochastic. The objective is minimizing the total cost of lengths of quoted due‐dates and expected deviations of completion times from declared due‐dates. The optimal solutions of medium‐sized problems are found by solving some nonlinear programming models. For larger problems, robust metaheuristics are developed and their performances are statistically analyzed.