Due-window assignment scheduling problem with stochastic processing times

In operational systems, scheduling and due-window assignment are two common decisions. At the same time, many sources of uncertainty existed in operational systems make the processing times of jobs stochastic. In this paper, two specific due-window assignment scheduling problems with different distributional information regarding the processing times are studied. In the first problem, the processing times follow normal distribution, whereas in the second problem, there is only information about the mean and variance of the processing time of each job, but no information about the specific distribution pattern. The objective of both problems is to determine a due window for each job and a processing schedule for all jobs to minimize total expected weighted costs for earliness, tardiness and due-window assignment. For the first problem, we analyze the optimal due-window assignment and propose a branch-and-bound algorithm to find an optimal solution. For the second problem, we first establish an approximated problem based on developed upper and lower bounds, and then develop a branch-and-bound algorithm to solve the approximated problem optimally. Finally, computational experiments are conducted to evaluate the performance of the proposed algorithms and the efficiency of the problem approximation. Through computational experiments, some managerial insights are derived. (C) 2020 Elsevier B.V. All rights reserved.