Min-Max Regret Scheduling to Minimize the Total Weight of Late Jobs with Interval Uncertainty

Abstract

We study the single machine scheduling problem with the objective to minimize the total weight of late jobs. It is assumed that the processing times of jobs are not exactly known at the time when a complete schedule must be dispatched. Instead, only interval bounds for these parameters are given. In contrast to the stochastic optimization approach, we consider the problem of finding a robust schedule, which minimizes the maximum regret of a solution. Heuristic algorithm based on mixed-integer linear programming is presented and examined through computational experiments.

Robust min–max regret scheduling to minimize the weighted number of late jobs with interval processing times

“…We have also shown that there may exist infinitely many worst-case scenarios. Another example of a min-max regret scheduling problem with the property that worst-case scenario is not always extreme is the minimization of the weighted number of late jobs with interval due-date uncertainty (Drwal 2017(Drwal , 2018.…”