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

Abstract

We consider the robust version of single machine scheduling problem with the objective to minimize the weighted number of jobs completed after their due-dates. The jobs have uncertain processing times represented by intervals, and decision-maker must determine their execution sequence that minimizes the maximum regret. We develop an exact solution algorithm based on a specialized branch and bound method, using mixed-integer linear programming formulations for a common due-date and for job-dependent due-dates. Finally, we examine the solution algorithm in a series of computational experiments.

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

“…Decision variable p j represents the worst-case processing time of jth job. Values of these variables are determined due to the set of constraints (5). These constraints are satisfied when q π(k) = 0, for such k that are on-time in π in the worst-case scenario, and for q π(k) = 1 for such k that are late.…”

“…Although the number of processing times scenarios in such case is potentially infinite, solution algorithms may take the advantage of the structural information of uncertainty sets. Unfortunately, the problem with interval data is also NP-hard [5], even if all weights are equal. Moreover, deterministic variant with arbitrary weights is already NP-hard.…”

Robust and Stable Flow Shop Scheduling Problem under Uncertain Processing Times and Machines’ Disruption

“…Besides, the job or machine-related uncertainties that lead to an interruption in the flow of jobs and result in unwanted delays are commonly occurring in the production environment, enhancing the problem's complexity. Arriving of an unanticipated new job [7], due date uncertainty [8], breakdown occurrence [9], uncertainty in job processing times [9,10], etc are the likes of uncertainties and disruptions. In 70% of uncertainty oriented flow shop scheduling studies in past decades, the job processing time is uncertain, by 25%, the disruption is machine failure, and by 10%, both of these factors consider [11].…”

“…The concept of robustness is very close to flexibility: the ease of schedule reparability and the power of converting to new, high quality scheduling in the face of uncertainties. The expected realized total completion time has been implemented as a robustness measure by itself [8]. Here we take this definition as robustness.…”

“…Here we take this definition as robustness. A function of the sum of deviation between each jobs' start/completion times in the initial and realized schedules are often the stability measure [8], and the same definition is accepted here. The value of the expected performance measure obtained by applying the righting shift policy on the initial schedule is a realized schedule.…”