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.
Highlights
If each job has the same due-date, the shortest processing time first (SPTF) schedule is optimal for the unweighted case, and in the presence of weights the problem is equivalent to knapsack (Karp 1972)
In this paper we develop new mixed-integer programming techniques for min–max regret scheduling with interval processing times, with the objective to minimize the weighted number of late jobs
We have addressed the problem of uncertain processing times, represented by intervals, in a basic single machine scheduling problem with due-dates
Summary
If each job has the same due-date, the shortest processing time first (SPTF) schedule is optimal for the unweighted case, and in the presence of weights the problem is equivalent to knapsack (Karp 1972). One of the standard techniques is to model the processing times as random variables with suitable probability distributions (Pinedo 1983) Such a problem can be solved by optimizing for the expected value of the objective function. It is more reasonable to seek a solution that has the value deviating the least from optimality, when faced with its worst-case scenario. In this paper we develop new mixed-integer programming techniques for min–max regret scheduling with interval processing times, with the objective to minimize the weighted number of late jobs. A branch and bound algorithm is presented and evaluated in a series of computational experiments
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