Accepted: 30 July 2015The uncertain flow-shop is considered. It is assumed that processing times are not given a priori, but they belong to intervals of known bounds. The absolute regret (regret) is used to evaluate a solution (a schedule) which gives the minmax regret binary optimization problem. The evolutionary heuristic solution algorithm is experimentally compared with a simple middle interval heuristic algorithm for three machines instances. The conducted simulations confirmed the several percent advantage of the evolutionary approach.
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.
An uncertain version of the task scheduling problem on unrelated machines to minimize the total flow time is considered. It is assumed that processing times are not known a priori, but they belong to intervals of known bounds. The absolute regret is applied to evaluate the uncertainty, and minmax regret task scheduling problem is solved. A simple 2-approximate middle intervals time efficient algorithm is proposed. More time consuming but better in terms of the quality of solutions scatter search based heuristic algorithm is described. Its usefulness is justified via computational experiments.
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