Minimax regret optimization for the Scheduling-Location problem

In this paper, we propose novel algorithms for the Scheduling and Location problem (called ScheLoc problem) that combine fields of job scheduling with the makespan criterion on unrelated machines and machine deployment. This research’s fundamental aim and distinguishing feature is the application of robust (nondeterministic) optimization with interval data for the ScheLoc problem (deterministic problem with precisely defined input parameters). The minimax regret criterion is considered as the measure of robustness, and the release dates of jobs are represented as well-defined intervals. We show that the algorithms designed for the robust optimization problem with interval release dates determined based on the ScheLoc problem can achieve a lower makespan than a schedule obtained by the greedy algorithm intended for the deterministic ScheLoc problem.