Tardiness Minimisation for Job Shop Scheduling with Interval Uncertainty

Robust schedules for tardiness optimization in job shop with interval uncertainty

“…Constraints ( 8) and ( 9) establish the relationship between the starting and completion time of each task. Constraints (10) and (11) correspond to precedence relations between tasks within each job, and constraints ( 12) and ( 13) establish that the execution of two tasks requiring the same machine cannot overlap. Clearly, this problem is NP-hard, since setting all processing times and due dates to crisp numbers yields the classical JSP, which is itself NP-hard [34].…”

“…This idea inspires the -robustness measure introduced in [32] for the job shop with fuzzy processing times and makespan minimisation, which measures the relative error of a performance metric between the a-priori and the a-posteriori solutions. In [11] we find a first proposal to adapt this measure to the interval framework and to total tardiness minimisation. It can be argued, however, that this first definition is ill-suited for the tardiness objective in the sense that it penalises the cases where the tardiness of the a-posteriori solution is lower than the predicted one.…”

“…There are however other cases where the worst case is not critical and, instead, solutions with an overall acceptable performance are preferred [20]. This is the stance taken in the definition of a robustness measure for tardiness minimisation in job shop with interval uncertainty given in [11]. To our knowledge, this is the only existing proposal in the literature for this variant of the problem but, as we shall argue in the sequel, it presents some flaws when tardiness minimisation is considered.…”

“…This paper is an extended version of the work presented at the 15th International Conference on Hybrid Artificial Intelligence Systems (HAIS '20) and published in [11]. The contributions of this new extended version are the following: A new robustness measure, better suited for the total tardiness objective function, is introduced in Section 3.…”

“…It was mentioned in the conclusions of [11] that there was a need to thoroughly analyse the influence of different ranking methods in order to make a proper choice. We address this issue here by performing a separate parameter tuning for each variant of the GA depending on the ranking method used.…”