Abstract
In this study, a multi-objective robust job-shop scheduling (JSS) model was developed. The model considered multijobs and multi-machines. The model also considered uncertain processing times for all tasks. Each job was assigned a specific due date and a tardiness penalty to be paid if the job was not delivered on time. If any job was completed early, holding expenses would be assigned. In addition, the model added idling penalties to accommodate the idling of machines while waiting for jobs. The problem assigned was to determine the optimal start times for each task that would minimize the expected penalties. A numerical problem was solved to minimize both the makespan and the total penalties, and a comparison was made between the results. Analysis of the results produced a prescription for optimizing penalties that is important to be accounted for in conjunction with uncertainties in the job-shop scheduling problem (JSSP).