A robust customer order scheduling problem along with scenario-dependent component processing times and due dates

The customer's order (CO) issues have received growing attention in the scheduling research community. In the CO design, a customer's order consists of several components, and the processed orders are assigned to m parallel machines. The completion time of an order is assumed at the time at which all components in a customer's order are finished. In the published articles, the processing times of all components were considered as fixed and known numbers in customer order scheduling problems. This assumption is indeed at odds in many real practical productions in which there exist a lot of relevant uncertainty factors; for example, machine may break down, the working situation may change, some operator's performance may become instability, and so on. In such a situation, the processing times of given jobs are impropriate assumed as fixed and constant numbers. Thus, this article introduces a customer's order scheduling problem on m parallel machines along with scenario-dependent processing times of all components and scenario-dependent due dates. Based on the worse case, the measurement rule is to find an appropriate policy to minimize the maximum total tardiness of given n customer's orders across the possible scenarios among all possible schedules. In this study we derive several dominant rules and lower bounds used in a branch-and-bound method searching for exact solutions. Subsequently, we propose several heuristics and an iterated greedy algorithm with and without a population-based for finding approximate solutions. Finally, the computational results of all proposed algorithms are tested and reported.