Maximizing Total Net Revenue for the Identical Parallel Machines Order Acceptance and Scheduling Problem with Sequence-Dependent Setup Times

This paper examines a production system where rejection of some orders is inevitable due to limited capacity, potentially leading to overloads, delays, and customer dissatisfaction. Firms often reject some orders due to the Order Acceptance and Scheduling (OAS) problem, which involves simultaneously deciding which orders and their associated schedules are accepted for processing. This problem is a real-world industrial issue, focusing on an OAS variant on identical parallel machines with sequence-dependent setup times. A series of jobs with distinct processing times, due dates, release dates, deadlines, income, and penalty weights have been scheduled for processing on identical parallel machines. When we receive orders from customers, our rejection criteria are typically determined by weighing the revenue that the business receives for accepting an order against the associated processing costs. These processing costs could include penalties for failing to deliver a specific order by the due date. The net revenue is the sum of difference between revenues and weighted tardiness. The ultimate goal is to maximize the total sum of the accepted orders’ net revenue. We modify the model studied in [1] in order to define a new model adequate for our configuration. Thus, we manage to build a model which can solve up to 50 jobs.