Unrelated Parallel Machine Scheduling with Sequence and Machine Dependent Setup Times and Resource Constraints

This study considers a real-life scheduling problem that arises in many industries including plastic injection molding. The study considers the scheduling of jobs on unrelated parallel machines. The machines require additional resources (such as molds) to process the jobs. There are machine and mold eligibility constraints as well as sequence and machine dependent setup times between the jobs. The machines and molds can be busy at the beginning of the scheduling horizon. The jobs have due dates and weights that indicate their priority. In addition, there are interdependent jobs, meaning that they belong to the same product that will be shipped to the same customer. As a consequence, the tardiness of interdependent jobs are calculated based on the completion time of the latest one of the interdependent jobs. The objective is to minimize the total weighted tardiness. This study develops a mathematical programming formulation for the problem and proposes a heuristic algorithm. We test the performance of the solution methods with a computational study.