Development of a scheduling method for unrelated parallel machines under machine eligibility restrictions and sequence dependent setup times to minimize total completion time: A case of bolt manufacturing

In the literature, there are lots of studies related to unrelated parallel machine scheduling. However, Constraint Programming (CP) is not used as much as other solution techniques for real-world problems. We aim to solve a real-world problem that occurs in a company, where the product range is too wide. Consequently, production planning related problems emerge. We focus on the bottleneck operation, which is the first operation in the production process in the company completed using cold-forging machines. We aim to minimize the total completion time by considering sequence-dependent setup times and machine eligibility. We model this scheduling problem as CP and Integer Programming (IP) and solve both models using IBM ILOG CPLEX Optimization Studio. We compare the results of CP and IP in real problem instances. We generate particular instances about machine eligibility for our scheduling problem. We set eligibility to fixed number of machines for each job and create lexicographically ordered eligibility matrices and set average eligibility to a fixed number but randomly assign eligibility to job-machine pairs. Using the generated problem instances, we extend our comparison of CP and IP. The results show that, for almost all instances, CP gives better solutions than IP when we consider the run-time limit. When complexity and number of constraints increase, CP surpasses IP.