Parallel Machine Scheduling with Fuzzy Processing Times and Sequence Dependent Setup Times: An Application in a Textile Company

Abstract

The textile company we consider receives orders from customers for different types of products and with different quantities. The company has several production lines as a machine and an order for a product type as a job to comply with the scheduling terminology. We assume that not all machines are suitable for processing all jobs i.e. jobs can only be processed on their eligible machines. When there is more than one eligible machine those machines are identical in terms of their setups and processing times. We assume that all jobs and machines are ready to be processed at time zero. We also assume that the times required to set up the machine for the next job depend on the job completed and the job in order hence setup times are sequence-dependent. The processing time of a job is not deterministic due to various factors such as operator learning curve and fatigue and machine maintenance requirements. Likewise setup times also vary depending on human and technical factors. We choose to model these uncertainties by assuming fuzzy processing times and fuzzy setup times. Our objective is to assign and schedule jobs to minimize the makespan the completion time of the last job. Our solution approach relies on the comparison of solutions through a randomized search algorithm a Monte Carlo simulation with an improvement routine. We conduct a numerical study and present the solution quality of the proposed methodology.