No idle flow shop scheduling models for optimization of machine rental costs with processing and separated setup times.

Scheduling is one of the many skills required for advancement in today's modern industry. The flow-shop scheduling problem is a well-known combinatorial optimization challenge. Scheduling issues for flow shops are NP-hard and challenging. The present research investigates a two-stage flow shop scheduling problem with decoupled processing and setup times, where a correlation exists between probabilities, job processing times, and setup times. This study proposes a novel heuristic algorithm that optimally sequences jobs to minimize the makespan and eliminates machine idle time, thereby reducing machine rental costs. The proposed algorithm's efficacy is demonstrated through several computational examples implemented in MATLAB 2021a. The results are compared with the existing approaches such as those by Johnson, Palmer, NEH, and Nailwal to highlight the proposed algorithm's superior performance. [ABSTRACT FROM AUTHOR]