An efficient constructive heuristic to balance trade-offs between makespan and flowtime in permutation flow shop scheduling

Balancing trade-offs between production cost and holding cost is critical for production and operations management. Utilization of a production line affects production cost, which relates to makespan, and work-in-process (WIP) inventories in a production line affect holding cost, which relate to flowtime. There are trade-offs between two objectives, to minimize makespan and to minimize flowtime. Without addressing trade-off balancing issues in flow shop scheduling, WIP inventories are still high in manufacturing, generating unnecessary holding cost. However, utilization is coupled with WIP inventories. Low WIP inventory levels might lower utilization and generate high production cost. Most existing constructive heuristics focus only on single-objective optimization. In the current literature, the NEH heuristic proposed by Nawaz, Enscore, and Ham (1983) is the best constructive heuristic to minimize makespan, and the LR heuristic proposed by Liu and Reeves (2001) is the best to minimize flowtime. In this paper, we propose a current and future deviation (CFD) heuristic to balance trade-offs between makespan and flowtime minimizations. Based on 5400 randomly generated instances, 120 instances in Taillard's benchmarks, and one-year historical records of operating room scheduling from University of Kentucky HealthCare (UKHC), our CFD heuristic outperforms the NEH and LR heuristics on trade-off balancing, and achieves the most stable performances from the perspective of statistical process control (SPC).