Minimizing makespan in a two-machine flowshop with dynamic arrivals allowed

Abstract

This paper considers a scheduling problem for a two-machine flowshop where a discrete processing machine is followed by a batch processing machine and a finite number of jobs arrive dynamically at the first machine. In the flowshop, the discrete processing machine processes one job at a time and the batch processing machine processes a batch of jobs simultaneously. The objective is to find the optimal schedule which minimizes the maximum completion time (makespan) of all jobs. In the situation where preemption is allowed on the discrete processing machine, it is shown that the optimal schedule can be found in polynomial time. However, in the situation where no preemption is allowed on the discrete processing machine, it is shown that the problem is NP-complete, for which an efficient heuristic solution algorithm is constructed and its tight worst-case error bound is derived. Numerical experiments show that the heuristic algorithm consistently generates good schedules. Scope and purpose There are many manufacturing systems that consist of both discrete processing machines and batch processing machines where each discrete processing machine can process one job at a time, whereas each batch processing machine (e.g., heat-treating oven, etching tank for creating circuitry in wafer fabrication) can process a batch of jobs simultaneously. This paper addresses a scheduling problem for a two-machine flowshop with the makespan measure where a discrete processing machine is followed by a batch processing machine. In the situation where preemption is allowed on the discrete processing machine, it is shown that the optimal schedule can be found in polynomial time. However, in the situation where no preemption is allowed on the discrete processing machine, it is proved that the scheduling problem is NP-complete. For this NP-complete problem, an efficient heuristic solution algorithm is proposed. Computational experiments show that the heuristic algorithm performs well on randomly generated problems.