The Shifting Bottleneck Procedure for Job Shop Scheduling

TLDR

The paper proposes an approximation method for minimizing makespan in job shop scheduling. The procedure iteratively selects the bottleneck machine among unscheduled machines, locally reoptimizes preceding sequences after each selection, and relies on repeatedly solving one‑machine scheduling problems; a variant extends this to nodes of a partial search tree. Computational testing shows the approach consistently outperforms other procedures, and in one case found an optimal schedule for a ten‑machine/ten‑job problem in just over five minutes, where other algorithms had taken hours.

Abstract

We describe an approximation method for solving the minimum makespan problem of job shop scheduling. It sequences the machines one by one, successively, taking each time the machine identified as a bottleneck among the machines not yet sequenced. Every time after a new machine is sequenced, all previously established sequences are locally reoptimized. Both the bottleneck identification and the local reoptimization procedures are based on repeatedly solving certain one-machine scheduling problems. Besides this straight version of the Shifting Bottleneck Procedure, we have also implemented a version that applies the procedure to the nodes of a partial search tree. Computational testing shows that our approach yields consistently better results than other procedures discussed in the literature. A high point of our computational testing occurred when the enumerative version of the Shifting Bottleneck Procedure found in a little over five minutes an optimal schedule to a notorious ten machines/ten jobs problem on which many algorithms have been run for hours without finding an optimal solution.