A Fluid Heuristic for Minimizing Makespan in Job Shops

We describe a simple on-line heuristic for scheduling job-shops. We assume there is a fixed set of routes for the jobs, and many jobs, say N, on each route. The heuristic uses safety stocks and keeps the bottleneck machine busy at almost all times, while the other machines are paced by the bottleneck machine. We perform a probabilistic analysis of the heuristic, under some assumptions on the distributions of the processing times. We show that our heuristic produces makespan which exceeds the optimal makespan by no more than c log N with a probability which exceeds 1 - 1/N for all N 1, where c is some constant independent of N. 1 The Job-Shop Scheduling Problem with Fixed Routes A job-shop consists of machines i = 1, . . . , I, and routes r = 1, . . . , R. Route r consists of steps (r, k) where k = 1, . . . , Kr indicate the steps along route r, in their required order of execution, and step (r, k) is carried out by machine (r, k). We let Ci denote the set of steps performed on machin...

• Type: Journal
• Year: 2002
• Where: IOR
• Authors: J. G. Dai, Gideon Weiss
• Keywords: Bottleneck Machine, Heuristic, IOR 2002, Machine