THE ONE-MACHINE PROBLEM WITH DELAYED PRECEDENCE CONSTRAINTS AND ITS USE IN JOB-SHOP SCHEDULING

We study the one machine scheduling problem with release and delivery times and the minimum makespan objective, in the presence of constrain ts that for certain pairs of jobs require a delay between the completi on of the first job and the start of the second (delayed precedence co nstraints). This problem arises naturally in the context of the Shifti ng Bottleneck Procedure for the general job shop scheduling problem, a s a relaxation of the latter, tighter than the standard one-machine re laxation. The paper first highlights the difference between the two re laxations through some relevant complexity results. Then it introduces a modified Longest Tail Heuristic whose analysis identifies those sit uations that permit efficient branching. As a result, an optimization algorithm is developed whose performance is comparable to that of the best algorithms for the standard one-machine problem. Embedding this a lgorithm into a modified version of the Shifting Bottleneck Procedure that uses the tighter one-machine relaxation discussed here results in a considerable overall improvement in performance on all classes of j ob shop scheduling problems.