New and “Stronger” Job-Shop Neighbourhoods: A Focus on the Method of Nowicki and Smutnicki (1996)

Abstract

Examination of the job-shop scheduling literature uncovers a striking trend. As methods for the deterministic job-shop problem have gradually improved over the years, they have come to rely on neighbourhoods for selecting moves that are more and more constrained. We document this phenomenon by focusing on the approach of Nowicki and Smutnicki (Management Science, 1996, 42(6), 797–813), noted for proposing and implementing the most restrictive neighbourhood in the literature. The Nowicki and Smutnicki (NS) method which exploits its neighbourhood by a tabu search strategy, is widely recognised as the most effective procedure for obtaining high quality solutions in a relatively short time. Accordingly, we analyse the contribution of the method's neighbourhood structure to its overall effectiveness. Our findings show, surprisingly, that the NS neighbourhood causes the method's choice of an initialisation procedure to have an important influence on the best solution the method is able to find. By contrast, the method's choice of a strategy to generate a critical path has a negligible influence. Empirical testing further discloses that over 99.7% of the moves chosen from this neighborhood (by the NS rules) are disimproving—regardless of the initial solution procedure or the critical path generation procedure employed. We discuss implications of these findings for developing new and more effective job-shop algorithms.