Climbing Depth-Bounded Adjacent Discrepancy Search for Solving Hybrid Flow Shop Scheduling Problems with Multiprocessor Tasks

Abstract

This paper considers multiprocessor task scheduling in a multistage hybrid flow-shop environment. The problem even in its simplest form is NP-hard in the strong sense. The great deal of interest for this problem, besides its theoretical complexity, is animated by needs of various manufacturing and computing systems. We propose a new approach based on limited discrepancy search to solve the problem. Our method is tested with reference to a proposed lower bound as well as the best-known solutions in literature. Computational results show that the developed approach is efficient in particular for large-size problems.

Improved bounds for hybrid flow shop scheduling with multiprocessor tasks

“…Actually, it is possible to improve LB S 2 by noting that γ i = max i∈J p ij is also a valid lower bound on the time span that is required for processing all the jobs in stage i [24]. Finally, a valid lower bound, that dominates all the other stage-based ones, is given by:…”