A New Slope Index for Solving NxM Flow Shop Sequencing Problems with Minimum Makespan

A flow shop sequencing problem is one of the classical problems in the production scheduling. In a flow shop, a particular case of manufacturing process follows a fixed linear structure. The purpose of this paper is to find the minimum total processing time (makespan) of sequencing ‘n’ jobs on ‘m’ machines for a flow shop problem in a static workshop. The proposed approach is based on the slope of each job on its journey from the first to the last machine. This approach is compared with five well-known heuristics (Palmer, Gupta, CDS, Dannenbring, Hundal) and one more recent technique that is based on the harmonic triangle. The results obtained from this study for different sizes of ‘n’x’m’ flow shop sequencing problems ranging from 4x4 to 50x20 indicate that the proposed approach is efficient with an encouraging percentage of improvements compared with all other six heuristic techniques