Analyzing a few Heuristic Algorithms Considering Machine Idle Time and Processing Time in Permutation Flow Shop Scheduling Problems

Abstract

Flow Shop Scheduling has been an interesting field of research for over six decades. They are easy to formulate, yet difficult to solve. In a shop, there are 'm' machines arranged in series to process a set of 'n' jobs having different processing times. Each job has to pass through each machine, in order. The problem is to find a sequence of jobs to be processed in all the machines, so that a given performance parameter is optimized. The total number of schedules is (n!) m . If the order of machines is not to be changed, the problem is simplified, and the overall number of solutions is reduced to n!. This problem is referred to a permutation flow shop scheduling problem, or PFSP in short. Starting from two machines, 'n' jobs, various Heuristics have been proposed over the years. After the invention of meta heuristics and evolutionary algorithms, and increased computational capabilities available today, finding optimal/ near optimal solutions become comparatively easier. In this paper, a few heuristic algorithms have been analyzed for makespan criterion considering machine idle time and processing time, by comparing the results with the well known CDS algorithm. Benchmark problems proposed by Taillard and Ruben Ruiz are used for the performance analysis.