Development and analysis of constructive heuristic algorithms for flow shop scheduling problems with sequence-dependent setup times

This paper focuses on the problem of determining a permutation schedule for n jobs in an m-machine flow shop that operates in a sequence-dependent setup time (SDST) environment. Two constructive heuristic algorithms are developed with the minimisation of makespan as the objective. The first heuristic algorithm termed as setup ranking algorithm obtains the sequence using the setup times of jobs only. The second heuristic algorithm, fictitious job setup ranking algorithm (FJSRA), is developed using the concept of fictitious jobs. Pairs of jobs with minimum setup time between them constitute the fictitious jobs. Both these algorithms are compared with an existing constructive algorithm. For the purpose of experimentation, Taillard benchmark problems are used to develop SDST benchmark problems at eight different levels of sequence-dependent setup times. Graphical analysis, relative performance index analysis and statistical analysis are carried out on the results obtained for all the eight sets of benchmark problems. The analysis reveals that FJSRA emerges as the better algorithm for larger problems and for smaller problems with higher level of setup time. The results of statistical analysis are used to develop setup time dominance matrix for deciding upon the algorithm to be used for a particular size of problem.