Effect of problem size on the performance of constructive algorithms for flow shop scheduling problems with sequence dependent setup times

Abstract

This paper focus on the scheduling problem of a flow shop operating in a sequence dependent setup time (SDST) environment. Two constructive algorithms of contrasting characteristics are analysed for the performance with respect to change in problem size; the first algorithm is processing time-based and the second algorithm is setup time-based. The problem size is characterised by the variables namely, number of jobs and number of machines. An extensive performance analysis of the two constructive algorithms has been carried out using 960 SDST flow shop benchmark problem instances. The graphical analysis of the results reveals the correlation between the relative performance of the algorithms and problem size. The study shows that the performance of the setup time-based algorithm increases with increase in number of jobs and decreases with increase in number of machines. The coefficient of variation analysis is used to investigate the performance variation of the algorithm with change in number of machines. The analysis reveals that as the number machines increases, the coefficient of variation of the summed setup time matrix decreases which causes the change in performance of the setup time-based algorithm.