Input Sequence of Jobs on NEH Algorithm for Permutation Flowshop Scheduling Problem

One of the most popular heuristics used to solve the permutation flowshop scheduling problem (PFSP) is the NEH algorithm. The reasons for the NEH popularity are its simplicity, short calculation time, and good-quality approximations of the optimal solution for a wide range of PFSP instances. Since its development, many works have been published analysing various aspects of its performance and proposing its improvements. The NEH algorithm includes, however, one unspecified and unexamined feature that is related to the order of jobs with equal values of total processing time in an initial sequence. We examined this NEH aspect using all instances from Taillard's and VRF benchmark sets. As presented in this paper, the sorting operation has a significant impact on the results obtained by the NEH algorithm. The reason for this is primarily the input sequence of jobs, but also the sorting algorithm itself. Following this observation, we have proposed two modifications of the original NEH algorithm dealing with sequencing of jobs with equal total processing time. Unfortunately, the simple procedures used did not always give better results than the classical NEH algorithm, which means that the problem of sequencing jobs with equal total processing time needs a smart approach and this is one of the promising directions for further research.