A two-stage three-machine assembly flow shop scheduling with learning consideration to minimize the flowtime by six hybrids of particle swarm optimization

There have been many applications of two-stage three-machine assembly flow shop in query scheduling, such as fire engine assembly, personal computer manufacturing, and distributed database system. Moreover, learning phenomenon has been shown present in many two-stage assembly flow shop environments. In conjunction with this learning phenomenon, we addressed, in this study, a two-stage three-machine flow shop scheduling problem with a cumulated learning function. Our objective was to search an optimal sequence for minimizing the flowtime (or total completion time). We developed some dominance propositions with a lower bound used in a branch-and-bound algorithm for small-size jobs. We also proposed six versions of hybrid particle swam optimization (PSO) algorithms to find approximate solutions for small-size and big-size jobs, and for three different data types. In addition, analysis of variance (ANOVA) was employed to examine the performances of the six PSOs for each data type. Subsequently, Fisher's least significant difference tests were carried out to further make pairwise comparisons among the performances of the six algorithms.