Most of group scheduling algorithms in the literature contain two phases. They first define part sequence in each group and then identify group sequence. Hitomi and Ham (1976) identified a lower bound for optimal maximum completion time and used branch-and-bound algorithm to reach optimal parts and group sequence. Yoshida and Hitomi (1979) then presented an algorithm to solve job shop scheduling of a two-machine problem with setup times optimally. Sekiguchi (1983) and Baker (1990) continued Yoshida and Hitomi’s work on scheduling of two machines where each group has its own setup times. Logendran and Nudtasomboon (1991) presented a heuristic algorithm, named LN, to solve group scheduling to minimize maximum completion time which was similar to NEH algorithm presented by Navaz et al. (1983). The only difference between NEH and LN is that in NEH, jobs are arranged with decreasing order of total processing time while in LN they are arranged with declining order of average processing times.
Wemmerlov and Vakharia (1991) compared the performance of scheduling algorithms considering eight families and reported that family-based scheduling algorithms were mainly used to minimize flow time and lateness. Mahmoodi and Dooley (1991) evaluated a job shop cell including part families with sequence dependent setup times. Sridhar and Rajendran (1993) formulated a new heuristic algorithm to minimize total production time inflow shop cells and solved it using Simulated Annealing (SA) method.
Skorin-Kapov and Vakharia (1993) compared two cellular manufacturing flow shop scheduling approaches considering independent setup times. They proposed a Tabu Search (TS) based technique and solved them by SA. Sridhar and Rajendran (1994) proposed a genetic algorithm to solve parts and families scheduling in a flow shop manufacturing cell. Later on, Chien (1997) suggested a two-phase algorithm for scheduling flow shop CMS problems considering intercellular parts routing.