An Ordered Flow Shop Scheduling Problem

The subject of the study is ordered flow shop scheduling problems which were first seen in the literature in the 1970s. The main objective is to get a fast and good solution. For the purpose of the study, firstly, the ordered flow shop scheduling problems were defined. Then, a heuristic method was suggested for the ordered flow shop scheduling problems and a sample problem was solved and discussed. A genetic algorithm (GA) based on the complexity property was developed. Full enumeration was applied to determine the optimal makespan values based on Smith’s rule because Smith had specified the conditions under which circumstances the permutation can be optimum. This study is one of the few studies in the literature to obtain optimum solutions up to 15 jobs ordered flow shop problems in a very short amount of time. The developed GA heuristic can also solve large size ordered flow shop scheduling problems very fast. The significant advantage of the proposed method is that, while Smith’s method rule not does not work with large size problems since it requires full enumeration to identify best solution to follow a convexity property where GA algorithm can find a good solution very fast.