This paper presents a mathematical model for scheduling of a single machine when there are preemptions in jobs. The primary objective of the study is to minimize different objectives such as earliness, tardiness and work in process. The proposed mathematical problem is considered as NP-Hard and the optimal solution is available for small scale problems. Therefore, a genetic algorithm (GA) is developed to solve the problem for large-scale problems. The implementation of the proposed model is compared with GA for problems with up to 50 jobs using three methods of roulette wheel sampling, random sampling and competition sampling. The results have indicated that competition sampling has reached optimal solutions for small scale problems and it could obtain better near-optimal solutions in relatively lower running time compared with other sampling methods.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.