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.

Vendor managed inventory (VMI) is one of the most effective methods for reducing bullwhip effect. This paper presents a mathematical VMI model where there are three levels of central storage, multi distribution centers and various retailors. The problem is formulated as a mixed integer programming by considering uncertainty on different input parameters. To cope with uncertainty, the study uses rectangular fuzzy numbers. We also propose two metaheuristics; namely, genetic algorithm and particle swarm optimization to solve the resulted problems for some large instances. The preliminary results have indicated that genetic algorithm could solve the proposed model faster than particle swarm optimization in terms of CPU time reaching to slightly better objective functions.Growing Science Ltd. All rights reserved. 7