Seyed Mahdi Homayouni - Department of Industrial Engineering, Lenjan Branch, Islamic Azad University, Isfahan, Iran
Ali Izadi - Department of Industrial Engineering, Najafabad Branch, Islamic Azad University, Isfahan, Iran
Mohammadreza Vasili - Department of Industrial Engineering, Lenjan Branch, Islamic Azad University, Isfahan, Iran

Many researches in inventory control area of knowledge have been focused on single objective and multi-objective problem of determining the economic quantity of order. In single objective problems, costs were considered as the objective. However, multi-objective problems have not been well investigated. For instance, there are no hint to transportation cost, budget, or holding costs, or only capacity and demand constraints have been considered in these researches. This study focuses on developing a model accompanied by costs, quality and the time of delivery.The economic order quantity of multi-product from multi-supplier in multi-period under uncertainty in demand and discounted prices are considered in this paper. In first step, a mathematical model is developed for this problem. This mathematical model is solved by using multi-objective optimization method i.e. goal programming. Then, a meta-heuristic method based on multi-objective particle swarm optimization is proposed. Results of the small size numerical examples show that solutions found by using the proposed meta-heuristic method are in average, ۵% worse than solutions found by using the mathematical methods; however, it needs much lower computational time.

Economic order quantity, Discounted price, Multi-objective Particle swarm optimization