A TWO-ECHELON SINGLE-PERIOD INVENTORY CONTROL PROBLEM UNDER A BUDGET CONSTRAINT AND DISCOUNT CONDITIONS WITH PARTICLE SWARM ALGORITHM

In this research, we investigate the two-echelon singleperiod inventory problem, in which the raw materials and the nal product should be provided at the beginning of the selling period. Raw materials that remain unused and the nal products that remain unsold until the end of the period, can be sold at a discount at the end of the period. the use of coecient in nal products is dierent from each raw material, so the raw materials and the nal product may not have a one-to-one relationship; we have a certain limited budget for buying the raw materials and producing the nal products. Supplier will oer the discount for each raw material to reduce his inventory level, if we buy more than a certain quantity of that raw materials. Since the price of the nal product at the end of the period is so Low, we set a cumulative discount policy to encourage customers for our nal product. Consequently, one of the costumers buys more than a certain quantity, and the price of each nal product for that costumer will be less than the normal price. If the nal product is sold out during the period, depending on the demand, some of our customers will wait for transforming raw materials into the nal product during the period. The objective of this problem is to nd the order of quantities of both the raw materials and the nal product, such that the expected prot can be maximized. A mathematical model was rst developed for this problem, then a particle swarm optimization algorithm (PSO) was proposed to solve it. Finally, a numerical example was given to illustrate the application of the proposed methodology. This example was solved by the developed PSO algorithm, and to receive a better answer from PSO, we ran the algorithm 50 times.