Deterministic Inventory Control Model for Perishable Items with Backordering Shortage and Guantity Discount

Document Type : Research Paper


1 Dept. of Industrial Engineering, Iran University of Science and Technology, Tehran, I.R. Iran

2 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, I.R. Iran


It is assumed in most of the existing models that the items can be stored for an unlimited time to meet the future’s demand and their quality and quantity does not change during that period. Nevertheless there are special kinds of products which deteriorate or become unusable (such as food products, alcohol, medicines, etc.). Therefore if the rate of deterioration is significantly high, the impact cannot be ignored. On the other hand, most of the times the final price of a product is dependent on the number of purchased products and with the increase of number of the orders, a lower price is paid for each item. Considering these partial rebates in the models help the increase of their usability in the real world. In this paper we develop an inventory control model for perishable items considering quantity discount from the seller’s side when the demand rate is fixed annually. In this model, inventory system is a single product, the rate of the deterioration is fixed, shortages are fully backlogged and the lead time is zero. For this model, first, a simple and efficient algorithm and solution for finding the optimal value is presented and then for describing the model and the algorithm we present numerical example and sensitivity analysis of the model.