An Economic Order Quantity Model With Discounts

Price is an important parameter of inventory system. In classical Economic Order Quantity Model, the prices of products are presumed to be a constant. But in reality, they are market environment variables. To promote the sales of the products and increase market competitiveness, the model often take into account the discounts that can be given by suppliers when the client acquires a larger volume of a given product. With this concern in mind, the following content developed.In Section 1, some basic concepts and the status of researches at home and abroad about inventory and discount are introduced, the main content and structure are proposed.In Section 2, five basic EOQ Models and the concept and model of quantity discounts are described.In Section 3, considering the situation of single product and single supplier from the perspective of customers. There exist two kinds of price discount that supplier gives clients. One is all-quantity discount, that is, when the order quantity exceed a given level, all of the order quantity are given a price discount on. The other is incremental discount, that is, when the order quantity exceed a given level, the excess is given a price discount on. To solve the inventory problem with these kinds of price discount, costs are usually expressed by piecewise functions. The minimum of cost and the minimum point for every piece are sought for first, and the global minimum and minimum point are found then by comparing the piecewise minimums. For the problem we,by introducing the binary variables, develop a mixed-integer non-linear programming model, which involves whether the holding cost depends on the price. For classical EQQ model with constant prices, the best choice is the same quantity to order every time. But it is not so for the model in which prices change with order quantities. So we consider the extension model in which order quantities maybe not the same.In section 4, the multiproduct case is deseribed. the all models seek to synchronize the replement of the products to prevent their disorganized arrival and the resulting costs of the management of the cargo and storage. Numerical examples are presented throughout the work in order to improve the understanding of the model. The results show that it is possible to find a solution for the multiproduct case, which is very close to the optimal solutions found for each product separately.In Section 5, the conclusions and future research on this paper are given.