عنوان مقاله [English]
Economic Production Quantity Model (EPQ) is one of the classic models of inventory control and it has a very important and practical role in manufacturing industry. As the most important things to reduce these internal risks, an efficient inventory control management and production planning can be mentioned, then as results of them, the best service level, cost reduction and optimal use of available resources can be achieved. For this purpose, an EPQ model is developed according to real-world conditions in this research. Shortage in this model is considered a mixture of backordered demand and lost sales and also, the products are divided into two categories of perfectly hale products and non-repairable defective products that fall into the category of scrap. In the other words, the important indicators studied in proposed model are the partial shortage and scrap. Costs related to the backorder demand are taken as fixed and time-dependent. In the proposed model, Inventory cycle length, the length of positive inventory cycle and backordered demand rate are determined during the shortage period to minimizing the total cost of inventory, So that all the stochastic and deterministic constraints of the model including holding costs, lost sales, backorder, budget, screening of products, disposal of scraps, total number of productions and average shortage times should be satisfied. Hence, in proposed model, due to the uncertainty of the real world situation and uncertainty in the availability of resources, a stochastic approach has been used. The presented multi-product model is in form of a single-objective nonlinear programming problem. Then, to solve the proposed model two methods including sequential quadratic programming and interior point algorithm are used. Furthermore, twenty numerical examples are solved by these two methods and SAS software, and the performance of the solution methods are compared using the Tukey's hypothesis test in terms of objective functions, the number of iterations need to achieve the optimal answer and infeasibility. Finally, in this paper, choosing the best method is done by applying the TOPSIS test.