An EPQ model for deteriorating products with delayed payments and shortage

Document Type : Research Paper


1 Assistant professor of department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran

2 Department of Industrial Engineering, University of Kurdistan, Sanandaj, Iran

3 Instructor, Department of technology and engineering, Payame Noor University, PO BOX 19395-3697, Tehran, Iran



Credit incentives are crucial tools in the supply chain and inventory management. Using this strategy, the buyer could pay the purchase cost with a delay. Therefore, it will increase the order quantity and the buyer's satisfaction. This paper investigates the economic production model considering the incentive conditions for supplier credit, variable demand, deteriorating items, and shortages. It is assumed that the supplier sends the ordered items to the manufacturer on time; however, he receives the purchase price of the products after a permitted delay.
Furthermore, the deterioration rate is a fixed percentage of the inventory level. Therefore, a nonlinear programming model is proposed for figuring out replenishment policy by minimizing the total inventory cost. The best replenishment policy is examined employing by Wolfram Mathematica. Moreover, a genetic algorithm is suggested due to the model's nonlinearity. Numerical analyses show that while the results do not significantly differ, the proposed GA reaches near-optimum solutions in less CPU time.