An Economic Order Quantity Model for Growing Items with Imperfect Quality and Shortages

Inventory models of growing items are used when the stored items (such as poultry, fish, and livestock) have the capability to grow during the inventory replenishment cycle. This paper extends inventory models for growing items by considering quality aspects, permissible shortages with complete backordering, and holding cost during both the growth period and the consumption period. Permitting shortages with complete backordering can reduce inventory holding costs while avoiding the loss of sales by paying delay penalties to consumers who wait for the fresh items. Since a proportion of fully grown mature items are defective, they are fully inspected and lower-quality items are removed at the end of the inspection period. A nonlinear programming model is formulated and used to determine the optimum cycle length and shortage level in order to minimize the total costs of the inventory system. These costs include the purchasing, setup, inspection, feeding, holding, and shortage costs. The convexity of the objective function is shown, and it is utilized to develop an efficient optimum solution algorithm.