An inventory model for growing items with quality inspections and permissible shortages

This paper extends inventory models for growing items by considering quality inspections, permissible shortages with complete backordering, and holding cost during both the growth period and the consumption period. By backordering shortages, the firm can avoid the loss of sales by paying delay penalties to customers who wait for late items. After items reach certain weight preferred by the customers, they are fully inspected, and inferior-quality items are removed at the end of inspection period. The model determines the optimum cycle length and shortage level to minimize the total cost of the inventory system. This cost includes the purchasing, setup, inspection, feeding, holding, and shortage costs. A nonlinear programming model is formulated and an optimum solution algorithm is presented.