Optimization Model for Determining Order Quantity for Growing Item Considering Incremental Discount and Imperfect Quality

This research develops an optimization model of order quantities for growing items by considering incremental discounts and imperfect quality. For growing items, the assumption that inventory weights that always fixed cannot be applied. The supply system has grown so that the weight of the inventory has increased over a certain period. The proposed inventory system has two periods namely growth and consumption period. Suppliers offer incremental discounts for certain purchases. In this research also considered the existence of imperfect quality, where for newborn items purchased at the beginning of each cycle found items with poor quality and death. During the growth period, not all items survive until the end of the period, therefore also considering the probability density function of survival and death of growing items. The proposed inventory system is maximization profit, with total profits being an objective function, and cycle times and order quantities as decision variables. Costs involved include purchased cost by considering by incremental discounts, setup costs, holding costs, and disposal costs. Application and model validation is demonstrated by numerical examples in the poultry industry. The model developed in this study can be used as a suggestion for companies to make purchasing decisions.