Maximum-Profit Inventory Model with Stock-Dependent Demand, Time-Dependent Holding Cost, and All-Units Quantity Discounts

A new production-planning model with a unique set of realistic features is considered. First, the demand rate is a function of the current inventory level. Second, a new order is gradually produced according to a finite production rate. Third, the unit holding cost per time period is a function of both the unit purchase cost and the storage time duration. Fourth, the unit purchase cost is a function of the production lot size. Fifth, the starting/ending inventory for each cycle is a decision variable to be optimized. Finally, the objective of the model is to maximize the total profit per unit time. The purchase cost per unit decreases with larger lot size according to all-units quantity discount. On the other hand, the holding cost per unit increases with longer storage duration, either retroactively or incrementally. Mathematical models are formulated to represent this production planning system, and optimum solution procedures are developed.