Production and inventory planning with variable holding cost and all-units quantity discounts

A new production-inventory planning model is considered, in which the holding cost is variable and the purchase cost is subject to quantity discounts. The new production-inventory planning model has three important and realistic features. First, the production rate is finite, so the whole order is not received in one instant, but is gradually produced. Second, the unit holding cost of each item per time period is not constant throughout the entire storage duration, but it increases with longer storage times. Third, the unit purchase cost of each item is not constant, but it decreases with larger orders according to an all-units quantity discount structure. Considering these features, mathematical formulations and optimum solution procedures are developed for two types of holding costs functions of storage time: retroactive increase, and incremental increase.