Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts

In typical EOQ-based inventory models, the demand rate and the holding cost are assumed to have constant values and the unit purchase cost is assumed constant regardless of the order size. In actual applications, however, the demand rate for a specific item can be affected by many variables such as seasonality, selling price, and availability. Moreover, the unit holding cost tends to be higher for extended storage periods. Additionally, the unit purchase cost is generally lower for larger order sizes due to quantity discounts. The objective of this paper is to simultaneously consider the variability of the demand rate, the unit holding cost, and the unit purchase cost. An inventory model is presented with a selling price-dependent demand rate, a storage time-dependent holding cost, and an order size-dependent purchase cost based on all-units quantity discount. A mathematical model is constructed, and a solution methodology is developed for determining the optimal solution. A numerical example is solved, and sensitivity analysis is conducted to study the effect of various parameters on the optimal solution.