Multi-Period Multi-Product Joint Pricing and Inventory Control with Deterministic Demand

A multi-period multi-product joint pricing and inventory control problem with applications to inventory planning is studied. Consider a retailer with a finite resource which it can use to order a variety of products. The demand for each product is non-increasing, deterministic and price dependent. The selling horizon is finite and divided into multiple periods. At the beginning of each period, the retailer has to decide how much of each product to order and at which price to maximize its expected profit. We consider two cases such as the models without and with resource constraint. There are unique optimal solutions in each period for optimal retail price and order size of each product. A Lagrangian Multiplier solution method for the problem is developed.