Determining Order Quantity and Selling Price by Geometric Programming: Optimal Solution, Bounds, and Sensitivity*

Abstract

ABSTRACT This paper presents a geometric programming (GP) approach to finding a profit‐maximizing selling price and order quantity for a retailer. Demand is treated as a nonlinear function of price with a constant elasticity. The proposed GP approach finds optimal solutions for both no‐quantity discounts and continuous quantity discounts cases. This approach is superior to the traditional approaches of solving a system of nonlinear equations. Since the profit function is not concave, the traditional approaches may require an exhaustive search, especially for the continuous discounts schedule case. By applying readily available theories in GP, we easily can find global optimal solutions for both cases. More importantly, the GP approach provides lower and upper bounds on the optimal profit level and sensitivity results which are unavailable from the traditional approaches. These bounding and sensitivity results are further utilized to provide additional important managerial implications on pricing and lot‐sizing policies.

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