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Determining Order Quantity and Selling Price by Geometric Programming: Optimal Solution, Bounds, and Sensitivity *
Author(s) -
Lee Won J.
Publication year - 1993
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1993.tb00463.x
Subject(s) - bounding overwatch , mathematical optimization , sizing , profit (economics) , sensitivity (control systems) , computer science , nonlinear system , schedule , nonlinear programming , nonlinear pricing , economic order quantity , pricing schedule , geometric programming , mathematics , economics , microeconomics , econometrics , supply chain , art , artificial intelligence , electronic engineering , law , engineering , visual arts , operating system , quantum mechanics , political science , physics , capital asset pricing model , rational pricing
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.