A simple approach with basic inequities on EOQ model

Professor Teng (2008) proposed a simple method by using the arithmetic-geometric mean inequality theorem to compute the global minimum economic order quantities. For EOQ or EPQ models to determine the only one decision variable, i.e., the size of order, Teng’s method yields the global minimum solution explicitly and immediately but fails to solve multi-variable inventory problem.

Dr. Tsupang Hsieh and I propose a simple approach with basic inequities such as Cauchy-Schwarz inequality and arithmetic-geometric mean inequality (or more briefly the AM-GM inequality) to solve the trandional EOQ model with shortages. Without taking differential calculus or using the method of completing the square, the solution procedure proposed by using basic inequities is easier to find the optimal solutions.

The annual cost function simplified by AM-GM inequality can be written in the form


Since Cauchy-Schwarz inequality implies that


Thus, we have



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Proof of the AM-GM inequality

Tags: Teaching

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