Short Communication
Some comments on “A simple method to compute economic order quantities”

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Abstract

In this note, we emphasize that the arithmetic–geometric-mean-inequality approach proposed by Teng [Teng, J.T., 2008. A simple method to compute economic order quantities. European Journal of Operational Research. doi:10.1016/j.ejor.2008.05.019] is not a general solution method. Teng’s approach happens to work and give the correct results when the two terms in an objective function are any functions such that their product is a constant. The classical EOQ model works fine since the product of the two terms is indeed a constant! When the product is not a constant, Teng’s approach is of little use. This is exemplified in Comment 1 via solving the EOQ model with complete backorders (where the model is regarded as having two decision variables). Comment 2 is generally valid for an algebraic method when it is used to solve an objective function with two decision variables.

Introduction

In this note, we expound and exemplify in Comment 1 that the arithmetic–geometric-mean-inequality approach proposed by Teng (2008) is not a general solution method. In addition, we advocate in Comment 2 that the checking of the global minimum solution is necessary when we solve an objective function with two decision variables without derivatives.

Section snippets

Comment 1

If the value of the fill rate r in Eq. (7) of Teng (2008) is given (somehow fixed by a decision maker), Eqs. (10) and (11) derived using the inequality of arithmetic and geometric-means are correct because the product of AdQ and Q2[hr2+v(1-r)2] is Ad2[hr2+v(1-r)2] which is a constant. However, if the value of r is not fixed and is taken to be a decision variable, Teng’s approach cannot completely solve the EOQ model with complete backorders, i.e. Case (2) in Teng (2008), let alone solving the

Comment 2

If the objective function given by Eq. (7) of Teng (2008) is regarded as having two decision variables Q and r and hence denoted by TC(Q,r), in order to determine which is the global minimum of TC(Q,r), we must compare the following three situations:

Situation (a): The existence of both positive inventory and negative inventory (i.e. complete backorders) implies that 0<r<1. The optimal solution (Q∗,r∗) is given by Eqs. (1), (2) and the resulting local minimum cost is given by Eq. (3) and denoted

Acknowledgements

The author is grateful to one of the three anonymous referees for constructive comments that led to essential improvement in this note. His/Her appropriate suggestions were included in the text.

References (15)

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