Approximate and exact formulas for the $(Q,r)$ inventory model

Zvi Drezner; Carlton Scott

doi:10.3934/jimo.2015.11.135

Article Contents

2015, Volume 11, Issue 1: 135-144. Doi: 10.3934/jimo.2015.11.135

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Approximate and exact formulas for the $(Q,r)$ inventory model

Zvi Drezner^1, and
Carlton Scott^2,

1.
Steven G. Mihaylo College of Business and Economics, California State University-Fullerton, Fullerton, CA 92634
2.
The Paul Merage School of Business, University of California, Irvine, CA 92697

Received: January 1, 2012

Revised: January 1, 2014

Published online: May 1, 2014

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Abstract

In this paper, new results are derived for the $(Q,r)$ stochastic inventory model. We derive approximate formulas for the optimal solution for the particular case of an exponential demand distribution. The approximate solution is within 0.29% of the optimal value. We also derive simple formulas for a Poisson demand distribution. The original expression involves double summation. We simplify the formula and are able to calculate the exact value of the objective function in $O(1)$ time with no need for any summations.

Keywords:

Mathematics Subject Classification: Primary: 90B05; Secondary: 33F05, 34K28.

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References

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