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A Single-Item Inventory Model for a Nonstationary Demand Process

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Stephen C. Graves at Massachusetts Institute of Technology
Stephen C. Graves
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Abstract

In preparing a review I recently discovered an important reference for a key result in Graves (1999). Wecker (1979) had previously derived the variance for demand over a deterministic lead-time for an IMA (0, 1, 1) demand process. I develop effectively the same result, given as Equation (8) in Graves (1999). I state this as the variance of the inventory random variable for an inventory system that is subject to an IMA (0, 1, 1) demand process, a deterministic replenishment lead-time and an adaptive base-stock control policy given by (7). But given these assumptions, the variance of the inventory is the same as the variance of the demand over the lead-time. Although the Wecker manuscript has not been published, Eppen and Martin (1988) reference it and use the key result as part of their research.
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Addendum to “A Single-Item Inventory Model for a
Nonstationary Demand Process”
Stephen C. Graves,
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Stephen C. Graves, (1999) Addendum to “A Single-Item Inventory Model for a Nonstationary Demand Process”. Manufacturing
& Service Operations Management 1(2):174-174. http://dx.doi.org/10.1287/msom.1.2.174
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Manufacturing & Service Operations Management
Vol. 1, No. 2, 1999, p. 174
1523-4614/99/0102/0174$05.00
Copyright 䉷1999, Institute for Operations Research
and the Management Sciences
Addendum to “A Single-Item Inventory
Model for a Nonstationary
Demand Process”
Stephen C. Graves
Leaders for Manufacturing Program and A. P. Sloan School of Management, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139-4307
In preparing a review I recently discovered an important reference for a key result in Graves
(1999). Wecker (1979) had previously derived the variance for demand over a deterministic
lead-time for an IMA (0, 1, 1) demand process. I develop effectively the same result, given as
Equation (8) in Graves (1999). I state this as the variance of the inventory random variable for
an inventory system that is subject to an IMA (0, 1, 1) demand process, a deterministic re-
plenishment lead-time and an adaptive base-stock control policy given by (7). But given these
assumptions, the variance of the inventory is the same as the variance of the demand over the
lead-time.
Although the Wecker manuscript has not been published, Eppen and Martin (1988) reference
it and use the key result as part of their research.
References
Eppen, Gary D., R. Kipp Martin. 1988. Determining safety stock in the presence of stochastic lead time and demand.
Management Sci. 34 1380–1390.
Graves, Stephen C. 1999. A single-item inventory model for a nonstationary demand process. M&SOM 150–61.
Wecker, William E. 1979. The variance of cumulative demand forecasts. Working Paper, Graduate School of Business.
University of Chicago, January, 5 pp.
Downloaded from informs.org by [159.8.54.34] on 28 August 2015, at 17:35 . For personal use only, all rights reserved.
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The variance of cumulative demand forecasts. Working Paper, Graduate School of Business
  • Jan 1979
  • pp
  • William E Wecker
Wecker, William E. 1979. The variance of cumulative demand forecasts. Working Paper, Graduate School of Business. University of Chicago, January, 5 pp.