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# Use of Erlang Distribution in Replenishment Control

IP.com Disclosure Number: IPCOM000049836D
Original Publication Date: 1982-Jul-01
Included in the Prior Art Database: 2005-Feb-09
Document File: 2 page(s) / 13K

IBM

## Related People

Dawkins, J: AUTHOR

## Abstract

Background Most of the theory associated with replenishment control is derived for product demands with Normal distributions. This is fine for demands which never approach zero, and which arise from a large number of uncorrelated sources. If this is not the case, then: * The negative tail of the distribution can no longer be ignored * The demand exhibits too much variability from period to period A candidate for characterizing the probability distribution of the demand in this case is the Erlang distribution.

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Use of Erlang Distribution in Replenishment Control

Background

Most of the theory associated with replenishment control is derived for product demands with Normal distributions. This is fine for demands which never approach zero, and which arise from a large number of uncorrelated sources. If this is not the case, then: * The negative tail of the distribution can no longer be ignored * The demand exhibits too much variability from period to period

A candidate for characterizing the probability distribution of the demand in this case is the Erlang distribution.

The family of Erlang distributions can be conceived as arising by convolving the Exponential distribution a number of times. In the limit, the Normal distribution is obtained. Although the distribution is asymmetric, it has no non- zero probabilities for demand values less than zero. Also, starting with the Exponential distribution, which has no correlation between periods, any degree of correlation can be modeled.

Description

An Erlang distribution can be characterized with two

factors, like the Normal distribution. These are:
1. Scale factor (b)
2. Shape factor (c).

The measurable quantities mean and mean absolute deviation (MAD) are related as follows: mean equals b * c

MAD equals 2 * b * c * exp(-c) / c!

Thus given mean and MAD, the scale and shape factors may be computed.

In order to get to compute the safety stock needed to support a given demand pattern and service level, we need to obtain an express...