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 Biological Sciences Biology |
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The Logarithmic Poisson Gamma Distribution: A Model for Leadtime Demand
Authors: Steven Nahmias; W. Steven Demmy; DECISION SYSTEMS BEAVERCREEK OH |
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Abstract: Many of the inventory models which are used in practice rely upon knowning the probability distribution of demand over a leadtime. The common assumption is that this distribution is normal. However, in certain circumstances, the normality assumption may be inappropriate. We consider a process in which demand occurrences obey a stationary Poisson process and at each occurrence a random number of units are demanded. Furthermore, the leadtime for replenishment is assumed to be random as well. Assuming a logarithmic compounding distribution and a gamma distribution of leadtime we derive the exact distribution of total demand in a leadtime. We call this the Logarithmic- Poisson-Gamma (LPG) distribution. An approximation is derived which is equivalent to a scaled version of the negative binomial distribution. In the final section we derive the first four central moments.
| Description: |
Interim rept. |
| Pages: |
19 |
| Report Date: |
DEC 1981 |
| Contract Number: |
F33600-80-C-0530 |
| Report Number: |
A045421 |
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