The Logarithmic Poisson Gamma Distribution: A Model for Leadtime Demand.

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.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1981
Accession Number
ADA124540

Entities

People

  • Steven Nahmias
  • W. Steven Demmy

Tags

Communities of Interest

  • C4I
  • Human Systems
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Binomials
  • Contracts
  • Distribution Functions
  • Estimators
  • Frequency
  • Inventory
  • Lead Time
  • Method Of Moments
  • Probability
  • Probability Distributions
  • Random Variables
  • Supply Chain Management

Fields of Study

  • Mathematics

Readers

  • Logistics and Supply Chain Management.
  • Statistical inference.