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Diagnosis of Lead Time Demand Based on the Characteristics of Negative Binomial Distribution  

Ahn, Sun-Eung (Department of Industrial Engineering, Hanyang University)
Kim, Woo-Hyun (Department of Industrial Engineering, Hanyang University)
Publication Information
Journal of Korean Society of Industrial and Systems Engineering / v.28, no.4, 2005 , pp. 79-84 More about this Journal
Abstract
Some distributions have been used for diagnosing the lead time demand distribution in inventory system. In this paper, we describe the negative binomial distribution as a suitable demand distribution for a specific retail inventory management application. We here assume that customer order sizes are described by the Poisson distribution with the random parameter following a gamma distribution. This implies in turn that the negative binomial distribution is obtained by mixing the mean of the Poisson distribution with a gamma distribution. The purpose of this paper is to give an interpretation of the negative binomial demand process by considering the sources of variability in the unknown Poisson parameter. Such variability comes from the unknown demand rate and the unknown lead time interval.
Keywords
Negative binomial distribution; Lead time demand; Parameter interpretation;
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1 Grohowski, G., Hausman, W. C., and Lamberson, L. R., 'A Bayesian statistical inference approach to automotive reliability estimation', Journal of Quality Technology, 8, 197-208, 1976
2 Ong, S. H., 'Characterization of the negative binomial and gamma distributions', Biometrical Journal, 37(2), 251-254, 1995   DOI   ScienceOn
3 Percy, D. F., 'Bayesian enhanced strategic decision making for reliability', European Journal of Operational Research, 139(1), 133-145, 2002   DOI   ScienceOn
4 Apostolakis, G., and Mosleh, A., 'Expert opinion and statistical evidence：An application to reactor core melt frequency', Nuclear Science and Engineering, 70(2), 135-149, 1979
5 H. Lee, P. Padmanabhan, and S. Whang, 'The bullwhip effect in supply chain', Sloan Manage Rew, 38(3), 93-102, 1997
6 Engel, J., and Zijlstra, M., 'A characterization of the gamma distribution by the negative binomial distribution', Journal of Applied Probability, 17, 1138-1144, 1980   DOI   ScienceOn
7 Kamath, K. R., & Pakkala, T. P. M., 'A Bayesian approach to a dynamic inventory model under an unknown demand distribution', Computer & Operations Research, 29(4), 403-422, 2002   DOI   ScienceOn
8 Agrawal, N., and Smith, S. A., 'Estimating Negative Binomial Demand for Retail Inventory Management with Unobservable Lost Sales', Naval Research Logistics, 43(6), 839-861, 1996   DOI   ScienceOn
9 Cacoullos, T., and Papageorgiou, H., 'Letter to the editor：Characterizing the negative binomial distribution', Journal of Applied Probability, 19, 742-743, 1982   DOI   ScienceOn
10 Gerber, H. U., 'From the generalized gamma to the generalized negative binomial distribution', Insurance：mathematics and economics, 10(4), 303-309, 1991
11 Osaki, S., & Li, X., 'Characterizations of gamma negative binomial distributions', IEEE Transactions on Reliability, 37(4), 379-382, 1988   DOI   ScienceOn