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A generalised incomplete beta function and its application to multi-line stock control

Published online by Cambridge University Press:  14 July 2016

J. C. Gittins and
M. J. Maher
J. C. Gittins
Affiliation:
University Engineering Laboratory, Cambridge
M. J. Maher
Affiliation:
Institute for Transport Studies, Leeds University
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Abstract

The distribution function for the negative binomial distribution is known to be an incomplete beta function. Here, some of the properties of the family of distribution functions for multivariate negative binomial distributions are explored. These properties are then used in deriving the expected cost per unit time for a multi-line joint-reordering system with Poisson demands. Policies are considered for which the quantity of any particular line in stock is the same at the beginning of every cycle. A method which gives good approximations to the optimal values of these quantities is described.

Keywords

GENERAL INCOMPLETE BETA FUNCTIONMULTI-LINE JOINT-REORDERING STOCK CONTROLNEGATIVE MULTINOMIAL DISTRIBUTIONOPTIMAL STOCHASTIC CONTROL

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973, pp. 748 - 760
Copyright
Copyright © Applied Probability Trust 1973 

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