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A continuous time inventory model

Published online by Cambridge University Press:  14 July 2016

J. A. Bather
J. A. Bather*
Affiliation:
University of Manchester
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Extract

This paper discusses an optimization problem arising in the theory of inventory control. Much of the previous work in this field has been focused on the Arrow-Harris-Marschak model, [1], [2], in which the inventory level can be modified only at the instants of discrete time. Here, we shall be concerned with a continuous time analogue of the model, in an attempt to avoid the difficulties experienced in solving the basic integral equations. The approach was suggested by recent investigations of a statistical decision problem, [3], [5], which exploited the advantages of a continuous treatment. Although the ideas discussed here are relatively straightforward and involve strong assumptions as to the behavior of the inventory, the explicit character of the optimal policy is encouraging and particular solutions might nevertheless provide useful restocking procedures.

Type
Research Papers
Information
Journal of Applied Probability , Volume 3 , Issue 2 , December 1966 , pp. 538 - 549
Copyright
Copyright © Applied Probability Trust 

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References

[1] Arrow, K. R., Harris, T. and Marschak, J. (1951) Optimal inventory policy. Econometrika 19, 250–272.CrossRefGoogle Scholar
[2] Arrow, K. J., Karlin, S. and Scarf, H. (1958) Studies in the mathematical theory of inventory and production. Stanford University Press.Google Scholar
[3] Bather, J. A. (1962) Bayes procedures for deciding the sign of a normal mean. Proc. Camb. Phil. Soc. 58, 599–620.Google Scholar
[4] Bather, J. A. (1965) On a quickest detection problem. Stanford University Technical Report No. 9.Google Scholar
[5] Chernoff, H. (1961) Sequential tests for the mean of a normal distribution. Proc. Fourth Berkeley Symposium, 1, 79–91.Google Scholar