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An application of the system-point method to inventory models under continuous review

Published online by Cambridge University Press:  14 July 2016

K. Azoury  and
P. H. Brill
K. Azoury*
Affiliation:
California State University, Northridge
P. H. Brill*
Affiliation:
University of Windsor
*
∗Postal address: Department of Management Science, California State University, Northridge, CA 91330, USA.
∗∗Postal address: Department of Industrial Engineering, University of Windsor, Windsor, Ontario, Canada N9B 3P4.
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Abstract

This paper derives the stationary probability distribution of inventory level for continuous-review models, by means of the system-point method of level-crossing analysis. We analyze inventory problems with decaying products under (nQ, r) and (s, S) ordering policies and zero lead-time, and derive the relevant cost functions. Our results have implications for the case of positive lead-time and to a non-decaying inventory problem with two types of demand processes.

Keywords

STATIONARY DISTRIBUTIONSLEVEL CROSSINGS
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 778 - 789
Copyright
Copyright © Applied Probability Trust 1986 

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References

[1] Arrow, K. J., Karlin, S. and Scarf, H. (eds.), 1958 Studies in the Mathematical Theory of Inventory and Production. Stanford University Press, Stanford, CA.Google Scholar
[2] Azoury, K. and Brill, P. H. (1983) A system-point approach to inventory models. Technical Report # 83–06, University of Waterloo, Department of Statistics and Actuarial Science.Google Scholar
[3] Boyce, W. E. and Di Prima, R. C. (1968) Elementary Differential Equations and Boundary Value Problems, 2nd edn. Wiley, New York.Google Scholar
[4] Brill, P. H. (1975) System-Point Theory in Exponential Queues. Ph.D. Dissertation, University of Toronto.Google Scholar
[5] Brill, P. H. (1979) An embedded level crossing technique for dams and queues. J. Appl. Prob. 16, 174–186.Google Scholar
[6] Brill, P. H. and Posner, M. J. M. (1981) The system-point method in exponential queues. A level crossing approach. Math. Operat. Res. 6, 31–47.Google Scholar
[7] Feldman, R. M. (1978) A continuous review (s, S) inventory system in a random environment. J. Appl. Prob. 15, 654–659.CrossRefGoogle Scholar
[8] Ghare, P. M. and Schrader, G. F. (1963) A model for exponentially decaying inventory. J. Ind. Engineering XIV, 238–243.Google Scholar
[9] Hadley, G. and Whitin, T. M. (1963) Analysis of Inventory Systems. Prentice-Hall, Toronto.Google Scholar
[10] Karlin, S. and Taylor, H. M. (1975) A First Course in Stochastic Processes, 2nd edn. Academic Press, New York.Google Scholar
[11] Nahmias, S. and Wang, S. S. (1979) A heuristic lot size reorder point model for decaying inventories. Management Sci. 25, 90–97.Google Scholar
[12] Peterson, R. and Silver, E. (1979) Decision Systems for Inventory Management and Production Planning. Wiley, New York.Google Scholar
[13] Richards, F. R. (1975) Comments on the distribution of inventory position in a continuous review (s, S) inventory system. Operat. Res. 23, 366–371.Google Scholar
[14] Sahin, I. (1979) On the stationary analysis of continuous review (s, S) inventory systems and constant lead times. Operat. Res. 27, 717–729.Google Scholar
[15] Shah, Y. K. and Jaiswal, M. (1977) An order level model for a system with constant rate of deterioration. Opsearch 14, 174–184.Google Scholar
[16] Sivazlian, D. B. (1974) A continuous review (s, S) inventory system with arbitrary interarrival distribution between unit demand. Operat. Res. 22, 65–76.Google Scholar
[17] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
[18] Tijms, H. C. (1972) Analysis of (s, S) Inventory Models. Mathematical Centre Tracts 40, Mathematich Centrum, Amsterdam.Google Scholar