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A new approach to (s, S) inventory systems

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Jian-Qiang Hu ,
Soracha Nananukul  and
Wei-Bo Gong
Jian-Qiang Hu*
Affiliation:
Boston University
Soracha Nananukul*
Affiliation:
University of Massachusetts, Amherst
Wei-Bo Gong*
Affiliation:
University of Massachusetts, Amherst
*
∗ Postal address: Department of Manufacturing Engineering, Boston University, 44 Cummington Street, MA 02215, USA.
∗∗ Postal address: Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA 01003, USA.
∗∗ Postal address: Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA 01003, USA.
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Abstract

In this paper, we consider period review (s, S) inventory systems with independent and identically distributed continuous demands and full backlogging. Using an approach recently proposed by Gong and Hu (1992), we derive an infinite system of linear equations for all moments of inventory level. Based on this infinite system, we develop two algorithms to calculate the moments of the inventory level. In the first one, we solve a finite system of linear equations whose solution converges to the moments as its dimension goes to infinity. In the second one, we in fact obtain the power series of the moments with respect to s and S. Both algorithms are based on some very simple recursive procedures. To show their efficiency and speed, we provide some numerical examples for the first algorithm.

(s, S) INVENTORY SYSTEMS; DYNAMIC RECURSIVE EQUATIONS; INFINITE LINEAR EQUATIONS; MACLAURIN SERIES

MSC classification

Primary: 90B05: Inventory, storage, reservoirs
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 4 , December 1993 , pp. 898 - 912
Copyright
Copyright © Applied Probability Trust 1993 

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References

Arrow, K. J., Harris, T. and Marschak, J. (1951) Optimal inventory policy. Econometrica XIX, 250–272.CrossRefGoogle Scholar
Crane, M. A. and Iglehart, D. L. (1975) Simulation stable stochastic systems III: Regenerative processes and discrete-event simulation. Operat. Res. 23, 33–45.CrossRefGoogle Scholar
Gong, W. B. and Hu, F. Q. (1992) The MacLaurin expansions for the GI/G/1 queue. J . Appl. Prob. 29, 176–184.CrossRefGoogle Scholar
Iglehart, D. (1963) Optimality of (s, S) policies in the infinite horizon dynamic inventory problem. Management Sci. 9, 259–267.CrossRefGoogle Scholar
Kantorovich, L. V. and Krylov, V. I. (1964) Approximate Methods of Higher Analysis, translated by Benster, C. D. Wiley, New York.Google Scholar
Sahin, I. (1982) On the objective function behavior in (5, S) inventory models. Operat. Res. 30, 709–724.CrossRefGoogle Scholar
Sahin, I. (1990) Regenerative Inventory Systems: Operating Characteristics and Optimization. Springer-Verlag, Berlin.CrossRefGoogle Scholar
Scarf, H. (1960) The optimality of (s, S) policies in the dynamic inventory problem. In Mathematical Methods in the Social Sciences, Stanford University Press.Google Scholar