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OPTIMIZATION AND OPTIMALITY OF (s,S) STOCHASTIC INVENTORY SYSTEMS WITH NON-QUASICONVEX COSTS

Published online by Cambridge University Press:  06 March 2006

Frank Y. Chen  and
Y. Feng
Frank Y. Chen
Affiliation:
Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong, China, E-mail: [email protected]; [email protected]
Y. Feng
Affiliation:
Department of Systems Engineering & Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong, China, E-mail: [email protected]; [email protected]
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Abstract

This article considers the optimization and optimality of single-item/location, infinite-horizon, (s,S) inventory models. Departing from the conventional approach, we do not assume the loss function describing holding and shortage costs per period to be quasiconvex. As the existing optimization algorithms have been established on the condition of quasiconvexity, our goal in this article is to develop a computational procedure for obtaining optimal (s,S) policies for models with general loss functions. Our algorithm is based on the parametric method commonly used in fractional programming and is intuitive, exact, and efficient. Moreover, this method allows us to extend the optimality of (s,S) policies to a broader class of loss functions that can be non-quasiconvex.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 2 , April 2006 , pp. 287 - 306
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Ballou, R.H. (1999). Business logistics management: Planning, organizing, and controlling the supply chain, 4th ed. Upper Saddle River, NJ: Prentice-Hall.
Bashyam, S. & Fu, M.C. (1998). Optimization of (s,S) inventory systems with random lead times and a service level constraint. Management Science 44: 243–256.Google Scholar
Chen, F. & Zheng, Y.-S. (1993). Inventory models with general backorder costs. European Journal of Operational Research 65: 175–186.Google Scholar
Chen, Y. & Feng, Y. (2004). Optimization and optimality of (s,S) stochastic inventory systems with non-quasiconvex costs. Unabridged version, Department of System Engineering & Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong, China. Downloadable from www.se.cuhk.edu.hk/yhchen.
Eppen, G.D. & Martin, R.K. (1988). Determining safety stock in the presence of stochastic lead time and demand. Management Science 34: 1380–1390.Google Scholar
Feng, Y. & Sun, J. (2001). An algorithm for deriving (r,R,d,D) inventory replenishment policy. Operations Research 49: 1380–1390.Google Scholar
Feng, Y. & Xiao, B. (2000). New algorithms for computing optimal (s,S) policies in a stochastic single item/location inventory system. IIE Transactions 32: 1081–1090.Google Scholar
Hadley, G. & Whitin, T.M. (1963). Analysis of inventory systems. Upper Saddle River, NJ: Prentice-Hall.
Iglehart, D. (1963). Optimality of (s,S) policies in the infinite horizon dynamic inventory problem. Management Science 10: 259–267.Google Scholar
Li, Z., Xu, S.H., & Hayya, J. (2004). A periodic-review inventory system with supply interruptions. Probability in the Engineering and Informational Sciences 18: 33–53.Google Scholar
Rosling, K. (2002). Applicable cost rate functions for single-item inventory control. Operations Research 50: 1007–1017.Google Scholar
Ross, S. (1983). Stochastic processes. New York: Wiley.
Scarf, H. (1960). The optimailtiy of (s,S) policies in the dynamic inventory problem. In K. Arrow, S. Karlin, & P. Suppes (eds.), Mathematical methods in the social sciences. Stanford, CA: Stanford University Press, Chap. 22.
Sethi, S. & Cheng, F. (1997). Optimality of (s,S) policies in inventory models with Markovian demands. Operations Research 45: 931–939.Google Scholar
Silver, E.A., Pyke D., &Peterson, R.A. (1998). Inventory management and production planning and scheduling, 3rd ed. New York: Wiley.
Song, J.-S. & Zipkin, P. (1993). Inventory control in a fluctuating demand environment. Operations Research 41: 351–370.Google Scholar
Veinott, A., Jr. (1966). On the optimality of (s,S) inventory policies: New conditions and a new proof. SIAM Journal of Applied Mathematics 14: 1067–1083.Google Scholar
Veinott, A., Jr. & Wagner, H.M. (1965). Computing optimal (s,S) inventory policies. Management Science 11: 690–723.Google Scholar
Zheng, Y.-S. (1991). A simple proof for optimality of (s,S) policies in infinite-horizon inventory systems. Journal of Applied Probability 28: 802–810.Google Scholar
Zheng, Y.-S. & Federgruen, A. (1991). Finding optimal (s,S) policies is about as simple as evaluating a single policy. Operations Research 39: 654–665.Google Scholar
Zipkin, P. (1999) Foundations of inventory management. Singapore: McGraw-Hill Higher Education, pp. 196–198.