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ON THE STRUCTURE OF OPTIMAL ORDERING POLICIES FOR STOCHASTIC INVENTORY SYSTEMS WITH MINIMUM ORDER QUANTITY

Published online by Cambridge University Press:  06 March 2006

Yao Zhao  and
Michael N. Katehakis
Yao Zhao
Affiliation:
Department of Management Science and Information Systems, Rutgers University, The State University of New Jersey, Newark, NJ 07102-1895, E-mail: yaozhao@andromeda.rutgers.edu
Michael N. Katehakis
Affiliation:
Department of Management Science and Information Systems, Rutgers University, The State University of New Jersey, Newark, NJ 07102-1895, E-mail: mnk@andromeda.rutgers.edu
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Abstract

We study a single-product periodic-review inventory model in which the ordering quantity is either zero or at least a minimum order size. The ordering cost is a linear function of the ordering quantity, and the demand in different time periods are independent random variables. The objective is to characterize the inventory policies that minimize the total discounted ordering, holding, and backorder penalty costs over a finite time horizon. We introduce the concept of an M-increasing function. These functions allow us to characterize the optimal inventory policies everywhere in the state space outside of an interval for each time period. Furthermore, we identify easily computable upper bounds and asymptotic lower bounds for these intervals. Finally, examples are given to demonstrate the complex structure of the optimal inventory policies.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 2 , April 2006 , pp. 257 - 270
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Axsater, S. (1993). Continuous review policies for multi-level inventory systems with stochastic demand. In S. Graves, A. Rinnooy Kan, & P. Zipkin (eds.), Logistics of production and inventory. Amsterdam: Elsevier (North-Holland).
Bertsekas, D.P. (1995). Dynamic programming and optimal control, Vol. 2. Belmont, MA: Athena Scientific.
Chan, E.W. & Muckstadt, J.A. (1999). The effects of load smoothing on inventory levels in a capacitated production inventory system. Technical Report, School of Operations Research and Industrial Engineering. Cornell University, Ithaca, NY.
Chen, F. (2000). Optimal policies for multi-echelon inventory problems with batch ordering. Operations Research 48: 376–389.Google Scholar
De Bodt, M.A. & Graves, S.C. (1985). Continuous-review policies for a multi-echelon inventory problem with stochastic demand. Management Science 31: 1286–1299.Google Scholar
Federgruen, A. & Katalan, Z. (1996). The stochastic economic lot scheduling problem: Cyclical base-stock policies with idle times. Management Science 42: 783–796.Google Scholar
Fisher, M. & Raman, A. (1996). Reducing the cost of demand uncertainty through accurate response to early sales. Operations Research 44: 87–99.Google Scholar
Gallego, G. & Wolf, A.S. (2000). Capacitated inventory problems with fixed order costs: Some optimal policy structure. European Journal of Operational Research 126: 603–613.Google Scholar
Heyman, D. & Sobel, M. (1984). Stochastic models in operations research, Vol. 2. New York: McGraw-Hill.
Karlin, S. (1958). Optimal inventory policy for the Arrow–Harris–Marschak dynamic model. In K.J. Arrow, S. Karlin, & H. Scarf (eds.), Studies in the Mathematical Theory of Inventory and Production. Stanford, CA: Stanford University Press.
Karmarkar, U. (1987). Lot sizes, lead-times and in-process inventories. Management Science 33: 409–419.Google Scholar
Katehakis, M. & Bradford, P. (2002). Contract constrained resource allocation. In INFORMS Annual Meeting, San Jose, CA.
Lee, H.L. & Moinzadeh, K. (1987). Two-parameter approximations for multi-echelon repairable inventory models with batch ordering policy. IIE Transaction 19: 140–149.Google Scholar
Porteus, E.L. (1971). On the optimality of generalized (s,S) policies. Management Science 17: 411–427.Google Scholar
Ross, S.M. (1970). Applied probability models with optimization applications. New York: Dover.
Scarf, H. (1960). The optimality of (s,S) policies in dynamic inventory problems. In K. Arrow, S. Karlin, & P. Suppes (eds.), Mathematical models in the social sciences. Stanford, CA: Stanford University Press.
Sethi, S.P. & Cheng, F. (1997). Optimality of (s,S) policies in inventory models with Markovian demand. Operations Research 45: 931–939.Google Scholar
Song, J.S. & Yao, D.D. (2001). Supply chain structures: Coordination, information and optimization. Boston: Kluwer Academic.
Veinott, A.F. (1965). The optimal inventory policy for batch ordering. Operations Research 13: 424–432.Google Scholar
Veinott, A.F. (1966). On the optimality of (s,S) inventory policies: New conditions and a new proof. SIAM Journal of Applied Mathematics 14: 525–552.Google Scholar
Veinott, A.F. & Wagner, H. (1965). Computing optimal (s,S) inventory policies. Management Science 11: 525–552.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. (2000). Foundations of inventory management. Boston: McGraw-Hill.