Average cost optimality in inventory models with markovian demands and lost sales

Analysis, Control and Optimization of Complex Dynamic Systems

Volumn , Issue , 2005, Pages 3-23

  Beyer, Dirk ^a   Sethi, Suresh P ^b  

^a HEWLETT PACKARD LABORATORIES   (United States)

^b UNIVERSITY OF TEXAS AT DALLAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77949425421     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/0-387-25477-3_1     Document Type: Chapter

References (18)

1. Bensoussan, A., Crouhy, M., and Proth, J. (1983). Mathematical Theory of Production Planning. North-Holland.
2. Beyer, D., Cheng, F., and Sethi, S.P. (2004). Inventory Models in Markovian Environments. Kluwer. Forthcoming
3. Beyer, D. and Sethi, S.P. (1997). Average cost optimality in inventory models with Markovian demand. Journal of Optimization Theory and Applications, 92(3):497-526.
4. Beyer, D. and Sethi, S.P. (1999). The classical average-cost inventory models of Iglehart and Veinott-Wagner revisited. Journal of Optimization Theory and Applications, 101(3):523-555.
5. Beyer, D., Sethi, S.P., and Taksar, M. (1998). Inventory models with Markovian demands and cost functions of polynomial growth. Journal of Optimization Theory and Application, 98(2):281-323.
6. Cheng, F. and Sethi, S.P. (1999). Optimality of state-dependent (s,S) policies in inventory models with Markov-modulated demand and lost sales. Production and Operations Management, 8(2):183-192.
7. Federgruen, A. and Zipkin, P. (1984). An efficient algorithm for computing optimal (s,S) policies. Operations Research, 32:1268-1285.
8. Feller, W. (1971). An Introduction to Probability Theory and its Application. Vol. 2, 2nd Edition, Wiley, New York, NY.
9. Gikhman, I. and Skorokhod, A. (1972). Stochastic Differential Equations. Springer Verlag, Berlin, Germany.
10. Karlin, S. and Fabens, A. (1960). The (s,S) inventory model under Markovian demand process. In: Mathematical Methods in the Social Sciences (K. Arrow, S. Karlin, and P. Suppes, eds.), pp. 159-175, Stanford University Press, Stanford, CA.
11. Ozekici, S. and Parlar, M. (1999). Inventory models with unreliable suppliers in random environment. Annals of Operations Research, 91:123-136.
12. Scarf, H. (1960). The Optimality of (s,S) Policies in the Dynamic Inventory Problem. In: Mathematical Methods in the Social Sciences (K. Arrow, S. Karlin, and P. Suppes, eds.), pp. 196-202, Stanford University Press, Stanford, CA.
13. Sethi, S.P. and Cheng, F. (1997). Optimality of (s,S) policies in inventory models with Markovian demand processes. Operations Research, 45(6):931-939.
14. Shreve, S.E. (1976). Abbreviated proof in the lost sales case. In: Dynamic Programming and Stochastic Control (D.P. Bertsekas, ed.), pp. 105-106 Academic Press, New York, NY.
15. Song, J.S. and Zipkin, P. (1993). Inventory control in a fluctuating demand environment. Operations Research, 41:351-370.
16. Sznadjer, R. and Filar, J.A. (1992). Some comments on a theorem of Hardy and Littlewood. Journal of Optimization Theory and Applications, 75(1):201-208.
17. Veinott, A. (1966). On the optimality of (s,S) inventory policies: New conditions and a new proof. SIAM Journal on Applied Mathematics, 14(5):1067-1083.
18. Yosida, K. (1980). Functional Analysis, 6th Edition, Springer Verlag, New York, New York.