On the structure of lost-sales inventory models

Operations Research

Volumn 56, Issue 4, 2008, Pages 937-944

  Zipkin, Paul ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BASIC MODELS; INVENTORY MODELS; INVENTORY SYSTEMS; NEW APPROACHES; OPTIMAL POLICIES; VARIABLE DEMANDS;

STRUCTURAL ANALYSIS;

INVENTORY CONTROL;

EID: 59249108112     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.1070.0482     Document Type: Article

References (29)

1. Arslan H., S. Graves, T. Roemer. 2007. A single-product inventory model for multiple demand classes. Management Sci. 53 1486-1500.
2. de Véricourt, F., F. Karaesmen, Y. Dallery. 2002. Optimal stock allocation for a capacitated supply system. Management Sci. 48 1486-1501.
3. Deshpande, V., M. Cohen, K. Donohue. 2003. A threshold inventory rationing policy for service-differentiated demand classes. Management Sci. 49 683-703.
4. Ehrhardt, R. 1984. (s, S) policies for a dynamic inventory model with stochastic leadtimes. Oper. Res. 32 121-132.
5. Federgruen, A., P. Zipkin. 1986. An inventory model with limited production capacity and uncertain demands. Math. Oper: Res. 11 193-215.
6. Ha, A. 1997. Inventory rationing in a make-to-stock production system with several demand classes and lost sales. Management Sci. 43 1093-1103.
7. Huh, W., G. Janakiraman. 2005. Average cost inventory models: An analysis using Schäl's vanishing discount results. Working paper, Stern School of Business, New York University, New York.
8. Iglehart, D., S. Karlin. 1962. Optimal policy for dynamic inventory process with nonstationary stochastic demands. K. Arrow, S. Karlin, H. Scarf, eds. Studies in Applied Probability and Management Science, Chapter 8. Stanford University Press, Stanford, CA.
9. Kaplan, R. 1970. A dynamic inventory model with stochastic lead times. Management Sci. 16 491-507.
10. Karlin, S., H. Scarf. 1958. Inventory models of the Arrow-HarrisMarschak type with time lag. K. Arrow, S. Karlin, H. Scarf, eds. Studies in the Mathematical Theory of Inventory and Production, Chapter 10. Stanford University Press, Stanford, CA.
11. Kranenburg, A., G. van Houtum. 2007. Cost optimization in the (S- 1,S) lost sales inventory model with multiple demand classes. Oper: Res. Lett. 35 493-502.
12. Lu, Y., J. Song. 2005. Order-based cost optimization in assemble-to-order systems. Oper: Res. 53 151-169.
13. Miller, B. 1971. On minimizing nonseparable functions defined on the integers with an inventory application. SIAM J. Appl. Math. 21 166-185.
14. Morton, T. 1969. Bounds on the solution of the lagged optimal inventory equation with no demand backlogging and proportional costs. SIAM Rev. 11 572-576.
15. Murota, K. 2003. Discrete Convex Analysis. SIAM, Philadelphia.
16. Murota, K. 2005. Note on multimodularity and L-convexity. Math. Oper: Res. 30 658-661.
17. Murota, K., A. Shioura. 2004a. Fundamental properties of M-convex and L-convex functions in continuous variables. IEICE Trans. Fundamentals Electronics, Comm. Comput. Sci. E87-A 1042-1052.
18. Murota, K., A. Shioura. 2004b. Conjugacy relationship between M-convex and L-convex functions in continuous variables. Math. Programming, Ser. A 101 415-433.
19. Nahmias, S. 1979. Simple approximations for a variety of dynamic leadtime lost-sales inventory models. Oper. Res. 27 904-924.
20. Porteus, E. 2002. Foundations of Stochastic Inventory Theory. Stanford University Press, Stanford, CA.
21. Sethi, S., F. Cheng. 1997. Optimality of (s, S) policies in inventory models with Markovian demand. Oper: Res. 45 931-939.
22. Smith, J., K. McCardle. 2002. Structural properties of stochastic dynamic programs. Oper: Res. 50 796-809.
23. Song, J. 1994. The effect of leadtime uncertainty in a simple stochastic inventory model. Management Sci. 40 603-613.
24. Song, J., P. Zipkin. 1993. Inventory control in a fluctuating demand environment. Oper. Res. 41 351-370.
25. Song, J., P. Zipkin. 1996. Inventory control with information about supply conditions. Management Sci. 42 1409-1419.
26. Stoyan, D. 1983. Comparison Methods for Queues and Other Stochastic Models. Wiley, New York.
27. Topkis, D. 1998. Super-modularity and Complementarity. Princeton University Press, Princeton, NJ.
28. Zipkin, P. 2000. Foundations of Inventory Management. McGraw-Hill, New York.
29. Zipkin, P. 2008. Old and new methods for lost-sales inventory systems. Oper. Res. Forthcoming.