Average cost single-stage inventory models: An analysis using a vanishing discount approach

Operations Research

Volumn 59, Issue 1, 2011, Pages 143-155

  Woonghee, Tim Huh ^a   Janakiraman, Ganesh ^b   Nagarajan, Mahesh ^b  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF TEXAS AT DALLAS   (United States)

Author keywords

Dynamic programming; Infinite horizon; Inventory; Optimal pol

Indexed keywords

ACTION SPACES; AVERAGE COST; AVERAGE COST CRITERION; AVERAGE-COST CRITERIA; DISCOUNT FACTORS; DISCOUNTED COST CRITERION; INFINITE HORIZONS; INVENTORY; INVENTORY MODELS; INVENTORY SYSTEMS; LEAD TIME; LOST SALE; MARKOV DECISION PROCESSES; OPTIMAL POL; OPTIMAL POLICIES; ORDERING COST; SETUP COSTS; SINGLE STAGE; STOCHASTIC INVENTORY MODEL; SUFFICIENT CONDITIONS;

COST BENEFIT ANALYSIS; COSTS; DECISION THEORY; INVENTORY CONTROL; MARKOV PROCESSES; OPTIMIZATION; STOCHASTIC MODELS;

DYNAMIC PROGRAMMING;

EID: 79952951027     PISSN: 0030364X     EISSN: 15265463     Source Type: Journal    
DOI: 10.1287/opre.1100.0845     Document Type: Article

References (36)

1. Aviv, Y., A. Federgruen. 1997. Stochastic inventory models with limited production capacity and periodically varying parameters. Probab. Engrg. Inform. Sci. 11(1) 107-135.
2. Aviv, Y., A. Federgruen. 1999. The value iteration method for countable state Markov decision processes. Oper. Res. Lett. 24(5) 223-234.
3. Bellman, R., I. Glicksberg, O. Gross. 1955. On the optimal inventory equation. Management Sci. 2(1) 83-104.
4. Beyer, D., S. P. Sethi. 1997. Average cost optimality in inventory models with Markovian demands. J. Optim. Theory Appl. 92(3) 497-526.
5. Beyer, D., S. P. Sethi. 1999. The classical average-cost inventory models of Iglehart and Veinott-Wagner revisited. J. Optim. Theory Appl. 101(3) 523-555.
6. Beyer, D., S. P. Sethi. 2005. Average cost optimality in inventory models with Markovian demands and lost sales. E. K. Boukas, R. P. Malhamé, eds. Analysis, Control and Optimization of Complex Dynamic Systems. Springer, New York.
7. Beyer, D., F. Cheng, S. P. Sethi, M. Taksar. 2008. Markovian Demand Inventory Models. International Series in Operations Research and Management Science. Springer, New York.
8. Chen, X., D. Simchi-Levi. 2004a. Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The finite horizon case. Oper. Res. 52(6) 887-896. (Pubitemid 40122349)
9. Chen, X., D. Simchi-Levi. 2004b. Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The infinite horizon case. Math. Oper. Res. 29(3) 698-723.
10. Chen, Y. F., S. Ray, Y. Song. 2006. Optimal pricing and inventory control policy in periodic-review systems with fixed ordering cost and lost sales. Naval Res. Logist. 53(2) 117-136.
11. Cheng, F., S. P. Sethi. 1999. Optimality of state-dependent (s,S) policies in inventory models with Markov-modulated demand and lost sales. Production Oper. Management 8(2) 183-192.
12. Federgruen, A., A. Heching. 1999. Combined pricing and inventory control under uncertainty. Oper. Res. 47(3) 454-475.
13. Federgruen, A., P. Zipkin. 1986. An inventory model with limited production capacity and uncertain demands I. The average-cost criterion. Math. Oper. Res. 11(2) 193-207. (Pubitemid 16566991)
14. Feinberg, E. A., M. E. Lewis. 2005a. Optimality of four-threshold policies in inventory systems with customer returns and borrowing/storage options. Probab. Engrg. Inform. Sci. 19(1) 45-71. (Pubitemid 40111704)
15. Feinberg, E. A., M. E. Lewis. 2005b. Optimality inequalities for average cost Markov decision processes and the optimality of (s,S) policies. Technical report, Cornell University, Ithaca, NY.
16. Feinberg, E. A., M. E. Lewis. 2007. Optimality inequalities for average cost Markov decision processes and the stochastic cash balance problem. Math. Oper. Res. 32(4) 769-785.
17. Gallego, G., A. Scheller-Wolf. 2000. Capacitated inventory problems with fixed order costs: Some optimal policy structure. Eur. J. Oper. Res. 126(3) 603-613.
18. Gatarek, D., L. Stettner. 1990. On the compactness method in general ergodic impulsive control of Markov processes. Stochastics: An Internat. J. Probab. Stochastic Processes 31(1) 15-25.
19. Hernandez-Lerma, O., J. B. Lassere. 1996. Discrete-Time Markov Control Processes: Basic Optimality Criteria. Springer-Verlag, New York.
20. Huh, W. T., G. Janakiraman. 2008. (s,S) optimality in joint inventorypricing control: An alternate approach. Oper. Res. 56(3) 783-790.
21. Huh, W. T., G. Janakiraman, M. Nagarajan. 2008. Capacitated multiechelon inventory systems: Policies and bounds. Working paper, University of British Columbia, Vancouver, British Columbia, Canada.
22. Iglehart, D. 1963. Optimality of (s,S) policies in the infinite horizon dynamic inventory problem. Management Sci. 9(2) 259-267.
23. Kapuscinski, R., S. Tayur. 1995. A capacitated production-inventory model with periodic demand. GSIA working paper, Carnegie Mellon University, Pittsburgh.
24. Kapuscinski, R., S. Tayur. 1998. A capacitated production-inventory model with periodic demand. Oper. Res. 46(6) 899-911. (Pubitemid 128665750)
25. Morton, T. E. 1969. Bounds on the solution of the lagged optimal inventory equation with no demand backlogging and proportional costs. SIAM Rev. 11(4) 572-596.
26. Nagarajan, M., S. Rajagopalan. 2008. Inventory models for substitutable products: Optimal policies and heuristics. Management Sci. 54(8) 1453-1466.
27. Parker, R., R. Kapuscinski. 2004. Optimal policies for a capacitated twoechelon inventory system. Oper. Res. 52(5) 739-755.
28. Porteus, E. 1971. On the optimality of generalized (s,S) policies. Management Sci. 17(7) 411-426.
29. Scarf, H. 1959. The optimality of (s,S) policies for the dynamic inventory problem. Proc. 1st Stanford Sympos. Math. Methods Soc. Sci., Stanford University Press, Stanford, CA.
30. Schäl, M. 1993. Average optimality in dynamic programming with general state space. Math. Oper. Res. 18(1) 163-172.
31. Sethi, S. P., F. Cheng. 1997. Optimality of (s, S) policies in inventory models with Markovian demand. Oper. Res. 45(6) 931-939. (Pubitemid 127684773)
32. Shaoxiang, C. 2004. The infinite horizon periodic review problem with setup costs and capacity constraints: A partial characterization of the optimal policy. Oper. Res. 52(3) 409-421.
33. Shaoxiang, C., M. Lambrecht. 1996. X-Y band and modified (s,S) policy. Oper. Res. 44(6) 1013-1019. (Pubitemid 126669574)
34. Veinott, A. F., Jr., H. M. Wagner. 1965. Computing optimal (s,S) policies. Management Sci. 11(5) 525-552.
35. Zheng, Y. S. 1991. A simple proof of the optimality of (s,S) policies in infinite-horizon inventory systems. J. Appl. Probab. 28(4) 802-810.
36. Zipkin, P. 2008. On the structure of lost-sales inventory models. Oper. Res. 56(4) 937-944.