Corrected diffusion approximations for a multistage production-inventory system

Mathematics of Operations Research

Volumn 22, Issue 1, 1997, Pages 186-201

  Glasserman, Paul ^a   Liu, Tai Wen ^b  

^a The Sanford C Bernstein Co Center for Leadership and Ethics   (United States)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Diffusion approximation; Heavy traffic; Perturbed random walks; Wald's identity

Indexed keywords

APPROXIMATION THEORY; ERROR CORRECTION; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PERTURBATION TECHNIQUES; PROBABILITY; PRODUCTION CONTROL; RANDOM PROCESSES;

CORRECTED DIFFUSION APPROXIMATIONS; ECHELON BASE STOCK POLICY;

INVENTORY CONTROL;

EID: 0031070836     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.22.1.186     Document Type: Article

References (20)

1. Asmussen, S. (1984). Approximations for the probability of ruin within finite time. Scand. Actuar. J. 31-57.
2. _ (1987). Applied Probability and Queues, Wiley, Chichester, England.
3. _ (1992). Phase-type representations in random walk and queueing problems. Ann. Probab. 20 772-789.
4. Chang, J. (1992). On moments of the first ladder height of random walks with small drift. Ann. Appl. Probab. 2 714-738.
5. Chung, K. L. (1974). A Course in Probability Theory, Academic Press, New York.
6. Clark, A. J., H. Scarf (1960). Optimal policies for a multi-echelon inventory problem. Management Sci. 6 475-490.
7. Federgruen, A., P. Zipkin (1986). An inventory model with limited production capacity and uncertain demands, I: The average cost criterion. Math. Oper. Res. 11 193-207.
8. Glasserman, P. (1993). Bounds and asymptotics for planning critical safety stocks. Working Paper, Columbia University, New York, NY. Oper. Res. (to appear).
9. _, S. Tayur (1994). The stability of a capacitated, multi-echelon production-inventory system under a base-stock policy. Oper. Res. 42 913-925.
10. _, _ (1996). A simple approximation for a multistage capacitated production-inventory system. Naval Res. Logist. 43 41-58.
11. Gut, A. (1992). First-passage times for perturbed random walks. Sequential Anal. 11 149-179.
12. Hogan, M. L. (1986). Comment on 'corrected diffusion approximations in certain random walk problems.' J. Appl. Probab. 23 89-96.
13. Liu, T.-W. (1995). Analysis of a Capacitated Multistage Production-Inventory Inventory System under a Base-Stock Policy. Ph.D. Dissertation, Graduate School of Business, Columbia University, New York, NY.
14. Lorden, G. (1970). On excess over the boundary. Ann. Math. Statist. 41 520-527.
15. Schraner, E. (1995). Optimal capacity allocation and inventory policies for capacitated multi-echelon systems. Working Paper, Department of Industrial Engineering, Stanford University, Stanford, CA.
16. Siegmund, D. (1979). Corrected diffusion approximations in certain random walk problems. Adv. Appl. Probab. 11 701-719.
17. _ (1985). Sequential Analysis: Tests and Confidence Intervals, Springer-Verlag, New York.
18. Speck, C. J., J. van der Wal (1991a). The capacitated multi-echelon inventory system with serial structure: 1. The push ahead effect, Memorandum COSOR 91-39, Eindhoven University of Technology, Eindhoven, The Netherlands.
19. _, _ (1991b). The capacitated multi-echelon inventory system with serial structure: 2. An average cost approximation method, Memorandum COSOR 91-40, Eindhoven University of Technology, Eindhoven, The Netherlands.
20. Van Houtum, G. J., K. Inderfurth, W. H. M. Zijm (1995). Materials Coordination in Stochastic Multiechelon Systems, Working Paper LPOM-95-16, University of Twente, The Netherlands.