Heavy traffic analysis of the dynamic stochastic inventory-routing problem

Transportation Science

Volumn 33, Issue 4, 1999, Pages 361-380

  Reiman, Martin I ^a   Rubio, Rodrigo ^b   Wein, Lawrence M ^c  

^a LUCENT TECHNOLOGIES   (United States)

^b MCKINSEY AND COMPANY   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DECISION MAKING; INVENTORY CONTROL; MATHEMATICAL MODELS; QUEUEING THEORY; TRANSPORTATION ROUTES;

DYNAMIC STOCHASTIC DISTRIBUTION SYSTEM; INVENTORY ROUTING PROBLEM;

HIGHWAY TRAFFIC CONTROL;

EID: 0033225180     PISSN: 00411655     EISSN: None     Source Type: Journal    
DOI: 10.1287/trsc.33.4.361     Document Type: Article

References (29)

1. R. L. ACKOFF, "OR, A Post Mortem," Opns. Res. 35, 471-474 (1987).
2. W. BELL, ET AL., "Improving the Distribution of Industrial Gases with an On-Line Computerized Routing and Scheduling Optimizer," Interfaces. 13, 4-23 (1983).
3. D. J. BERTSIMAS AND D. SIMCHI-LEVI, "A New Generation of Vehicle Routing Research: Robust Algorithms, Addressing Uncertainty," Opns. Res. 44, 286-304 (1996).
4. P. BILLINGSLEY, Convergence of Probability Measures. John Wiley and Sons, New York, 1968.
5. L. M. A. CHAN, A. FEDERGRUEN, AND D. SIMCHI-LEVI, Probabilistic Analyses and Practical Algorithms for Inventory-Routing Models, Opns. Res. 46, 96-106 (1998).
6. E. G. COFFMAN, JR., A. A. PUHALSKII, AND M. I. REIMAN, "Polling Systems with Zero Switchover Times: A Heavy-Traffic Averaging Principle," Ann. Appl. Probab. 5, 681-719 (1995).
7. E. G. COFFMAN, A. A. PUHALSKII, AND M. I. REIMAN, "Polling Systems in Heavy Traffic: A Bessel Process Limit," Math. Opns. Res. 23, 257-304 (1998).
8. M. DROR AND M. BALL, "Inventory Routing: Reduction from an Annual to Short Period Problem," Naval Res. Log. Quart. 34, 891-905 (1987).
9. A. FEDERGRUEN AND Z. KATALAN, "The Stochastic Economic Lot Scheduling Problem: Cyclic Base-Stock Policies with Idle Times," Management Sci. 42, 783-796 (1996).
10. A. FEDERGRUEN AND D. SIMCHI-LEVI, "Analytical Analysis of Vehicle Routing and Inventory-Routing Problems," in Handbooks in Operations Research and Management Science, Networks and Distribution, M. Ball, T. Magnanti, C. Monma and G. Nemhauser, (eds.), 1992.
11. A. FEDERGRUEN AND P. ZIPKIN, "A Combined Vehicle Routing and Inventory Allocation Problem," Opns. Res. 32, 1019-1037 (1984).
12. B. GOLDEN, A. ASSAD, AND R. DAHL, "Analysis of a Large Scale Vehicle Routing Problem with an Inventory Component," Large Scale Systems. 7, 181-190 (1984).
13. B. L. GOLDEN AND A. A. ASSAD (Editors), Vehicle Routing: Methods and Studies, North-Holland Publishers, 1988.
14. J. M. HARRISON, "Brownian Models of Queueing Networks with Heterogeneous Customer Populations," in Stochastic Differential Systems, Stochastic Control Theory and Applications, IMA Vol. 10, W. Fleming and P. L. Lions (eds.), Springer-Verlag, New York, 147-186, 1988.
15. J. M. HARRISON, Brownian Motion and Stochastic Flow Systems. John Wiley and Sons, New York, 1985.
16. D. L. IGLEHART AND W. WHITT, "Multiple Channel Queues in Heavy Traffic I," Adv. Appl. Probab. 2, 150-177 (1970).
17. A. KUMAR, L. B. SCHWARZ, AND J. E. WARD, "Risk-Pooling Along a Fixed Delivery Route Using a Dynamic Inventory-Allocation Policy," Management Sci. 41, 344-362 (1995).
18. H. J. KUSHNER, Probability Methods for Approximations in Stochastic Control and for Elliptic Equations, Academic Press, New York, 1977.
19. H. J. KUSHNER AND P. G. DUPUIS, Numerical Methods for Stochastic Control Problems in Continuous Time, Springer-Verlag. New York, 1992.
20. R. C. LARSON, "Transporting Sludge to the 106-Mile Site: An Inventory/Routing Model for Fleet Sizing and Logistics System Design," Transp. Sci. 22, 186-198 (1988).
21. D. M. MARKOWITZ, M. I. REIMAN, AND L. M. WEIN, The Stochastic Economic Lot Scheduling Problem: Heavy Traffic Analysis of Dynamic Cyclic Policies, To appear in Opns. Res. 1999.
22. A. S. MINKOFF, "A Markov Decision Model and Decomposition Heuristic for Dynamic Vehicle Dispatching," Opns. Res. 41, 77-90 (1993).
23. W. P. PETERSON, "A Heavy Traffic Limit Theorem for Networks of Queues with Multiple Customer Types," Math. Opns. Res. 16, 90-118 (1991).
24. M. I. REIMAN, "Open Queueing Networks in Heavy Traffic," Math. Opns. Res. 9, 441-458 (1984).
25. M. I. REIMAN, R. RUBIO, AND L. M. WEIN, Heavy Traffic Analysis of the Dynamic Stochastic Inventory-Routing Problem, Working Paper, Sloan School of Management, MIT, Cambridge, MA, 1997.
26. R. RUBIO, Dynamic-Stochastic Vehicle Routing and Inventory Problem, Ph.D. thesis, Operations Research Center, MIT, Cambridge, MA, 1995.
27. D. SIMCHI-LEVI, "Hierarchical Planning for Probabilistic Distribution Systems in Euclidean Spaces," Management Sci. 38, 198-211 (1992).
28. P. TRUDEAU AND M. DROR, "Stochastic Inventory Routing: Route Design with Stockouts and Route Failures," Transp. Sci. 26, 171-184 (1992).
29. L. M. WEIN, "Dynamic Scheduling of a Multiclass Maketo-Stock Queue," Opns. Res. 40, 724-735 (1992).