A network design problem for a distribution system with uncertain demands

SIAM Journal on Optimization

Volumn 7, Issue 2, 1997, Pages 560-578

  Blanchini, Franco ^a   Rinaldi, Franca ^a   Ukovich, Walter ^a  

^a NONE

Author keywords

Dynamic games; Dynamic networks; Network design

Indexed keywords

EID: 0031513857     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1052623494266262     Document Type: Article

References (36)

1. R. K. AHUJA, T. L. MAGNANTI, AND J. B. ORLIN, Network Flows: Theory, Algorithms and Applications, Prentice-Hall, Englcwood Cliffs, NJ, 1993.
2. J. E. ARONSON, A survey of dynamic network flows, Ann. Oper. Res., 20 (1989), pp. 1-66.
3. ∞-Optimal Control and Related Minimax Design Problems, Birkhäuser, Boston, MA, 1991.
4. D. P. BERTSEKAS, Infinite-time reachability of state-space regions by using feedback control, IEEE Trans. Automat. Control, 17 (1972), pp. 604-613.
5. D. P. BERTSEKAS, Dynamic Programming: Deterministic and Stochastic Models, Prentice-Hall, Englewood Cliffs, NJ, 1987.
6. D. P. BERTSEKAS, Linear Network Optimization, MIT Press, Cambridge, MA, 1991.
7. D. P. BERTSEKAS AND I. B. RHODES, On the minmax reachability of target set and target tubes, Automatica J. IFAC, 7 (1971), pp. 233-247.
8. F. BLANCHINI AND W. UKOVICH, A linear programming approach to the control of discrete-time periodic systems with uncertain inputs, J. Optim. Theory Appl., 78 (1993), pp. 523-539.
9. F. BLANCHINI, M. QUEYRANNE, F. RINALDI, AND W. UKOVICH, A feedback strategy for periodic network flows, Networks, 27 (1996), pp. 25-34.
10. A. FRANK AND E. TARDOS, Generalized polymatroids and submodular flows, Math. Programming, 42 (1988), pp. 489-563.
11. S. FUJISHIGE, Submodular functions and optimization, Ann. Discrete Math., 47, North Holland, Amsterdam, 1991.
12. J. D. GLOVER, D. KLINGMAN, AND N. V. PHILLIPS, Network Models in Optimization and Their Applications in Practice, John Wiley & Sons, New York, 1992.
13. J. D. GLOVER AND F. C. SCHWEPPE, Control of linear dynamic systems with set constrained disturbances, IEEE Trans. Automat. Control, 16 (1971), pp. 411-423.
14. S. C. GRAVES, A. H. G. RINNOOY KAN, AND P. H. ZIPKIN, EDS., Handbooks in Operations Research and Management Science, Vol. 4: Logistics of Production and Inventory, North-Holland, Amsterdam, 1993.
15. M. GRÖTSCHEL, L. LOVASZ, AND A. SCHRIJVER, Geometric Algorithms and Combinatorial Optimization, Springer-Verlag, Berlin, New York, 1988.
16. H. GROENEVELT, The just-in-time system, in Handbooks in Operations Research and Management Science, Vol. 4: Logistics of Production and Inventory, S. C. Graves, A. H. G. Rinnooy Kan, and P. H. Zipkin, eds., North-Holland, Amsterdam, 1993, pp. 629-670.
17. P. O. GUTMAN AND M. CWIKEL (1986), Admissible sets and feedback control for discrete-time linear dynamical systems with bounded controls and states, IEEE Trans. Automat. Control, 31 (1986), pp. 373-376; part 2 in IEEE Trans. Automat. Control, 31 (1986), pp. 457-459.
18. P. O. GUTMAN AND M. CWIKEL (1986), Admissible sets and feedback control for discrete-time linear dynamical systems with bounded controls and states, IEEE Trans. Automat. Control, 31 (1986), pp. 373-376; part 2 in IEEE Trans. Automat. Control, 31 (1986), pp. 457-459.
19. R. W. HALL, Zero Inventories, Dow-Jones Irwin, Homewood, IL, 1983.
20. A. IFTAR AND E. J. DAVISON, Decentralized robust control for dynamic routing of large scale networks, in Proc. American Control Conference, San Diego, 1990, pp. 441-446.
21. A. IFTAR AND E. J. DAVISON, A decentralized discrete-time controller for dynamic routing, in Proc. 29th Conference on Decision and Control, Honolulu, 1990, pp. 1362-1366.
22. S. S. KEERTHI AND E. G. GILBERT, Computation of minimum-time feedback control laws for discrete-time systems with state-control constraints, IEEE Trans. Automat. Control, 32 (1987), pp. 432-435.
23. L. LOVASZ, Submodular functions and optimization, in Mathematical Programming: The State of Art, Springer-Verlag, Berlin, New York, 1982, pp. 253-257.
24. T. L. MAGNANTI AND R. T. WONG, Network design and transportation planning: Models and algorithms, Transportation Sci., 18 (1984), pp. 1-55.
25. R. O. MASON AND E. G. FLAMHOLTZ, Human resource management, in Handbook of Operations Research: Models and Applications, Vol. 2, J. J. Moder and S. E. Elmaghraby, eds., Van Nostrand Reinhold, New York, 1978, pp. 92-126.
26. S. T. MCCORMICK, Submodular containment is hard, even for networks, UBC Faculty of Commerce Working Paper 94-MSC-010, OR Letters, 19 (1996), pp. 95-99.
27. K. S. MOORTHY, Competitive marketing strategies: Game-theoretic models, in Handbooks in Operations Research and Management Science, Vol. 5: Marketing, J. Eliasberg and G. L. Lilien, eds., North-Holland, Amsterdam, 1993, pp. 143-190.
28. R. J. T. MORRIS AND R. F. BROWN, Extension of validity of the GRG method in optimal control calculation, IEEE Trans. Automat. Control, 21 (1976), pp. 420-422.
29. F. H. Moss AND A. SEGALL, An optimal control approach to dynamic routing in networks, IEEE Trans. Automat. Control, 27 (1982), pp. 329-339.
30. J. A. MUCKSTADT AND R. O. ROUNDY, Analysis of multistage production systems, in Handbooks in Operations Research and Management Science, Vol. 4: Logistics of Production and Inventory, S. C. Graves, A. H. G. Rinnooy Kan, and P. H. Zipkin, eds., North-Holland, Amsterdam, 1993, pp. 59-131.
31. A. PRÈKOPA AND E. BOROS, On the existence of feasible flow in a stochastic transportation networks, Oper. Res., 39 (1991), pp. 119-129.
32. J. B. ORLIN, Minimum convex cost dynamic network flow, Math. Oper. Res., 9 (1984), pp. 190-207.
33. R. T. ROCKAFELLAR, Network Flows and Monotropic Optimization, John Wiley & Sons, New York, 1984.
34. R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1970.
35. E. A. SILVER AND R. PETERSON, Decision Systems for Inventory Management and Production Planning, Wiley, New York, 1985.
36. S. W. WALLACE AND R. J. B. WETS, The facets of the polyhedral set determined by the GaleHoffman inequalities, Math. Programming, 62 (1993), pp. 215-222.