On stability problems of supply networks constrained with transport delay

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Volumn 131, Issue 2, 2009, Pages 1-9

  Sipahi, Rifat ^a   Lämmer, Stefan ^b   Helbing, Dirk ^c,d   Niculescu, Silviu Iulian ^e  

^a Northeastern University   (United States)

^b DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

^c ETH ZURICH   (Switzerland)

^d INSTITUTE FOR ADVANCED STUDY   (Hungary)

^e UNIV PARIS SUD   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONTINUOUS TIME; DELAY SYSTEMS; FINITE TIME; MULTIPLE DELAYS; PRODUCTION RATES; QUALITATIVE BEHAVIOR; STABILITY PROBLEM; SUPPLY NETWORKS; SYNCHRONIZATION PROBLEM; TRANSPORT DELAY; TRANSPORTATION DELAY; TRANSPORTATION LINE; UNDESIRABLE EFFECTS;

DIFFERENTIAL EQUATIONS;

EID: 70349970317     PISSN: 00220434     EISSN: 15289028     Source Type: Journal    
DOI: 10.1115/1.3072144     Document Type: Article

References (57)

1. Helbing, D., Armbuster, D., Mikhailov, A. S., and Lefeber, E., 2006, "Information and Material Flows in Complex Networks," Physica A, 363, pp. 11-16.
2. Helbing, D., 2003, "Modelling Supply Networks and Business Cycles as Unstable Transport Phenomena," New J. Phys., 5, pp. 90.1-90.28.
3. Riddalls, C. E., and Bennett, S., 2002, "The Stability of Supply Chains," Int. J. Prod. Res., 40(2), pp. 459-475.
4. Riddalls, C. E., and Bennett, S., 2002, "Production-Inventory System Controller Design and Supply Chain Dynamics," Int. J. Syst. Sci., 33(3), pp. 181-195.
5. Sipahi, R., Lammer, S., Niculescu, S.-I., and Helbing, D., 2006, "On Stability Analysis and Parametric Design of Supply Networks Under the Presence of Transportation Delays," ASME-IMECE Conference, Chicago, IL, Paper No. 14782.
6. Sterman, J., 2000, Business Dynamics: Systems Thinking and Modeling for a Complex World, McGraw-Hill, Boston.
7. Daganzo, C., 2003, A Theory of Supply Chains, Springer, New York.
8. Simchi-Levi, D., Kaminsky, P., Simchi-Levi, E., 2003, Designing & Managing the Supply Chain, McGraw-Hill, New York.
9. Warburton, D. H. R., 2004, "An Exact Analytical Solution to the Production Inventory Control Problem," Int. J. Prod. Econ., 92(1), pp. 81-96.
10. Siegele, L., 2002, "Chain Reaction: Managing a Supply Chain is Becoming a Bit Like Rocket Science," Economist, 362(8258), pp. 13-15.
11. Agrawal, M., Kumaresh, T. V., and Mercer, G. A., 2001, "The False Promise of Mass Customization," McKinsey Quarterly, 3, pp. 62-71.
12. Ceroni, J. A., and Nof, S. Y., 2005, "Task Parallelism in Distributed Supply Organizations: A Case Study in the Shoe Industry," Prod. Plan. Control, 16(5), pp. 500-513.
13. Helbing, D., Lämmer, S., Witt, U., and Brenner, T., 2004, "Network-Induced Oscillatory Behavior in Material Flow Networks and Irregular Business Cycles," Phys. Rev. E, 70, p. 056118.
14. Nagatani, T., and Helbing, D., 2004, "Stability Analysis and Stabilization Strategies for Linear Supply Chains," Physica A, 335, pp. 644-660.
15. Helbing, D., Lämmer, S., Seidel, T., Šeba, P., and Płatkowski, T., 2004, "Physics, Stability and Dynamics of Supply Networks," Phys. Rev. E, 70, p. 066116.
16. Mosekilde, E., and Larsen, E. R., 1988, "Deterministic Chaos in the Beer Production-Distribution Model," Syst. Dyn. Rev., 4(1-2), pp. 131-147.
17. Chen, F., Drezner, Z., Ryan, J. K., and Simchi-Levi, D., 2000, "Quantifying the Bullwhip Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times, and Information," Manage. Sci., 46(3), pp. 436-443.
18. Dejonckheere, J., Disney, S. M., Lambrecht, M. R., and Towill, D. R., 2002, "Transfer Function Analysis of Forecasting Induced Bullwhip in Supply Chain," Int. J. Prod. Econ., 78, pp. 133-144.
19. Hoberg, K., Thonemann, U. W., and Bradley, J. R., 2003, "Analyzing the Bullwhip Effect of Installation-Stock and Echelon-Stock Policies With Linear Control Theory," Operations Research Proceedings 2003, D. Ahr, R. Fahrion, M. Oswald, and G. Reinelt, eds., Springer, Heidelberg, pp. 63-70.
20. Lee, H. L., Padmanabhan, V., and Whang, S., 1997, "Information Distortion in a Supply Chain: The Bullwhip Effect," Manage. Sci., 43(4), pp. 546-558.
21. Toker, O., and Ozbay, H., 1996, "Complexity Issues in Robust Stability of Linear Delay-Differential Systems," Math. Control, Signals, Syst., 9, pp. 386-400.
22. Sipahi, R., and Delice, I. I., 2009, "Advanced Clustering With Frequency Sweeping Methodology for the Stability of Multiple Time Delay Systems," IEEE Trans. Autom. Control, submitted.
23. Sipahi, R., Atay, F. M., and Niculescu, S.-I., 2008, "Stability of Traffic Flow Behavior With Distributed Delays Modeling the Memory Effects of the Drivers," SIAM J. Appl. Math., 68(3), pp. 738-759.
24. Sipahi, R., and Niculescu, S.-I., 2006, "Some Remarks on the Characterization of Delay Interactions in Deterministic Car Following Models," 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, July 24-28.
25. Sterman, J., 1989, "Modeling Managerial Behavior: Misperceptions of Feedback in a Dynamic Decision Making Experiment," Manage. Sci., 35(3), pp. 321-339.
26. Halanay, A., 1966, Differential Equations: Stability, Oscillations, Time Lags, Academic, New York.
27. Hale, J. K., and Verduyn Lunel, S. M., 1993, An Introduction to Functional Differential Equations, Springer-Verlag, New York.
28. Niculescu, S.-I., 2001, Delay Effects on Stability: A Robust Control Approach, Vol. 269, Springer-Verlag, Heidelberg.
29. S.-I. Niculescu and K. Gu, eds., 2004, Advances in Time-Delay Systems, Springer-Verlag, Berlin.
30. Niculescu, S.-I., Verriest, E. I., Dugard, L., and Dion, J. M., 1997, "Stability and Robust Stability of Time-Delay System: A Guided Tour," Stability and Control of Time Delay Systems, Vol. 228, L. Dugard and E. I. Verriest, eds., Springer, London, pp. 1-71.
31. Chen, J., and Latchman, H. A., 1995, "Frequency Sweeping Tests for Stability Independent of Delay," IEEE Trans. Autom. Control, 40, pp. 1640-1645.
32. Gu, K., Niculescu, S.-I., and Chen, J., 2005, "On Stability Crossing Curves for General Systems With Two Delays," J. Math. Anal. Appl., 311, pp. 231-253.
33. Michiels, W., Niculescu, S.-I., 2007, "Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach," SIAM Advances in Design and Control, 12.
34. Sipahi, R., and Olgac, N., 2006, "Stability Map of Systems With Three Independent Delays," Proceedings of the American Control Conference, Minneapolis, MN.
35. Richard, J. P., 2003, "Time-Delay Systems: An Overview of Some Recent Advances and Open Problems," Automatica, 39, pp. 1667-1694.
36. Engelborghs, K., 2000, "DDE-BIFTOOL: A Matlab Package for Bifurcation Analysis of Delay Differential Equations," Department of Computer Science, Katholieke Universiteit Leuven, Leuven, Belgium.
37. Michiels, W., 2002, "Stability and Stabilization of Time-Delay Systems," Ph.D. thesis, Katholieke Universiteit Leuven, Leuven.
38. Sipahi, R., and Olgac, N., 2005, "Complete Stability Robustness of Third-Order LTI Multiple Time-Delay Systems," Automatica, 41, pp. 1413-1422.
39. Sipahi, R., and Olgac, N., 2003, "Active Vibration Suppression With Time Delayed Feedback," ASME J. Vibr. Acoust., 125, pp. 384-388.
40. Datko, R., 1978, "A Procedure for Determination of the Exponential Stability of Certain Differential-Difference Equations," Q. Appl. Math., 36, pp. 279-292.
41. El'sgol'ts, L. E., and Norkin, S. B., 1973, Introduction to the Theory and Application of Differential Equations With Deviating Arguments, Academic, New York.
42. Hsu, C. S., 1970, "Application of the Tau-Decomposition Method to Dynamical Systems Subjected to Retarded Follower Forces," ASME J. Appl. Mech., 37, pp. 258-266.
43. Olgac, N., and Holm-Hansen, B., 1994, "A Novel Active Vibration Absorption Technique: Delayed Resonator," J. Sound Vib., 176, pp. 93-104.
44. Bellman, R. E., and Cooke, K. L., 1963, Differential-Difference Equations, Academic, New York.
45. Cooke, K. L., and van den Driessche, P., 1986, "On Zeros of Some Transcendental Equations," Funkc. Ekvac., 29, pp. 77-90.
46. Oguztoreli, M. N., 1966, Time-Lag Control Systems, Academic, New York.
47. Stepan, G., 1989, Retarded Dynamical Systems: Stability and Characteristic Functions, Longman Scientific & Technical, New York/Wiley, New York.
48. Volterra, V., 1931, Théorie mathématique de la lutte pour la vie, Gauthier-Villars, Paris, in French.
49. Ergenc, A. F., Olgac, N., and Fazelinia, H., 2007, "Extended Kronecker Summation for Cluster Treatment of LTI Systems With Multiple Delays," SIAM J. Control Optim., 46(1), pp. 143-155.
50. Fazelinia, H., Sipahi, R., and Olgac, N., 2007, "Stability Analysis of Multiple Time Delayed Systems Using 'Building Block' Concept," IEEE Trans. Autom. Control, 52(5), pp. 799-810.
51. Jarlebring, E., 2008, "Critical Delays and Polynomial Eigenvalue Problems," J. Comput. Appl. Math., 224(1), pp. 296-306.
52. Sipahi, R., 2005, "Cluster Treatment of Characteristic Roots, CTCR, A Unique Methodology for the Complete Stability Robustness Analysis of Linear Time Invariant Multiple Time Delay Systems Against Delay Uncertainties," Ph.D. thesis, University of Connecticut, Storrs.
53. Breda, D., Maset, S., and Vermiglio, R., 2004, "Computing the Characteristic Roots for Delay Differential Equations," IMA J. Numer. Anal., 24(1), pp. 1-19.
54. Vyhlidal, T., and Zitek, P., 2003, "Quasipolynomial Mapping Based Rootfinder for Analysis of Time Delay Systems," IFAC Workshop on Time-Delay Systems, TDS'03, Rocquencourt.
55. Ogata, K., 2002, Modern Control Engineering, 4th ed., Prentice-Hall, Englewood Cliffs, NJ.
56. Fait, B., Arnold, D., and Furmans, K., 2003, "The Impact of the Exchange of Market and Stock Information on the Bullwhip Effect in Supply Chains," Operations Research Proceedings 2003, D. Ahr, R. Fahrion, M. Oswald, and G. Reinelt, eds., Springer, Heidelberg, pp. 55-32.
57. Forrester, J. W., 1961, Industrial Dynamics, MIT, Cambridge, MA.