Caos determinístico em um modelo simplificado de cadeia produtiva
Deterministic chaos in simplified supply chain model
Figueiredo, Julio Cesar B. de
http://dx.doi.org/10.1590/S0103-65132012005000050
Prod, vol.23, n2, p.257-268, 2013
Resumo
Este trabalho tem por objetivo apresentar um modelo teórico simplificado de cadeia produtiva onde as relações entre o número de competidores, os tempos de resposta para ajustes da produção e a intensidade da resposta das empresas levam intrinsecamente ao surgimento de oscilações caóticas na oferta e na demanda. No modelo proposto, desenvolvido com o uso da metodologia de dinâmica de sistemas, as flutuações irregulares na demanda e nos preços estão intimamente relacionadas com a própria estrutura da cadeia, ou seja, com suas regras, políticas e capacidades produtivas. São feitas considerações sobre a importância do estudo de caos aplicado à economia e são discutidas técnicas para caracterização de comportamento caótico em séries econômicas.
Palavras-chave
Cadeia de suprimentos. Ciclos caóticos. Dinâmica de sistemas
Abstract
The purpose of this study was to present a simplified supply chain model where the relations between the number of competitors, the delay in production adjustments, and the intensity response of each company lead, intrinsically, to the emergence of chaotic oscillations in supply and demand. In the considered model, developed with the use of the System Dynamics methodology, the irregular fluctuations in demand and prices are closely related to the supply chain structure, that is, its rules, policies and capabilities. Discussions about the importance of the study of chaos applied to the economy are developed and specific techniques for characterization of chaotic behavior in economic time series are presented.
Keywords
Supply chain. Chaotic cycles. System dynamics
References
ARTHUR, W. B. Increasing Returns and Path Dependence in the Economy. University of Michigan Press, 1994.
BAKER, C.; BOCHAROV, G.; RIHAN, F. A report on the use of delay differential equations in numerical modelling in the biosciences. Numerical Analysis Report, v. 343, 1999.
BARNETT, W. A.; CHEN, P. The aggregation-theoretic monetary aggregates are chaotic and have strange attractors: an econometric application of mathematical chaos. In: INTERNATIONAL SYMPOSIUM IN ECONOMIC THEORY AND ECONOMETRICS, 3., 1988, Austin. Proceedings... Cambridge University Press, 1988. http://dx.doi.org/10.1017/CBO9780511664342.012
BEAN, L. H. The Farmers' Response to Price. Journal of Farm Economics, v. 11, n. 3, p. 368-385, 1929. http://dx.doi.org/10.2307/1229848
BELLEN, A.; ZENNARO, M. Numerical methods for delay differential equations. Oxford University Press, 2003. http://dx.doi.org/10.1093/acprof:oso/9780198506546.001.0001
BENABOU, R.; TIROLE, J. Self-Knowledge and Self-Regulation An Economic Approach. The Psychology of Economic Decisions, 2004.
BOX, G.; JENKINS, G.; REINSEL, G. Time series analysis. San Francisco: Holden-day, 1970.
BROCK, W. A.; DECHERT, W. D. Nonlinear Dynamical Systems: Instability and Chaos in Economics. Social Systems Research Institute, University of Wisconsin, 1990.
CAMERER, C. F. Does Strategy Research Need Game Theory? Strategic Management Journal, v. 12, p. 137-152, 1991. http://dx.doi.org/10.1002/smj.4250121010
EBERLEIN, R. Vensim 5.1 Reference Manual. Ventana Systems, 2003.
ECKMANN, J. P. Roads to turbulence in dissipative dynamical systems. Reviews of Modern Physics, v. 53, n. 4, p. 643-654, 1981. http://dx.doi.org/10.1103/RevModPhys.53.643
FARMER, D. Chaotic attractors of an infinite-dimensional dynamical system. Physica D: Nonlinear Phenomena, v. 4, n. 3, p. 366-393, 1982.
FEIGENBAUM, M. J. Quantitative universality for a class of nonlinear transformations. Journal of Statistical Physics, v. 19, n. 1, p. 25-52, 1978. http://dx.doi.org/10.1007/BF01020332
FERNANDES, A. Dinâmica de Sistemas e Business Dynamics: Tratando a Complexidade no Ambiente de Negócios. In: ENCONTRO NACIONAL DE ENGENHARIA DE PRODUÇÃO - ENEGEP, 11., 2001, Salvador. Anais... Salvador: ABEPRO, 2001.
FERRARA, N. F.; DO PRADO, C. P. C. Caos, uma introducao. Sao Paulo: Edgard Blucher, 1994.
FIGUEIREDO, J. et al. Chaos in two-loop negative feedback systems. Physical Review E, v. 65, n. 5, p. 51905, 2002.
FORRESTER, J. W. Industrial dynamics. MIT Press, 1961.
FORRESTER, J. W. Urban Dynamics. Productivity Press, 1969.
FRASER, R. W. A method for evaluating supply response to price underwriting. Australian Journal of Agricultural Economics, v. 32, n. 1, p. 22-36, 1988.
GEORGANTZAS, N. C.; ACAR, W. Scenario-driven planning: learning to manage strategic uncertainty. Quorum Books, 1995.
GLASS, L.; MALTA, C. Chaos in multi-looped negative feedback systems. Journal of theoretical biology, v. 145, n. 2, p. 217-223, 1990.
GRASSBERGER, P.; PROCACCIA, I. Characterization of Strange Attractors. Physical Review Letters, v. 50, n. 5, p. 346-349, 1983a. http://dx.doi.org/10.1103/PhysRevLett.50.346
GRASSBERGER, P.; PROCACCIA, I. Measuring the strangeness of strange attractors. Physica D: Nonlinear Phenomena, v. 9, n. 1-2, p. 189-208, 1983b. http://dx.doi.org/10.1016/0167-2789(83)90298-1
GUCKENHEIMER, J.; HOLMES, P. Nonlinear Oscillations. New York: Springer-Verlag, 1983. v. 8291 Dynamical Systems, and Bifurcations of Vector Fields.
HEIDEL, J.; MALONEY, J. When can sigmoidal data be fit to a Hill curve. J. Australian Mathematical Society (Series A, Pure Mathematics and Statistics), v. 41, p. 83-92, 1999.
KANTZ, H. A robust method to estimate the maximal Lyapunov exponent of a time series. Physics Letters A, v. 185, n. 1, p. 77-87, 1994. http://dx.doi.org/10.1016/0375-9601(94)90991-1
KANTZ, H.; SCHREIBER, T. Nonlinear time series analysis. Cambridge University Press, 2004.
LEBARON, B. Chaos and Nonlinear Forecastability in Economics and Finance. Philosophical Transactions: Physical Sciences and Engineering, v. 348, n. 1688, p. 397-404, 1994.
LEE, H. L.; PADMANABHAN, V.; WHANG, S. Information Distortion in a Supply Chain: The Bullwhip Effect. Management Science, v. 50, n. 12, p. 1875-1886, 2004. Supplement. http://dx.doi.org/10.1287/mnsc.1040.0266
MACKEY, M. C. Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors. Journal of Economic Theory, v. 48, n. 2, p. 497-509, 1989. http://dx.doi.org/10.1016/0022-0531(89)90039-2
MALTA, C. P.; FIGUEIREDO, J. C. B. Modelling with delay equations: criterium for convergence of a chaotic solution. In: COLÓQUIO BRASILEIRO DE DINÂMICA ORBITAL, 10., 2000, São José dos Campos. Anais... INPE, 2000. v. 2, p. 224-236.
MALTA, C.; TELES, M. Nonlinear delay differential equation: comparison of integration methods. International Journal of Applied Mathematics, v. 3, n. 4, p. 379-395, 2000.
MANDELBROT, B. B.; WHEELER, J. A. The Fractal Geometry of Nature. American Journal of Physics, v. 51, p. 286, 1983. http://dx.doi.org/10.1119/1.13295
MORECROFT, J. D. W.; ASAY, D.; STERMAN, J. D. Modeling for Learning Organizations. Productivity, Incorporated, 1994.
PIDD, M. Computer simulation in management science. New York: John Wiley & Sons, Inc., 1984.
PIDD, M. Modelagem empresarial: ferramentas para tomada de decisão. Bookman, 1996.
RAMSEY, J. B.; ROTHMAN, P. Comment on" Nonlinear Monetary Dynamics" by DeCoster and Mitchell. Journal of Business & Economic Statistics, v. 12, n. 1, p. 135-136, 1994.
RUELLE, D.; TAKENS, F. On the nature of turbulence. Communications in Mathematical Physics, v. 20, n. 3, p. 167-192, 1971.
SENGE, P. M. The fifth discipline fieldbook: strategies and tools for building a learning organization-1994. New York: Currency, Doubleday, 1994. http://dx.doi.org/10.1007/BF01646553
SIMON, H. A. Rational decision making in business organizations. American Economic Review, v. 69, n. 4, p. 493-513, 1979.
STERMAN, J. Business Dynamics. New York: McGraw-Hill, Inc., 2000.
TAKENS, F. Detecting strange attractors in turbulence. Lecture Notes in Mathematics, v. 898, n. 1, p. 366-381, 1981. http://dx.doi.org/10.1007/BFb0091924
THOMPSON, J. M. T.; STEWART, H. B. Nonlinear Dynamics and Chaos. Wiley, 2002.
WEI, W. Time series analysis. Addison-Wesley Reading, MA, 1990.
WILDING, R. Chaos theory: implications for supply chain management. International Journal of Logistics Management, v. 9, n. 1, p. 43, 1998.
Facebook
Google+
Twitter
LinkedIn
Mendeley
StumbleUpon
CiteULike
Reddit
Email