SIMULATED CHAOS IN BULLWHIP EFFECT

Abstract

The main purpose of the research is to investigate nonlinear dynamics in bullwhip effect and search chaotic behavior. In the paper, a generalized supply chain model is simulated with safety stock regulations to expose the bullwhip effect. A seasonal demand model which fits Poisson distribution is utilized to generate orders from customers to retailers, continuously to distributors and a single factory. Using largest Lyapunov exponent analysis, orders are reconstructed in phase space and investigated chaotic behavior variations. Although it is assumed that increasing fluctuations of demand cause chaos and unpredictability, it is seen that predictability increases in bullwhip effect. In chaotic research aspect, demands from customers are still more chaotic than orders reach to the factory. Due to data generation, it is still a realization of a supply chain, therefore working on real data is suggested. The paper includes implications for giving ideas of nonlinear dynamics of bullwhip effect. This paper provides a novel approach to supply chains with comparing dynamics of demands and orders to identify which exhibits more chaotic behavior. 

References

1. Abarbanel, H. D. I., Brown R., Sidorowich J. J., Tsimrin L. S., 1993. The Analysis of Observed Chaotic Data in
2. Physical Systems. Reviews of Modern Physics 65(4). 1331-1392.
3. Anne, K. R., Chedjou, J. C., Kyamakya, K., 2009. Bifurcation analysis and synchronisation issues in a three-echelon supply chain. International Journal of Logistics Research and Applications: A Leading Journal of Supply Chain Management 12(5).
4. Brown R., Bryant P., Abarbanel H. D. I., 1991. Computing the Lyapunov spectrum of a dynamical system from observed time series. Phys. Rev. A 43. 2787-2806.
5. Buzug, T., Pfister G., 1992. Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behavior of strange attractors. Physical Review A 45(10). 7073-7084.
6. Eckmann, J. P., Kamphorst, S. O., Ruelle, D., Ciliberto, S., 1986. Liapunov exponents from time series. Phys. Rev. A 34(6), 4971-4979.
7. Forrester, J. W., 1961. Industrial Dynamics, The MIT Press, John Wiley & Sons, New York, USA
8. Fraser, A. M., Swinney, H. L., 1986. Independent coordinates for strange attractors from mutual information.

9. Physical Review A 33(2). 1134-1140.
10. Gullberg, J., 1997. Mathematics from the birth of numbers. W. W. Norton, New York, U.S.A.
11. Kantz, H., Schreiber, T., 1997, Nonlinear Time Series Analysis. Cambridge University Press.
12. Lei, Z., Yi-jun, L., Yao-qun, X., 2006. Chaos Synchronization of Bullwhip Effect in a Supply Chain Conference on
13. Management Science and Engineering, ICMSE '06. 2006 International. 557 – 560.
14. Ma, J., Feng, Y., 2008. The Study of the Chaotic Behavior in Retailer’s Demand Model, Discrete Dynamics in
15. Nature and Society 2008. 1 – 12.
16. Machuca, J. A. D., Barajas, R. P., 2004. The impact of electronic data interchange on reducing bullwhip effect and supply chain inventory costs. Transportation Research Part E 40. 209–228
17. Peters, E. E., 1996. Chaos and order in the capital markets: A new view of cycles, prices, and market volatility 2nd ed. John Wiley & Sons Inc, New York, USA.
18. Renzhong, L., Gongyun, G., 2011. Research on Chaos Synchronization of Bullwhip Effect in Supply Chain,
19. Conference on Product Innovation Management (ICPIM), 2011 6th International. 398 – 401.
20. Rosenstein, M. T., Collins J. J., De Luca C. J., 1993. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D 65, 117-134.
21. Sato, S., Sano, M., Sawada, Y., 1987. Practical methods of measuring the generalized dimension and the largest
22. Lyapunov exponent in high dimensional chaotic systems, Progress of Theoretical Physics. 77(1). 1-5. Schuster, H. G., Just, W., 2004. Deterministic Chaos, An Introduction. Wiley VCH.
23. Sprott, J. C., 2003. Chaos and Time Series Analysis. Oxford University Press.
24. Stapleton, D., Hanna, J. B. Ross, J. R., (2006) "Enhancing supply chain solutions with the application of chaos theory", Supply Chain Management: An International Journal, Vol. 11 Iss: 2, pp.108 – 114
25. Takens, F., (1981). Detecting Strange Attractors in Turbulence. Lecture Notes in Mathematics 898. 366-381.
26. Williams, G. P., (1997). Chaos Theory Tamed. Joseph Henry Press. Washington D.C. U.S.A.
27. Wolf, A., Swift, J. B., Swinney H. L., Vastano, J. A., (1985). Determining Lyapunov exponents from a time series. Physica D 16. 285-317.