Yeni bir 4-boyutlu tedarik zinciri sisteminde hiperkaos

Yıl 2018, Cilt: 22 Sayı: 2, 799 - 805, 01.04.2018

Gültekin Çağıl , Neslihan Açıkgöz

https://doi.org/10.16984/saufenbilder.342278

Cited By: 1

Öz

Tedarik zinciri, müşteri ihtiyaçlarını karşılayabilmek için
hammadde tedarikinden başlayarak müşteriye ürün teslimine kadar devam eden tüm
süreçlerdeki birçok faktörün etkisi altında olması bakımından karmaşık ve
kaotik bir yapıya sahiptir.  Kaotik
tedarik zinciri, sistemi oluşturan değişkenlerin beklenmedik bazı davranışlar
sergilemesi ve bu davranışların uzun süreli tahminlerinin yapılamaması anlamına
gelmektedir. Literatürde farklı tedarik zinciri sistemlerinin matematiksel
modelleri oluşturularak kaotik yapılarının incelendiği çalışmalar mevcuttur. Bu
çalışmada ilk kez daha önce sunulan bir tedarik zinciri modelinin talep durum
denklemine lineer kontrolör eklenmiş ve oluşturulan bu yeni tedarik zinciri
sisteminin hiperkaotik davranış sergilediği görülmüştür. Elde edilen yeni 4
boyutlu hiperkaotik sistemin Matlab-Simulink programı kullanılarak sayısal
analizleri yapılmış ve hiperkaotik davranışı faz portreleri ile ortaya
konmuştur. Faz portresinde krank mili ya da çok katlı kelebek kanadı gibi bir
şekle benzeyen kaotik bir çekici oluştuğu gözlemlenmiştir. Çalışmanın sonucunda
tedarik zinciri sisteminde farklı davranışların meydana gelmesine neden olan
yeni terimin müşteri sadakati olarak tanımlanabileceği vurgulanmıştır.

Anahtar Kelimeler

Tedarik Zincirinde Kaos, Tedarik Zincirinde Hiperkaos

Hyperchaos in a new 4d supply chain system

Öz

The supply chain has a complex and chaotic structure in that
it is under the influence of many factors in all the processes from raw
material supply to customer delivery in order to meet customer needs. Chaotic
supply chain means that the variables that make up the system exhibit some
unexpected behaviors and can not make long-term predictions of these behaviors.
In the literature, there are studies in which chaotic structures are examined
by creating mathematical models of different supply chain systems. In this
study, a linear controller was added to the demand state equation of a
previously presented supply chain model for the first time and it is seen that
this new supply chain system exhibited hyperchaotic behavior. Numerical
analysis of the new 4-dimensional hypechaotic system was examined by using
Matlab-Simulink program and hyperchaotic behavior was revealed with
phase-portraits. It has been observed that there is a chaotic attractor similar
to a crankshaft or multi-layered butterfly wing in phase portrait. As a result
of the study, it is emphasized that the new term that leads to different
behaviors in the supply chain system can be defined as "customer
loyalty".

Anahtar Kelimeler

Supply Chain Chaos, Supply Chain Hyperchaos

Kaynakça

• O.E. Rössler, "An equation for hyperchaos," Physics Letters A, vol. 71, no. 2–3, pp. 155–156, 1979.
• X. Wang, J. Song, "Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control", Commun Nonlinear Sci Numer Simulat, vol. 14, pp. 3351–3357, 2009.
• W. Xingyuan, W. Yaqın, "Adaptive generalized synchronization of hyperchaos systems", International Journal of Modern Physics B, vol. 25, no. 32, pp. 4563–4571, 2011.
• J. A, Zheng, "Simple universal adaptive feedback controller for chaos and hyperchaos control", Computers and Mathematics with Applications, vol. 61, no. 8, pp. 2000–2004, 2011.
• F. Dou, J. Sun, W. Duan, K. Lu, "Controlling hyperchaos in the new hyperchaotic system", Communications in Nonlinear Science and Numerical Simulation , vol. 14, no. 2, pp. 552–559, 2009.
• C. Di, X. Yang, D. Huang, "A new water resources supply-demand system and its hyperchaos control", Procedia Engineering, vol. 15, pp. 734 – 738, 2011.
• J. Ding, W.Yang, H.Yao, "A New Modified Hyperchaotic Finance System and its Control", International Journal of Nonlinear Science, vol. 8, no. 1, pp. 59-66, 2009.
• U.E.Kocamaz, H.Taşkın, Y.Uyaroğlu, A.Göksu “Control and synchronization of chaotic supply chains using intelligent approaches” Computers & Industrial Engineering, vol. 102, pp. 476-487, 2016.
• X. Wang, M. Wang, "A hyperchaos generated from Lorenz system," Physica A, vol. 387, no. 14, pp. 3751–3758, 2008.
• W. Wu, Z. Chen, Z.Yuan, "The evolution of a novel four-dimensional autonomous system: Among 3-torus, limit cycle, 2-torus, chaos and hyperchaos", Chaos, Solitons and Fractals, vol. 39, no. 5, pp. 2340–2356, 2009.
• A.M.A. El-Sayed, H.M. Nour, A. Elsaid, A.E. Matouk, A. Elsonbaty, "Circuit realization, bifurcations, chaos and hyperchaos in a new 4D system", Applied Mathematics and Computation, vol. 239, pp. 333–345, 2014.
• K.L.Croxton, S.J. Dastugue-Garcıa, D.M. Lambert, et All, “The Supply Chain Management Process”, The International Journal of Logistics Management, vol. 12, no. 2, pp. 13-35, 2001.
• L.W. Snyder, Z. Atan, P. Peng, Y. Rong A.J. Schmitte, B. Sinsoysal, "OR/MS models for supply chain disruptions: a review", IIE Transactions, vol. 48, no. 2, pp. 89-109, 2016.
• H. Singh, A. Singh, “Principles of Complexity and Chaos Theory in Project Execution: A New Approach to Management”, Cost Engineering, vol. 44, no. 12, pp. 23-33, 2002.
• M. Grabinski, "Chaos – Limitation Or Even End Of Supply Chain Management", High Speed Flow of Material, Information and Capital, İstanbul, 2008.
• D. Levy, "Chaos Theory And Strategy: Theory, Application, And Managerial Implications", Strategic Management Journal, vol. 15, pp. 167-178, 1994.
• E.R. Larsen, J.D.V. Morecroft, J.S. Thomsen, "Complex behaviour in a production-distribution model", European Journal of Operational Research, vol. 119, pp. 61-74, 1999.
• X.Wang, S.M. Disney, J. Wang, “Stability analysis of constrained inventory systems with transportation delay”, European Journal of Operational Research, vol. 223, no. 1, pp. 86 - 95, 2012.
• X. Wang, S.M. Disney, J. Wang, "Exploring the oscillatory dynamics of a forbidden returns inventory system", International Journal of Production Economics, vol. 147, pp. 3-12, 2014.
• R. C. Hilborn, "Chaos and nonlinear dynamics: an introduction for scientists and engineers". New York: Oxford University Press, 1994.
• R. Barri, M.A. Martínez, S. Serrano, D. Wilczak, "When chaos meets hyperchaos: 4D Rössler model", Physics Letters A, vol. 379, no. 38, pp.2300-2305, 2015.
• W. Wu, Z. Chen, "Hopf bifurcation and intermittent transition to hyperchaos in a novel strong four-dimensional hyperchaotic system", Nonlinear Dyn, vol. 60, pp. 615–630, 2010.
• D. Cafagna, G. Grassi, "New 3D-scroll attractors in hyperchaotic Chua’s circuits forming a ring", Int. J. Bifurc. Chaos, vol. 13, pp. 2889–2903, 2003.
• Y.X. Li, G.R. Chen, W.K.S. Tang, "Controlling a uni- fied chaotic system to hyperchaotic", IEEE Trans. Circuits Syst. II, vol. 52, pp. 204–207, 2005.
• Z.Q. Chen, Y. Yang, G.Y. Qi, Z.Z. Yuan, "A novel hyperchaos system only with one equilibrium", Phys. Lett. A, vol. 360, pp. 696–701, 2007.
• T.G. Gao, G.R. Chen, Z.Q. Chen, S.J. Cang, "The generation and circuit implementation of a new hyperchaos based upon Lorenz system", Phys. Lett. A, vol. 361, pp. 78–86, 2007.
• G.Y. Qi, M.A. Van Wyk, B.J. Van Wyk, G.R. Chen, "On a new hyperchaotic system", Phys. Lett. A, vol. 372, pp. 124–136, 2008.
• J.Z. Wang, Z.Q. Chen, Z.Z. Yuan, "The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system", Chin. Phys., vol. 15, pp. 1216–1225, 2006.
• L. Zhang, Y.-J.Li, Y.-Q. Xu, "Chaos synchronization of bullwhip effect in a supply chain," ICMSE '06, International Conference on Management Science and Engineering, pp. 557–560, 2006.
• K. Giannakopoulos, T.Deliyannis, J. Hadjidemetriou, "Means for Detecting Chaos and Hyperchaos in Nonlinear Electronic Circuits", DSP, vol. 2, pp. 951-954, 2002.
• A.B. Özer, E. Akın, " Tools For Detecing Chaos" , SAÜ, Fen Bilimleri Enstitüsü Dergisi vol. 9, no. 1, 2005.