A Study of the Stability of Supply Chain with Predator-Prey Model

doi:10.3969/j.issn.1007-7375.e17-3135

Abstract

Abstract: Stability of the supply chain has become an important research area in supply chain. To study the interactive mechanism between disruption and supply chain, a Predator-Prey Model of disruption and supply chain is built based on supply chain resilience coefficient and disruption interference coefficient, representing the two states of disruptions and supply chain. Then the equilibrium points are found and interdependent correlation of disruption and supply chain is analyzed, and the stability of supply chain under disruption simulated by Matlab. The results show that, in order to ensure the stability of the supply chain when the equilibrium point P₄ is reached, the resilience coefficient of the supply chain should be σ₁> 1 and approaching 2, and the disturbance coefficient of the disruption should be σ₂> 1 and gradually approaching 1. When the equilibrium point P₂ is reached, the resilience coefficient of the supply chain should be σ₁> 0 and approaching 2, and the disturbance coefficient of the disruption should be 0< σ₂< 1 and gradually approaching 0. The model is effective to formulate the interdependent correlation between disruption and the stability of supply chain. The exploration is meaningful to enrich the modeling methodology of supply chain disruption, and it is also significant to prevent and handle the disruption effectively.

Key words: disruption, supply chain, stability, Predator-Prey Model

CLC Number:

N949

HU Hui, MA Hai, LI Bo, ZHAO Jiao. A Study of the Stability of Supply Chain with Predator-Prey Model[J]. Industrial Engineering Journal , 2017, 20(6): 39-46.

References

[1] BUSE C, BARBU D. The Lyapunov equations and nonuniform exponential stability[J]. Mathematical Reports, 1997, 49(1): 25-31.
[2] PAL B, SANA S S, CHAUDHURI K. A multi-echelon production-inventory system with supply disruption[J]. Journal of Manufacturing Systems, 2014, 33(2): 262-276.
[3] PALSULE-DESAI O D, TIRUPATI D, CHANDRA P. Stability issues in supply chain networks: Implications for coordination mechanisms[J]. International Journal of Production Economics, 2013, 142(1): 179-193.
[4] SCHÖNLEIN M, MAKUSCHEWITZ T, WIRTH F, et al. Measurement and optimization of robust stability of multiclass queueing networks: Applications in dynamic supply chains[J]. European Journal of Operational Research, 2013, 229(1): 179-189.
[5] 覃正, 姚公安. 基于信息熵的供应链稳定性研究[J]. 控制与决策, 2006, 21(6): 693-696.
QIN Zheng, YAO Gongan. Evaluation on stability of supply chain with information entropy[J]. Control and Decision, 2006, 21(6): 693-696.
[6] 罗文彬. 供应链系统稳定性与混沌动力学行为分析[D]. 南京: 东南大学, 2007.
LUO Wenbin. Analysis of the stability and chaos dynamics behavior of supply chain system[D]. Nanjing: Southeast Univeristy, 2007.
[7] 张学龙, 王云峰. 基于LMI的灰色非线性精敏供应链稳定性判定方法[J]. 工业工程, 2014, 17(2): 64-69.
ZHANG Xuelong, WANG Yunfeng. LMI-based research on stability of leagile supply chain with grey non-linear characteristics[J]. Industrial Engineering Journal, 2014, 17(2): 64-69.
[8] 李京文, 何喜军. 供应链网络稳定性研究评述[J]. 经济与管理研究, 2014, (4): 99-103.
LI Jingwen, HE Xijun. Review on the stability of supply chain network[J]. Research on Economics and Management, 2014, (4): 99-103.
[9] 胡卉, 胡大伟, 陈栋. 面向供应链协同的实体关联稳定性[J]. 工业工程, 2011, 14(5): 31-35.
HU Hui, HU Dawei, CHEN Dong. Study on entity correlation stability in supply chain coordination. Industrial Engineering Journal, 2011, 14(5): 31-35.
[10] HU H, SHI L, MA H, et al. Stability of the supply chain based on disruption classification[J]. Technical Gazette, 2017, 24(4): 1187-1195.
[11] OHMORI S, YOSHIMOTO K. A framework of managing supply chain disruption risks using network reliability[J]. Industrial Engineering and Management Systems, 2013, 12(2): 103-111.
[12] CANTOR D E, BLACKHURST J V, CORTES J D. The clock is ticking: The role of uncertainty, regulatory focus, and level of risk on supply chain disruption decision making behavior[J]. Transportation Research Part E: Logistics and Transportation Review, 2014, 72: 159-172.
[13] PAL B, SANA S S, CHAUDHURI K. A multi-echelon production-inventory system with supply disruption[J]. Journal of Manufacturing Systems, 2014, 33(2): 262-276.
[14] FAHIMNIA B, TANG C S, DAVARZANI H, et al. Quantitative models for managing supply chain risks: A review[J]. European Journal of Operational Research, 2015, 247(1): 1-15.
[15] HAN J, SHIN K S. Evaluation mechanism for structural robustness of supply chain considering disruption propagation[J]. International Journal of Production Research, 2016, 54(1): 1-17.
[16] 朱新球, 苏成. 应对供应链风险的弹性供应链机制研究[J]. 北京工商大学学报(社会科学版), 2010, 25(6): 45-55.
ZHU Xinqiu, SU Cheng. Research on the mechanisms of supply chain for supply chain risk[J]. Journal of Beijing Technology and Business University (Social Science Edition), 2010, 25(6): 45-55.
[17] 李永红, 赵林度. 基于弹性模型的供应链风险响应分析[J]. 系统管理学报, 2010, 19(5): 563-570.
LI Yonghong, ZHAO Lindu. Analyzing supply chain risk response based on resilience model[J]. Journal of System and Management, 2010, 19(5): 563-570.
[18] 赵林度, 王新平. 供应链弹性管理研究进展[J]. 东南大学学报(哲学社会科学版), 2013, 15(4): 21-27.
ZHAO Lindu, WANG Xinping. Review on the supply chain resilience[J]. Journal of Southeast University (Philosophy and Social Science Edition), 2013, 15(4): 21-27.
[19] 吕文栋, 田丹, 赵杨. 弹性企业风险管理体系建构的探讨——基于供应链弹性等领域的文献回顾与拓展[J]. 科学决策, 2015, (3): 1-27.
LYU Wendong, TIAN Dan, ZHAO Yang. Study on resilient enterprise risk management: based on review and expansion of supply chain resilience, engineering resilience, and organizational resilience[J]. Scientific Decision-Making, 2015, (3): 1-27.
[20] NOWAK V, VALLACHER R R. Dynamical social psychology[M]. New York: Guilford Press, 1998.
[21] RICKLEFS R, RELYEA R. Ecology: The economy of nature[M]. 7th edition, New York: W. H. Freeman and Company, 2013.
[22] FELMLEE D H, GREENBERG D F. A dynamic systems model of dyadic interaction[J]. The Journal of Mathematical Sociology, 1999, 23(3): 155-180.
[23] ELTON C S. Periodic fluctuations in the numbers of animals: their causes and effects[J]. Journal of Experimental Biology, 1924, 2(1): 119-163.
[24] BRAUER C, CASTILLO-CHAVEZ C. Mathematical models in population biology and epidemiology[J]. American Mathematical Monthly, 2012, 40(3): 267-291.