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Stabilization of two-echelon supply networks with uncertain demand, multiple delays and switching topology using robust control

  • Azeddine Zemzam
  • Jamila El Alami
  • Nourddine El Alami
Article
  • 8 Downloads

Abstract

In this paper, a two-level supply network (SN) system composed of multiple retailers and multiple distributors is developed. The dynamic equations for each echelon are described individually considering the varying possibility of vertical and lateral transshipment of product. Then a SN model is formulated with switched topologies, multiple time-varying delays and uncertain customer demand. By use of the switched Lyapunov stability theory and the average dwell time approach, sufficient conditions of linear matrix inequalities is proposed for the existence of robust \(\hbox {H}\infty \) state feedback controller. This control strategy guarantee the reduction of inventory levels, delivery rates and orders fluctuations under the worst fluctuation of demand as well as the mitigation of the bullwhip effect (BE). A real case example is presented to demonstrate the effectiveness of the proposed inventory control. The simulation proves that proportionality between vertical and lateral delays as well as cooperation rates have significant impacts on the achievement of best tradeoff between improving inventory dynamics and reducing order fluctuations.

Keywords

Supply network Inventory management Robust control Switched system Time delays 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

References

  1. 1.
    Lototsky VA, Mandel’ AS (1991) Models and methods of stock management. Nauka Publishers, Moscow (in Russian)Google Scholar
  2. 2.
    Harland CM, Lamming RC, Zheng J, Johnsen TE (2002) A taxonomy of supply networks. IEEE Eng Manag Rev 30(4):79–85CrossRefGoogle Scholar
  3. 3.
    Render B, Stair RM Jr, Hanna ME (2009) Quantitative analysis for management, 10th edn. Pearson Educ. Up, Saddle RiverGoogle Scholar
  4. 4.
    Koumanakos DP (2008) The effect of inventory management on firm performance. Int J Product Perform Manag 57(5):355–369CrossRefGoogle Scholar
  5. 5.
    Min W, Pheng LS (2005) Re-modelling EOQ and JIT purchasing for performance enhancement in the ready mixed concrete industries of Chongqing, China and Singapore. Int J Product Perform Manag 54(4):256–277CrossRefGoogle Scholar
  6. 6.
    Simchi-Levi D, Kaminsky P, Simchi-Levi E (2000) Designing and managing the supply chain: concepts, strategies, and case studies. McGraw-Hill, IllinoiszbMATHGoogle Scholar
  7. 7.
    Grieger M (2003) Electronic marketplaces: a literature review and a call for supply chain management research. Eur J Oper Res 144(2):280–294CrossRefzbMATHGoogle Scholar
  8. 8.
    Lee HL (2004) The triple—a supply chain. Harv Bus Rev 82(10):102–112Google Scholar
  9. 9.
    Lee HL, Padmanabhan V, Whang S (1997) The bullwhip effect in supply chains. Sloan Manag Rev 38(3):93–102zbMATHGoogle Scholar
  10. 10.
    Backx T, Bosgra O, Marquardt W (2000) Integration of model predictive control and optimization of processes: enabling technology for market driven process operation. Advanced Control of Chemical Processes 2000 (ADCHEM 2000): Proceedings volume from the IFAC Symposium, pp 249–260Google Scholar
  11. 11.
    Ivanov D, Sokolov B, Dolgui A (2012) Applicability of optimal control theory to adaptive supply chain planning and scheduling. Annu Rev Control 36(1):73–84CrossRefGoogle Scholar
  12. 12.
    Hoberg K, Bradley J, Thonemann U (2007) Analyzing the effect of the inventory policy on order and inventory variability with linear control theory. Eur J Oper Res 176(3):1620–1642CrossRefzbMATHGoogle Scholar
  13. 13.
    Dong M (2006) Development of supply chain network robustness index. Int J Serv Oper Inform 1(1–2):54–66Google Scholar
  14. 14.
    Tang CS (2006b) Robust strategies for mitigating supply chain disruptions. Int J Logist Res Appl 9(1):33–45CrossRefGoogle Scholar
  15. 15.
    Christopher M, Peck H (2004) Building the resilient supply chain. Int J Logist Manag 15(2):1–14CrossRefGoogle Scholar
  16. 16.
    Klibi W, Martel A (2012) Modeling approaches for the design of resilient supply networks under disruptions. Int J Prod Econ 135(2):882–898CrossRefGoogle Scholar
  17. 17.
    Ivanov D, Sokolov B (2013) Control and system–theoretic identification of the supply chain dynamics domain for planning, analysis and adaptation of performance under uncertainty. Eur J Oper Res 224(2):313–323MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Ivanov D, Sokolov B, Dolgui A (2014) The ripple effect in supply chains: trade-off efficiency–flexibility–resilience in disruption management. Int J Prod Res 52(7):2154–2172CrossRefGoogle Scholar
  19. 19.
    Zemzam A, Maataoui ME, Hlyal M, Alami JE, Alami NE (2017) Inventory management of supply chain with robust control theory: literature review. Int J Logist Syst Manag 27(4):438–465CrossRefGoogle Scholar
  20. 20.
    Ouyang Y, Li X (2010) The bullwhip effect in supply chain networks. Eur J Oper Res 201(3):799–810CrossRefzbMATHGoogle Scholar
  21. 21.
    Dominguez R, Framinan JM, Cannella S (2014) Serial versus divergent supply chain networks: a comparative analysis of the bullwhip effect. Int J Prod Res 2015:1–17Google Scholar
  22. 22.
    Khosroshahi H, Husseini SMM, Marjani MR (2014) The bullwhip effect in a 3-stage supply chain considering multiple retailers using a moving average method for demand forecasting. Appl Math Model 40:8934–8951MathSciNetCrossRefGoogle Scholar
  23. 23.
    Fridman E (2014) Introduction to time-delay systems. Systems and control: foundations and applications. Birkhauser, BostonCrossRefzbMATHGoogle Scholar
  24. 24.
    Graves SC (1999) A single-item inventory model for a nonstationary demand process. Manuf Serv Oper Manag 1(1):50–61MathSciNetCrossRefGoogle Scholar
  25. 25.
    Sipahi R, Lämmer S, Helbing D, Niculescu S-I (2009) On stability problems of supply networks constrained with transport delay. J Dyn Syst Meas Control 131(2):21005CrossRefGoogle Scholar
  26. 26.
    Dorofieiev YI, Lyubchyk LM, Nikulchenko a a (2014) Robust stabilizing inventory control in supply networks under uncertainty of external demand and supply time-delays. J Comput Syst Sci Int 53(5):761–775MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Cox A, Sanderson J, Watson G (2001) Supply chains and power regimes: toward an analytic framework for managing extended networks of buyer and supplier relationships. J Supply Chain Manag 37(1):28–35CrossRefGoogle Scholar
  28. 28.
    Choi TY, Dooley KJ, Rungtusanatham M (2001) Supply networks and complex adaptive systems: control versus emergence. J Oper Manag 19(3):351–366CrossRefGoogle Scholar
  29. 29.
    Pathak SD, Dilts DM, Biswas G (2007) On the evolutionary dynamics of supply network topologies. IEEE Trans Eng Manag 54(4):662–672CrossRefGoogle Scholar
  30. 30.
    Wei Y, Wang H, Chen F (2015) Exploring the impact of network structure and demand collaboration on the dynamics of a supply chain network using a robust control approach. Math Probl Eng 2015 Article ID 102727, p 13Google Scholar
  31. 31.
    Li S, Zhang J, Tang W (2013) Stabilization strategies of supply networks with stochastic switched topology. J Appl Math 5:18MathSciNetzbMATHGoogle Scholar
  32. 32.
    Qiu X, Yu L, Zhang D (2015) Stabilization of supply networks with transportation delay and switching topology. Neurocomputing 155:247–252CrossRefGoogle Scholar
  33. 33.
    Haifeng G (2010) LMI-based H-infinity control of CLSC networks with the third party reverse provider. In: 2010 International conference on measuring technology and mechatronics automation (ICMTMA), vol. 2, pp 587–590Google Scholar
  34. 34.
    Sun XM, Zhao J, Hill DJ (2006) Stability and L2-gain analysis for switched delay systems: a delay-dependent method. Automatica 42(10):1769–1774MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Hespanha JP, Morse AS (1999) Stability of switched systems with average dwell-time. In: Proceedings of 38th IEEE conference on decision control (Cat. No.99CH36304) 3(December), pp 2655–2660Google Scholar
  36. 36.
    Liu S, Xiang Z (2013) Exponential H output tracking control for switched neutral system with time-varying delay and nonlinear perturbations. CircuitsSyst Signal Process 32(1):103–121MathSciNetCrossRefGoogle Scholar
  37. 37.
    Zhang S, Zhao X (2015) Fuzzy robust control for an uncertain switched dual-channel closed-loop supply chain model. IEEE Trans Fuzzy Syst 23(3):485–500MathSciNetCrossRefGoogle Scholar
  38. 38.
    Li J, Xiong N, Park JH et al (2012) Chain-to-chain inventory transshipment model and robust switch control in CSC networks. Concurr Comput Pract Exp 24(4):423–443CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Azeddine Zemzam
    • 2
  • Jamila El Alami
    • 1
  • Nourddine El Alami
    • 2
  1. 1.LASTIMI LaboratoryMohammed V University/Technology High School SaléRabatMorocco
  2. 2.Mohammed V University/Mohammedia School of EngineersRabatMorocco

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