Supply Network Dynamics and Delays; Performance, Synchronization, Stability

Recent research results in operations research specifically emphasize the critical role of delays in the functionality of supply networks. Delays arise due to the time needed for material deliveries, information flow and human perception towards adjusting to new decisions. Delays contaminate decision-making and lead to poor performance, synchronization problems and fluctuations in inventory levels resulting in major economical losses. This paper surveys continuous time deterministic mathematical models developed at system-level for supply network dynamics along with standard delay models pertaining to material deliveries, information flows and human perception. Next, the analogy between such delay models arising in supply networks and other real-life applications is pointed out. It is foreseen that complexity of the problem requires multi-disciplinary research bridging operations research, business, systems and control engineering, and mathematics. The paper concludes with an illustrative example and discussions of specific challenges anticipated in future research.

[1]  D. Sterman,et al.  Misperceptions of Feedback in a Dynamic Decision Making Experiment , 1989 .

[2]  G. Stépán.  Retarded dynamical systems : stability and characteristic functions , 1989 .

[3]  J. Hale,et al.  Global geometry of the stable regions for two delay differential equations , 1993 .

[4]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[5]  J. Forrester.  Industrial Dynamics , 1997 .

[6]  J. Sterman.  Business Dynamics , 2000 .

[7]  T. V. Kumaresh,et al.  The false promise of mass customization , 2001 .

[8]  S. Niculescu.  Delay Effects on Stability: A Robust Control Approach , 2001 .

[9]  Rifat Sipahi,et al.  An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems , 2002, IEEE Trans. Autom. Control..

[10]  Wim Michiels.  Stability and stabilization of time-delay systems , 2002 .

[11]  J Swanson,et al.  Business Dynamics—Systems Thinking and Modeling for a Complex World , 2002, J. Oper. Res. Soc..

[12]  M. Lambrecht,et al.  Transfer function analysis of forecasting induced bullwhip in supply chains , 2002 .

[13]  S. Bennett,et al.  Production-inventory system controller design and supply chain dynamics , 2002, Int. J. Syst. Sci..

[14]  Modelling supply networks and business cycles as unstable transport phenomena , 2003, cond-mat/0307366.

[15]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[16]  Dirk Helbing,et al.  Network-induced oscillatory behavior in material flow networks and irregular business cycles. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Jie Chen,et al.  On stability crossing curves for general systems with two delays , 2004 .

[18]  Roger D. H. Warburton,et al.  An exact analytical solution to the production inventory control problem , 2004 .

[19]  D. Helbing,et al.  Physics, stability, and dynamics of supply networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Carlos F. Daganzo,et al.  On the Stability of Supply Chains , 2002, Oper. Res..

[21]  D. Helbing,et al.  Stability analysis and stabilization strategies for linear supply chains , 2003, cond-mat/0304476.

[22]  E.M. Atkins,et al.  A survey of consensus problems in multi-agent coordination , 2005, Proceedings of the 2005, American Control Conference, 2005..

[23]  Nejat Olgaç,et al.  Complete stability robustness of third-order LTI multiple time-delay systems , 2005, Autom..

[24]  S. Y. Nof,et al.  Task parallelism in distributed supply organizations: a case study in the shoe industry , 2005 .

[25]  Dirk Helbing,et al.  Information and material flows in complex networks , 2006 .

[26]  Dirk Helbing,et al.  Delays, inaccuracies and anticipation in microscopic traffic models , 2006 .

[27]  Silviu-Iulian Niculescu,et al.  Stability of Traffic Flow Behavior with Distributed Delays Modeling the Memory Effects of the Drivers , 2007, SIAM J. Appl. Math..

[28]  Philip M. Kaminsky,et al.  Designing and managing the supply chain : concepts, strategies, and case studies , 2007 .

[29]  Dirk Helbing,et al.  On Stability Problems of Supply Networks Constrained With Transport Delay , 2009 .