Revealing instabilities in a generalized triadic supply network: A bifurcation analysis.

Supply networks are exposed to instabilities and thus a high level of risk. To mitigate this risk, it is necessary to understand how instabilities are formed in supply networks. In this paper, we focus on instabilities in inventory dynamics that develop due to the topology of the supply network. To be able to capture these topology-induced instabilities, we use a method called generalized modeling, a minimally specified modeling approach adopted from ecology. This method maps the functional dependencies of production rates on the inventory levels of different parts and products, which are imposed by the network topology, to a set of elasticity parameters. We perform a bifurcation analysis to investigate how these elasticities affect the stability. First, we show that dyads and serial supply chains are immune to topology-induced instabilities. In contrast, in a simple triadic network, where a supplier acts as both a first and a second tier supplier, we can identify instabilities that emerge from saddle-node, Hopf, and global homoclinic bifurcations. These bifurcations lead to different types of dynamical behavior, including exponential convergence to and divergence from a steady state, temporary oscillations around a steady state, and co-existence of different types of dynamics, depending on initial conditions. Finally, we discuss managerial implications of the results.

[1]  Denis Royston Towill,et al.  A discrete transfer function model to determine the dynamic stability of a vendor managed inventory supply chain , 2002 .

[2]  Young Won Park,et al.  Supply chain lessons from the catastrophic natural disaster in Japan , 2013 .

[3]  Daniel R. Krause,et al.  An empirical investigation of supplier development: reactive and strategic processes , 1998 .

[4]  S. Disney,et al.  On bullwhip in supply chains--historical review, present practice and expected future impact , 2006 .

[5]  Thilo Gross,et al.  Bifurcations and chaos in the MAPK signaling cascade. , 2010, Journal of theoretical biology.

[6]  Jayashankar M. Swaminathan,et al.  Modeling Supply Chain Dynamics: A Multiagent Approach , 1998 .

[7]  Yanjun Li,et al.  A Framework to Model the Topological Structure of Supply Networks , 2011, IEEE Transactions on Automation Science and Engineering.

[8]  Thilo Gross,et al.  How to predict community responses to perturbations in the face of imperfect knowledge and network complexity , 2013, Proceedings of the Royal Society B: Biological Sciences.

[9]  Thilo Gross,et al.  Generalized models as a universal approach to the analysis of nonlinear dynamical systems. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  A. Raman,et al.  Aligning incentives in supply chains. , 2004, Harvard business review.

[11]  Young-Jun Son,et al.  Effect of information update frequency on the stability of production–inventory control systems , 2007 .

[12]  Andreas Norrman,et al.  Ericsson’s Proactive Supply Chain Risk Management-approach After a Serious Supplier Accident , 2004 .

[13]  Thilo Gross,et al.  General analysis of mathematical models for bone remodeling. , 2010, Bone.

[14]  Frank Y. Chen,et al.  Quantifying the Bullwhip Effect in a Simple Supply Chain: The Impact of Forecasting, Lead Times, and Information.: The Impact of Forecasting, Lead Times, and Information. , 2000 .

[15]  Philippa Pattison,et al.  Manufacturing Relations: An Empirical Study of the Organization of Production Across Multiple Networks , 2006, Organ. Sci..

[16]  John D. Sterman,et al.  “I’m not hoarding, I’m just stocking up before the hoarders get here.”: Behavioral causes of phantom ordering in supply chains , 2015 .

[17]  Erik Mosekilde,et al.  Border-collision bifurcations in a dynamic management game , 2006, Comput. Oper. Res..

[18]  Daniel R. Krause,et al.  The relationships between supplier development, commitment, social capital accumulation and performance improvement , 2007 .

[19]  Terry P. Harrison,et al.  The Bullwhip Effect—Impact of Stochastic Lead Time, Information Quality, and Information Sharing: A Simulation Study , 2004 .

[20]  M. Barratt,et al.  Exploring the experiences of collaborative planning initiatives , 2001 .

[21]  M. Christopher,et al.  Agent-based modelling of complex production/distribution systems to improve resilience , 2007 .

[22]  Ilhyung Kim,et al.  Measuring endogenous supply chain volatility: Beyond the bullwhip effect , 2008, Eur. J. Oper. Res..

[23]  J. Mentzer,et al.  Global supply chain risk management strategies , 2008 .

[24]  Li Chen,et al.  Bullwhip Effect Measurement and Its Implications , 2012, Oper. Res..

[25]  M. Christopher,et al.  Building the Resilient Supply Chain , 2004 .

[26]  Petri Helo,et al.  Dynamic modelling of surge effect and capacity limitation in supply chains , 2000 .

[27]  J. Sterman,et al.  Order Stability in Supply Chains: Coordination Risk and the Role of Coordination Stock , 2004 .

[28]  Thilo Gross,et al.  Generalized Models Reveal Stabilizing Factors in Food Webs , 2009, Science.

[29]  Göran Svensson,et al.  Vulnerability scenarios in marketing channels , 2002 .

[30]  Erik Mosekilde,et al.  Nonlinear dynamic phenomena in the beer model , 2007 .

[31]  H. Peck Drivers of supply chain vulnerability: an integrated framework , 2005 .

[32]  Gérard P. Cachon,et al.  Contracting to Assure Supply: How to Share Demand Forecasts in a Supply Chain , 2001, Manag. Sci..

[33]  Thilo Gross,et al.  Structural kinetic modeling of metabolic networks , 2006, Proceedings of the National Academy of Sciences.

[34]  Yves Nievergelt,et al.  The Concept of Elasticity in Economics , 1983 .

[35]  H. Brian Hwarng,et al.  Understanding supply chain dynamics: A chaos perspective , 2008, Eur. J. Oper. Res..

[36]  Gregory M. Magnan,et al.  The rhetoric and reality of supply chain integration , 2002 .

[37]  A. Dubois,et al.  Co-operating and competing in supply networks: Making sense of a triadic sourcing strategy , 2008 .

[38]  Brian Tomlin,et al.  Capacity Investments in Supply Chains: Sharing the Gain Rather Than Sharing the Pain , 2003, Manuf. Serv. Oper. Manag..

[39]  Jay W. Forrester,et al.  Industrial Dynamics---After the First Decade , 1968 .

[40]  Bodo Werner,et al.  Computation of Hopf bifurcation with bordered matrices , 1996 .

[41]  Lei Wang,et al.  Modelling and analysis of the bullwhip effect with customers’ baulking behaviours and production capacity constraint , 2014 .

[42]  Ashutosh Tiwari,et al.  Supply Networks as Complex Systems: A Network-Science-Based Characterization , 2017, IEEE Systems Journal.

[43]  Mohamed Mohamed Naim,et al.  A control engineering approach to the assessment of supply chain resilience , 2012 .

[44]  Xun Wang,et al.  The bullwhip effect: Progress, trends and directions , 2016, Eur. J. Oper. Res..

[45]  T. Comes,et al.  A critical review on supply chain risk – Definition, measure and modeling ☆ , 2015 .

[46]  Stephan M. Wagner,et al.  AN EMPIRICAL EXAMINATION OF SUPPLY CHAIN PERFORMANCE ALONG SEVERAL DIMENSIONS OF RISK , 2008 .

[47]  J. L. Cavinato Supply chain logistics risks: From the back room to the board room , 2004 .

[48]  Christos D. Tarantilis,et al.  Dynamic modeling and control of supply chain systems: A review , 2008, Comput. Oper. Res..

[49]  Jing Wang,et al.  Stability analysis of constrained inventory systems with transportation delay , 2012, Eur. J. Oper. Res..

[50]  Boris V. Sokolov,et al.  Control and system-theoretic identification of the supply chain dynamics domain for planning, analysis and adaptation of performance under uncertainty , 2013, Eur. J. Oper. Res..

[51]  S. Chopra,et al.  Managing Risk To Avoid Supply-Chain Breakdown , 2004 .

[52]  Markku Tuominen,et al.  Risk analysis and assessment in network environments: A dyadic case study , 2002 .

[53]  Roger D. H. Warburton,et al.  An Analytical Investigation of the Bullwhip Effect , 2004 .

[54]  Amit Surana,et al.  Supply-chain networks: a complex adaptive systems perspective , 2005 .

[55]  Chao Qi,et al.  On the stability and bullwhip effect of a production and inventory control system , 2013 .

[56]  Alexandra Brintrup,et al.  Topological robustness of the global automotive industry , 2016, Logist. Res..

[57]  Thomas Y. Choi,et al.  Taking the leap from dyads to triads: Buyer–supplier relationships in supply networks , 2009 .

[58]  M. Ortega,et al.  Control theory applications to the production–inventory problem: a review , 2004 .

[59]  Thilo Gross,et al.  Analytical search for bifurcation surfaces in parameter space , 2004 .

[60]  Hau L. Lee,et al.  The bullwhip effect in supply chains , 2015, IEEE Engineering Management Review.

[61]  Joachim Selbig,et al.  From structure to dynamics of metabolic pathways: application to the plant mitochondrial TCA cycle , 2007, Bioinform..

[62]  Thilo Gross,et al.  Identifying dynamical instabilities in supply networks using generalized modeling , 2019, Journal of Operations Management.

[63]  Lothar Reichel,et al.  Tridiagonal Toeplitz matrices: properties and novel applications , 2013, Numer. Linear Algebra Appl..

[64]  Stephen M. Disney,et al.  Measuring and avoiding the bullwhip effect: A control theoretic approach , 2003, Eur. J. Oper. Res..

[65]  Thilo Gross,et al.  Computation and Visualization of bifurcation Surfaces , 2008, Int. J. Bifurc. Chaos.