Bounded growth of the bullwhip effect under a class of nonlinear ordering policies

This paper analyzes the bullwhip effect in multi-echelon supply chains under a general class of nonlinear ordering policies. A describing-function approach from control theory is used to derive closed-form formulas to predict amplification of order fluctuations along the supply chain. It is proven that with consideration of nonlinearity in the ordering policy, the magnitude of the bullwhip effect will eventually become bounded after growing through the first few stages of the supply chain. It is also proven that the average customer demand as well as the demand fluctuation frequency would directly affect the bounded magnitude, while the suppliers’ demand forecasting method has no effect at all. For illustration, analytical results for a class of order-up-to policies are derived and verified by numerical simulations. The proposed modeling framework holds the promise to not only explain empirical observations, but also serve as the basis for developing counteracting strategies against the bullwhip effect.

[1]  J. Forrester.  Industrial Dynamics: A Major Breakthrough for Decision Makers , 2012 .

[2]  Yanfeng Ouyang,et al.  The bullwhip effect in supply chain networks , 2010, Eur. J. Oper. Res..

[3]  D. Simchi-Levi,et al.  The impact of exponential smoothing forecasts on the bullwhip effect , 2000 .

[4]  Rex Acton,et al.  The Design of Production Systems , 1968 .

[5]  Stephen C. Graves,et al.  A Single-Item Inventory Model for a Nonstationary Demand Process , 1999, Manuf. Serv. Oper. Manag..

[6]  R. Adelson,et al.  The Dynamic Behaviour of Linear Forecasting and Scheduling Rules , 1966 .

[7]  H. Davis.  Introduction to Nonlinear Differential and Integral Equations , 1964 .

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

[9]  Yanfeng Ouyang,et al.  Counteracting the bullwhip effect with decentralized negotiations and advance demand information , 2005 .

[10]  L. C. Edie.  Car-Following and Steady-State Theory for Noncongested Traffic , 1961 .

[11]  Yanfeng Ouyang,et al.  Characterization of the Bullwhip Effect in Linear, Time-Invariant Supply Chains: Some Formulae and Tests , 2006, Manag. Sci..

[12]  S. Hohmann.  The Bullwhip Effect in Supply Chains , 2014 .

[13]  Yanfeng Ouyang,et al.  Characterization of Traffic Oscillation Propagation Under Nonlinear Car-Following Laws , 2011 .

[14]  Taylor Randall,et al.  In Search of the Bullwhip Effect , 2007, Manuf. Serv. Oper. Manag..

[15]  Yanfeng Ouyang,et al.  Prediction and Field Validation of Traffic Oscillation Propagation Under Nonlinear Car-Following Laws , 2012 .

[16]  Y. Ouyang,et al.  Measurement and estimation of traffic oscillation properties , 2010 .

[17]  K Jalaleddini,et al.  Elimination of limit cycles in wireless communication networks using three-level comparators , 2010, Proceedings of the 2010 American Control Conference.

[18]  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 .

[19]  D. P. Deziel,et al.  A linear production-inventory control rule , 1967 .

[20]  El-Houssaine Aghezzaf,et al.  A model predictive control framework for centralised management of a supply chain dynamical system , 2014 .

[21]  Xiaolong Zhang,et al.  Technical Note: Evolution of ARMA Demand in Supply Chains , 2004, Manuf. Serv. Oper. Manag..

[22]  Yanfeng Ouyang,et al.  Taming the Bullwhip Effect : from traffic to supply chains , 2006 .

[23]  Morris A. Cohen,et al.  The Stabilizing Effect of Inventory in Supply Chains , 1998, Oper. Res..

[24]  Hau L. Lee,et al.  Information distortion in a supply chain: the bullwhip effect , 1997 .

[25]  Stephen M. Disney,et al.  The impact of information enrichment on the Bullwhip effect in supply chains: A control engineering perspective , 2004, Eur. J. Oper. Res..

[26]  Kenneth Gilbert,et al.  An ARIMA Supply Chain Model , 2005, Manag. Sci..

[27]  Vineet Padmanabhan,et al.  Comments on "Information Distortion in a Supply Chain: The Bullwhip Effect" , 1997, Manag. Sci..

[28]  Yanfeng Ouyang,et al.  The effect of information sharing on supply chain stability and the bullwhip effect , 2007, Eur. J. Oper. Res..

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

[30]  Herbert E. Scarf,et al.  Optimal Policies for a Multi-Echelon Inventory Problem , 1960, Manag. Sci..

[31]  A. Blinder.  Can the Production Smoothing Model of Inventory Behavior Be Saved? , 1986 .

[32]  Ralph J. Kochenburger,et al.  A Frequency Response Method for Analyzing and Synthesizing Contactor Servomechanisms , 1950, Transactions of the American Institute of Electrical Engineers.

[33]  Yanfeng Ouyang,et al.  Robust tests for the bullwhip effect in supply chains with stochastic dynamics , 2008, Eur. J. Oper. Res..

[34]  J. S. Goodwin,et al.  The Beer Distribution Game: Using Simulation to Teach Systems Thinking , 1994 .

[35]  Dirk Helbing.  Production, Supply, and Traffic Systems: A Unified Description , 2004 .

[36]  S. Disney,et al.  Damped trend forecasting and the order-up-to replenishment policy , 2014 .

[37]  Sridhar Seshadri,et al.  Information Sharing in a Supply Chain Under ARMA Demand , 2005, Manag. Sci..

[38]  Arthur Gelb,et al.  Multiple-Input Describing Functions and Nonlinear System Design , 1968 .

[39]  Y. Ouyang.  Experimental study on using advance demand information to mitigate the bullwhip effect via decentralised negotiations , 2014 .

[40]  C. Urquhart,et al.  The impact of information. , 1997, Nursing standard (Royal College of Nursing (Great Britain) : 1987).

[41]  Herbert J. Vassian.  Application of Discrete Variable Servo Theory to Inventory Control , 1955, Oper. Res..

[42]  T. Hughes,et al.  Signals and systems , 2006, Genome Biology.

[43]  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..