A state-space model of a three tier APVIOBPCS supply chain

Purpose – The purpose of this paper is to investigate a control engineering-based system model that allows for any value of production delay for a three-tier supply chain with information delays between tiers or systems with epos. Design/methodology/approach – A discrete z transform model of automatic pipeline, variable inventory and order based production control system three-tier supply chain is obtained using a state-space model using a reachable control formulation. This model provides a discrete time state-space model conversion using an exponential production delay with no loss of generality. Findings – This work allows a three-tier supply chain model to be computed via a spreadsheet using any production delay and can be modified to include different sales smoothing procedures. The model is fully controllable and observable. Stability of these models is obtained from the system eigenvalues and agrees with our previously published stability boundaries. Practical implications – The system is described...

[1]  D. Towill,et al.  Information enrichment: designing the supply chain for competitive advantage , 1997 .

[2]  Mohamed Mohamed Naim,et al.  Dynamic analysis of a WIP compensated decision support system , 1994 .

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

[4]  Nicoleta S. Tipi,et al.  Modelling the dynamics of supply chains , 2000, Int. J. Syst. Sci..

[5]  Mohammed M. Naim,et al.  The System Simplification Approach in Understanding the Dynamic Behaviour of a Manufacturing Supply Chain , 1992 .

[6]  A. S. White,et al.  Observations on modelling strategies for vendor‐managed inventory , 2006 .

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

[8]  D. Teichroew,et al.  Optimal control of dynamic operations research models , 1969 .

[9]  Maurice Bonney,et al.  The application of discrete linear control theory to the analysis and simulation of multi-product, multi-level production control systems , 1987 .

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

[11]  Peter W. Zehna,et al.  An application of servomechanisms to inventory , 1968 .

[12]  Yohanes Kristianto Nugroho.  Production ramp up in built‐to‐order supply chains , 2011 .

[13]  Pradeep Kumar,et al.  Analytical modeling of third party service provider selection in lead logistics provider environments , 2010 .

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

[15]  Marc Lambrecht,et al.  The dynamics of aggregate planning , 2003 .

[16]  Denis Royston Towill,et al.  Industrial dynamics model building of a close-coupled production-distribution system , 1988 .

[17]  Sven Axsäter,et al.  Control theory concepts in production and inventory control , 1985 .

[18]  Richard Edward DeWinter.  Inventory Applications of Servomechanism Models , 1966 .

[19]  Denis Royston Towill,et al.  Some features common to inventory system and process controller design , 1982 .

[20]  P. Valigi,et al.  H-infinity control of a Supply Chain model , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[21]  B. Porter,et al.  Optimal control of production-inventory systems , 1973 .

[22]  Adrian Gambier,et al.  A new inventory level APIOBPCS-based controller , 2008, 2008 American Control Conference.

[23]  A. S. White.  Management of inventory using control theory , 1999 .

[24]  Susmita Bandyopadhyay,et al.  A review of the causes of bullwhip effect in a supply chain , 2011 .

[25]  T. R. Crossley,et al.  Synthesis of control policies for manufacturing systems using eigenvalue-assignment techniques † , 1972 .

[26]  A. Dobell,et al.  Optimal investment policy: An example of a control problem in economic theory , 1967, IEEE Transactions on Automatic Control.

[27]  C. E. Riddalls,et al.  The optimal control of batched production and its effect on demand amplification , 2001 .

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

[29]  Rambabu Kodali,et al.  An application of analytic hierarchy process for the selection of a methodology to improve the product development process , 2012 .

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

[31]  B. D. Sivazlian,et al.  Dynamic analysis of multi-echelon supply systems , 1978 .

[32]  Keith Tizzard,et al.  Management System Dynamics , 1977 .

[33]  J. Fransoo,et al.  Measuring the bullwhip effect in the supply chain , 2000 .

[34]  Jane Edghill,et al.  Industrial case-study on the dynamics and sensitivity of a close-coupled production-distribution system† , 1988 .

[35]  I. Boyd.  On the optimal control of a manufacturing firm producing several distinct products , 1977 .

[36]  Bong Wie.  Dynamic Systems Control , 2016 .

[37]  Chandra Lalwani,et al.  Controllable, observable and stable state space representations of a generalized order-up-to policy , 2006 .

[38]  Christos I. Papanagnou,et al.  Supply-chain modelling and control under proportional inventory-replenishment policies , 2008, Int. J. Syst. Sci..

[39]  B. Beamon.  Supply chain design and analysis:: Models and methods , 1998 .

[40]  J. Venkateswaran,et al.  Impact of modelling approximations in supply chain analysis – an experimental study , 2004 .

[41]  M. K. Yurtseven,et al.  Regulating Bullwhip Effect in Supply Chains through Modern Control Theory , 2007, PICMET '07 - 2007 Portland International Conference on Management of Engineering & Technology.

[42]  Lansing Alexander Gordon.  The e-skip-gen effect. The emergence of a cybercentric management model and the F2B market segment for industry , 2002 .

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

[44]  S. Disney,et al.  Vendor-managed inventory and bullwhip reduction in a two-level supply chain , 2003 .

[45]  Anthony S. White,et al.  An alternative state-space representation for APVIOBPCS inventory systems , 2013 .

[46]  B. Porter,et al.  Modal control of production-inventory systems , 1972 .

[47]  B. Porter,et al.  Synthesis of control policies for a production-inventory tracking system , 1975 .

[48]  H. Simon,et al.  On the Application of Servomechanism Theory in the Study of Production Control , 1952 .

[49]  Denis Royston Towill,et al.  Dynamic analysis of an inventory and order based production control system , 1982 .

[50]  Behrouz Zarei,et al.  Developing and manipulating business models applying system dynamics approach , 2013 .

[51]  W. L. Brogan,et al.  Modelling and optimal control of a production process , 1971 .

[52]  Paul Streeten,et al.  The Mechanism of Economic Systems , 1956 .