An alternative state-space representation for APVIOBPCS inventory systems

Purpose – Lalwani et al. devised a controllable state-space model for a general APVIOBPCS production and inventory system. However, their procedure did not cater for production delays of other than one time unit. The authors have sought to devise a model that allows for any value of production delay. Design/methodology/approach – A discrete z transform model of APVIOBPCS inventory is obtained using conventional algebra and converted to a state-space model using a reachable control formulation. This is then analysed to produce an analytic expression for the eigenvalues and then the general stability solution is derived from the unit circle condition. Findings – This model allows a state-space model conversion from a discrete time input-output model using an exponential production delay with no loss of generality and is fully controllable and observable. Stability of these models can be obtained from the system eigenvalues and agrees with the authors' previously published stability boundaries using transfor...

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

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

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

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

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

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

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

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

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

[10]  Robert W. Grubbström,et al.  Introducing capacity limitations into multi-level, multi-stage production-inventory systems applying the input-output/Laplace transform approach , 2000 .

[11]  Joakim Wikner,et al.  Inventory trigger control policies developed in terms of control theory , 1996 .

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

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

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

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

[16]  S. Disney,et al.  On the bullwhip and inventory variance produced by an ordering policy , 2003 .

[17]  Ahmed M. Deif,et al.  Agile MPC system linking manufacturing and market strategies , 2007 .

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

[19]  Gerald L. Thompson,et al.  Management Applications of Modern Control Theory , 1977 .

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

[21]  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 .

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

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

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

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

[26]  Robert W. Grubbström,et al.  A net present value approach to safety stocks in planned production , 1998 .

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

[28]  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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[49]  Robert Goodell Brown,et al.  Smoothing, forecasting and prediction of discrete time series , 1964 .

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

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

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

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

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