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

Anthony S White (School of Engineering and Information Systems, Middlesex University, London, UK)
Michael Censlive (School of Engineering and Information Systems, Middlesex University, London, UK)

Journal of Modelling in Management

ISSN: 1746-5664

Article publication date: 16 March 2015



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.


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.


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 by a linear control model of the production process and does not include production limits or other resource limitations, including history of sales demand and response.


This present model is an extension of the model devised by White and Censlive, in that it allows accurate modelling of multi-tier inventory production systems by permitting flexible selection of delay parameter values for real systems.



White, A.S. and Censlive, M. (2015), "A state-space model of a three tier APVIOBPCS supply chain", Journal of Modelling in Management, Vol. 10 No. 1, pp. 76-104.



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