An alternative state-space representation for APVIOBPCS inventory systems
Journal of Manufacturing Technology Management
ISSN: 1741-038X
Article publication date: 29 April 2013
Abstract
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 transform models.
Research limitations/implications
The system is described by a linear control model of the production process and does not include production limits or other resource limitations. It does not include any past history of sales demand and responses.
Practical implications
This work allows a model to be implemented in a spreadsheet of APVIOBPCS PIC that can be used for any production delay and can be modified to include different sales smoothing procedures.
Originality/value
This present model is an extension and improvement of the model devised by Lalwani, in that it allows more accurate modelling of inventory production systems by permitting a more flexible selection of delay parameter values, closer to those of real systems.
Keywords
Citation
White, A.S. and Censlive, M. (2013), "An alternative state-space representation for APVIOBPCS inventory systems", Journal of Manufacturing Technology Management, Vol. 24 No. 4, pp. 588-614. https://doi.org/10.1108/17410381311327413
Publisher
:Emerald Group Publishing Limited
Copyright © 2013, Emerald Group Publishing Limited