Synthesis of control policies for manufacturing systems using eigenvalue-assignment techniques †

Porter, B.; Crossley, T. R.

doi:10.1080/00207727208920253

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…Their state-space discrete model of production man-hours used a unit delay in computing an optimal response to a sales disturbance. Early representations of supply chains using state-space models were produced by Porter and Taylor (1972), Porter and Crossley (1972) and Bradshaw and Porter (1973). Porter and Taylor obtained a modal control model of a production-inventory system using two state variables (SVs), whereas Porter and Crossley used eigenvalue assignment solutions for Christensen and Brogan's model, showing results with little overshoot.…”

Section: Reviewmentioning

confidence: 99%

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

White

Censlive

2015

Journal of Modelling in Management

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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 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. Originality/value – 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.

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Section: Reviewmentioning

confidence: 99%

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

White

Censlive

2015

Journal of Modelling in Management

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“…This model of production man-hours incorporated a unit delay to obtain an optimal solution to a sales disturbance. Amongst the first representations of supply chains using SS models was the work of Porter and Taylor (1972), Porter and Crossley (1972) and Bradshaw and Porter (1973). Porter and Taylor produced a modal control model of a production-inventory system using two state variables.…”

Section: Ss Models Of Inventory/supply Chainsmentioning

confidence: 99%

“…The development of control system methods applied to inventory is summarised in Table I. Campbell (1953) Laplace transforms Evaluation of P and PI control Tustin (1953) Laplace and z transforms Economic systems Vassian (1955) DCE and z transforms Inventory and order based scheduling algorithms Brown (1962) z Transforms Inventory and order based scheduling algorithms Adelson (1966) z transforms Exponential smoothing algorithms De Winter (1966) Transform methods Application to inventory Deziel and Eilon (1967) z transforms and cost functions Automatic pipeline APIOBPCS with equal Tw and Ti Connors and Teichroew (1967) Transform methods Simple economic models Dobell and Ho (1967) Transform methods Simple economic models Bessler and Zehna (1968) z transforms Expanded Vassian's model using exponential smoothing Christensen and Brogan (1971) Discrete state space Optimal control applied to work scheduling system Porter and Taylor (1972) State space Modal control of production system Porter and Crossley (1972) Discrete state space Eigenvalue assignment for inventory system Bradshaw and Porter (1973) State space Optimal state regulator for inventory system Bensoussan et al (1974) State space Optimal solutions using Pontryagin's method for various cost functions Boyd (1977) State space Optimal control of a manufacturing firm producing multiple products Coyle (1977) SDs models Outlined APIOBPCS for first time Burns and Sivazlian (1978) z transforms Order amplification of four echelon supply chains Sharp and Henry (1952) SD model Zeigler-Nichols tuning of PID controlled manufacturing process Popplewell (1980) Discrete state space PhD thesis multiproduct and multi level production systems O'Grady (1981) Discrete state space PhD thesis application of discrete modern control theory to multi level production Towill (1982) Laplace transforms Inventory and order based systems Towill and Yoon (1981) Laplace transforms, frequency response…”

Section: Ss Models Of Inventory/supply Chainsmentioning

confidence: 99%

An alternative state-space representation for APVIOBPCS inventory systems

White

Censlive²

2013

Journal of Manufacturing Technology Management

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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.

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Analysis of a production-inventory control system for a diffusion department

Bertrand

1980

International Journal of Systems Science

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Synthesis of control policies for manufacturing systems using eigenvalue-assignment techniques †

Cited by 3 publications

References 8 publications

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

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

An alternative state-space representation for APVIOBPCS inventory systems

Analysis of a production-inventory control system for a diffusion department

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