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A CLASS OF MIX DESIGN PROBLEMS: FORMULATION, SOLUTION METHODS AND APPLICATIONS

Part of: Design of experiments Miscellaneous topics in calculus of variations and optimal control

Published online by Cambridge University Press:  29 July 2009

Zhong Wan ,
K. L. Teo ,
LingShuang Kong  and
Chunhua Yang
Zhong Wan
Affiliation:
School of Mathematical Science and Computing Technology, Central South University, Hunan Changsha, PR China (email: wanmath@163.com)
K. L. Teo*
Affiliation:
Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia (email: K.L.Teo@curtin.edu.au)
LingShuang Kong
Affiliation:
School of Information Sciences and Engineering, Central South University, Hunan Changsha, PR China
Chunhua Yang
Affiliation:
School of Information Sciences and Engineering, Central South University, Hunan Changsha, PR China
*
✉For correspondence; e-mail: K.L.Teo@curtin.edu.au
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Abstract

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In this paper, we consider a linear program with only equality constraints but containing interval and random coefficients. We first address the linear program with interval coefficients, and establish some structural properties of this linear program. On this basis, a solution method is proposed. We then move on to consider the linear program with random coefficients. Using the chance constraint approach and a new approach, the satisfaction degree approach, we obtain the two respective deterministic equivalent formulations. Then the results and the numerical solution methods obtained for these two linear models are applied to the original linear problem which contains both interval and random coefficients. By way of illustration, we consider a practical problem, where the optimal mixing proportions need to be determined for the mix slurry in the production process of aluminium with sintering. This gives rise to a linear program with interval and random coefficients. Its deterministic equivalent formulations are presented. Preliminary numerical examples show that the proposed models and the solution methods are promising.

Keywords

linear programmingrandom linear programschance constrained programminglinear programming with interval coefficientsmixture makingalumina sintering

MSC classification

Secondary: 62K05: Optimal designs 49N10: Linear-quadratic problems

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 4 , April 2009 , pp. 455 - 474
Copyright
Copyright © Australian Mathematical Society 2009

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