Journal Article

Inventory constraint control with uncertain stochastic demands: attractive ellipsoid technique application

Hussain Sagi Alazki and Alexender Poznyak Gorbatch

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 29, issue 3, pages 399-425
Published in print September 2012 | ISSN: 0265-0754
Published online February 2012 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnr038
Inventory constraint control with uncertain stochastic demands: attractive ellipsoid technique application

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In this paper, we consider the inventory robust constraint control problem with an uncertain demand. The considered system deals with a non-linear discrete-time stochastic model of a special structure. The robust control designing, consisting in the inventory product level minimization by the corresponding adjustment of the production rate, is shown to be converted into certain attractive ellipsoid ‘minimization’ problem under some specific constraints of bilinear matrix inequalities (BMI's) type. The application of an adequate coordinate changing transforms these BMI's into a set of linear matrix inequalities that permits to use directly the standard MATLAB-toolbox. The matrix generalization of the strong law of large numbers provides an instrument for the stochastic analyses of the considered process.

Keywords: stochastic models; inventory control; attractive ellipsoid method; linear matrix inequalities

Journal Article.  0 words. 

Subjects: Mathematics

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