Interval multi-linear systems for tensors in the max-plus algebra and their application in solving the job shop problem

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• Sedighe Khaleghzade (University of Hormozgan, Iran)
• Tuesday 15 November 2022, 14:00-15:00
• Zoom: https://bham-ac-uk.zoom.us/j/81011075520?pwd=bXArZHZ6UW1MbkFKZUEveXJvWHR0dz09.

If you have a question about this talk, please contact Sergey Sergeev.

Max-plus algebra provides mathematical theory and techniques for solving nonlinear problems that can be given the form of linear systems when arithmetical addition is replaced by the operation of maximum and arithmetical multiplication is replaced by addition. Problems of this kind are sometimes of a managerial nature, arising in areas such as manufacturing, transportation, allocation of resources, and information processing technology. In this talk, I propose the notions of the max-plus algebra of the interval tensors, which can be used for the extension of interval linear systems to interval multi-linear systems in the max-plus algebra. Some properties and basic results of interval multi-linear systems in max-plus algebra are derived. An algorithm is developed for computing the solution of the multi-linear systems in the max-plus algebra. Necessary and sufficient conditions for the interval multi-linear systems for weak solvability over max-plus algebra are obtained as well. As an application, I briefly sketch how our results can be used in the max-plus algebraic system theory for synchronized discrete event systems, more precisely in the job shop problem. Finally, some examples are given for illustrating the obtained results.

This talk is part of the Optimisation and Numerical Analysis Seminars series.

This talk is included in these lists:

• Optimisation and Numerical Analysis Seminars
• School of Mathematics events
• Zoom: https://bham-ac-uk.zoom.us/j/81011075520?pwd=bXArZHZ6UW1MbkFKZUEveXJvWHR0dz09

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