title: Solving a tropical optimization problem with application to optimal scheduling
metadata.name: dc.contributor.author
metadata.value: Krivulin, Nikolai K.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Basko, Ulyana L.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2019-09-05T16:52:56Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2019-09-05T16:52:56Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2019-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Krivulin N.K., Basko U. L. Solving a tropical optimization problem with application to optimal scheduling. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6 (64), issue 3, pp. 440–451.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu01.2019.309
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/16320
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A multidimensional optimization problem is considered, which is formulated and solved in terms of tropical mathematics focused on the theory and applications of semirings with idempotent addition. To solve the problem, which has an objective function given by a matrix, methods and results of idempotent algebra and tropical optimization are used. A strict lower bound for the objective function of the problem is first derived to allow the evaluation of the minimum value of the objective function. Then, an equation is formed and solved for the objective function and its minimum value, from which a complete solution is obtained in the form of all eigenvectors of the matrix in the problem. As an application of the result obtained, an explicit solution is given to the problem of optimal scheduling of a project that consists of a set of activities to be done under given constraints on the start and finish times of the activities. The optimality criterion for scheduling is defined as the minimum of maximal deviation, over all activities, of the working cycle time, which is given by the time interval between start and finish of the activity. The analytical result obtained extends and supplements the existing algorithmic numerical solutions to optimal scheduling problems. An example is presented to illustrate application of the result with a scheduling problem for a project consisting of three activities.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The work is supported by Russian Foundation for Basic Research (project N18-010-00723).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: idempotent semifield
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: (max,+)-algebra
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: eigenvalue and eigenvector of matrix
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: tropical optimization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: scheduling problem
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Solving a tropical optimization problem with application to optimal scheduling
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 440-451.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/16320/1/440-451.pdf
resources.format: Adobe PDF
resources.size: 333,02 kB