title: Algebraic solution of a problem of optimal project scheduling in project management
metadata.name: dc.contributor.author
metadata.value: Krivulin, Nikolay K.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Gubanov, Sergey A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-05-04T19:17:17Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-05-04T19:17:17Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Krivulin N.K., Gubanov S.A. Algebraic solution of a problem of optimal project scheduling in project management. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2021, vol. 8 (66), issue 1, pp. 73–87.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2021.107
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/28435
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A problem of optimal scheduling is considered for a project that consists of a certain set of
  works to be performed under given constraints on the times of start and finish of the works.
  As the optimality criterion for scheduling, the maximum deviation of the start time of works
  is taken to be minimized. Such problems arise in project management when it is required,
  according to technological, organizational, economic or other reasons, to provide, wherever
  possible, simultaneous start of all works. The scheduling problem under consideration is
  formulated as a constrained minimax optimization problem and then solved using methods
  of tropical (idempotent) mathematics which deals with the theory and applications of
  semirings with idempotent addition. First, a tropical optimization problem is investigated
  defined in terms of a general idempotent semifield (an idempotent semiring with invertible
  multiplication), and a complete analytical solution of the problem is derived. The result
  obtained is then applied to find a direct solution of the scheduling problem in a compact
  vector form ready for further analysis of solutions and straightforward computations. As
  an illustration, a numerical example of solving optimal scheduling problem is given for a
  project that consists of four works.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work is supported by Russian Foundation for Basic Research (grant No. 20-010-00145).
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.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 8 (66); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: idempotent semifield
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: tropical optimization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: minimax optimization problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: project scheduling
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: project management
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Algebraic solution of a problem of optimal project scheduling in project management
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 73-87.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/28435/1/73-87.pdf
resources.format: Adobe PDF
resources.size: 324,69 kB