title: Algebraic solution of optimal sheduling problems subject to due dates for start time of project jobs
metadata.name: dc.contributor.author
metadata.value: Gubanov, Sergei А.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2022-12-27T12:30:25Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2022-12-27T12:30:25Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2022-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Gubanov S.A. Algebraic solution of optimal sheduling problems subject to due dates for start time of project jobs. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2022, vol. 9 (67), issue 4, pp. 602–611. https://doi.org/10.21638/spbu01.2022.403 (In Russian)
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2022.403
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/38716
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A direct solution is proposed for problems of drawing up the optimal schedule for jobs in a
  project based on using models and methods of tropical optimization. The problems of the
  development of an optimal plan are reduced to problems of tropical optimization, which
  consist in minimizing the objective function under given strict constraints on the start and
  finish time of jobs. As optimality criteria of the plan the maximum deviation from the due
  dates of the start of the jobs of the project is taken, which needs to be minimized. Strict
  time constraints for the jobs are given in the form of precedence relations and bounds for
  the start and finish times of the jobs. Such tasks arise if it is necessary for one reason or
  another (for example, due to technological limitations or safety requirements) to start jobs
  at specified time. In the article constraints and objective functions are first described in
  terms of ordinary mathematics and then the considered problems of project sheduling are
  set. Elements of tropical mathematics are discussed which are necessary for the presentation
  of the problems of drawing up the optimal schedule in a tropical form. Then the
  sheduling problems are formulated in terms of the idempotent mathematics and reduced to
  the problem of tropical optimization. Solution of the problems are presented in an explicit
  analytical form, which well suited for both formal analysis and numerical computations.
  An explanatory numerical example is provided at the end of the article.
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 9 (67); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: tropical mathematics
metadata.lang: en_GB
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: project sheduling
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: network planning
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Algebraic solution of optimal sheduling problems subject to due dates for start time of project jobs
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 602-611.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/38716/1/602-611.pdf
resources.format: Adobe PDF
resources.size: 285,99 kB