title: Direct solution of a minimax location problem on the plane with rectilinear metric in a rectangular area
metadata.name: dc.contributor.author
metadata.value: Plotnikov, Pavel V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Krivulin, Nikolai K.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-07-18T11:57:39Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-07-18T11:57:39Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Plotnikov P. V., Krivulin N. K. Direct solution of a minimax location problem on the plane with rectilinear metric in a rectangular area. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2018, vol. 14, iss. 2, pp. 116–130.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11702/spbu10.2018.204
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/10442
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A minimax single-facility location problem with rectilinear (Manhattan) metric is examined
  under constraints on the feasible location region, and a direct, explicit solution of the problem
  is suggested using methods of tropical (idempotent) mathematics. When no constraints are
  imposed, this problem, which is also known as the Rawls problem or the messenger boy
  problem, has known geometric and algebraic solutions. In the present article, a solution to
  the problem is investigated subject to constraints on the feasible region, which is given by a
  rectangular area. At first, the problem is represented in terms of tropical mathematics as a
  tropical optimization problem, a parameter is introduced to represent the minimum value of
  the objective function, and the problem is reduced to a parametrized system of inequalities.
  This system is solved for one variable, and the existence conditions of solution are used to
  obtain optimal values of the second parameter by using an auxiliary optimization problem.
  Then, the obtained general solution is transformed into a set of direct solutions, written in
  a compact closed form for different cases of relations between the initial parameters of the
  problem. Graphical illustrations of the solution are given for several positions of the feasible
  location region on the plane.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке Российского фонда фундаментальных исследований (грант № 18-010-00723).
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.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 14; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: Rawls location problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: constrained location
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: rectilinear metric
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: complete solution
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Direct solution of a minimax location problem on the plane with rectilinear metric in a rectangular area
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 04-Plotnikov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/10442/1/04-Plotnikov.pdf
resources.format: Adobe PDF
resources.size: 322,94 kB