{
  "id": "1303.5457",
  "version": "v2",
  "published": "2013-03-21T20:37:57.000Z",
  "updated": "2013-11-10T22:46:20.000Z",
  "title": "Explicit solution of a tropical optimization problem with application to project scheduling",
  "authors": [
    "Nikolai Krivulin"
  ],
  "comment": "Mathematical Methods and Optimization Techniques in Engineering: Proc. 1st Intern. Conf. on Optimization Techniques in Engineering (OTENG '13), Antalya, Turkey, October 8-10, 2013, WSEAS Press, 2013, pp. 39-45. ISBN 978-960-474-339-1",
  "categories": [
    "math.OC",
    "cs.SY"
  ],
  "abstract": "A new multidimensional optimization problem is considered in the tropical mathematics setting. The problem is to minimize a nonlinear function defined on a finite-dimensional semimodule over an idempotent semifield and given by a conjugate transposition operator. A special case of the problem, which arises in just-in-time scheduling, serves as a motivation for the study. To solve the general problem, we derive a sharp lower bound for the objective function and then find vectors that yield the bound. Under general conditions, an explicit solution is obtained in a compact vector form. This result is applied to provide new solutions for scheduling problems under consideration. To illustrate, numerical examples are also presented.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-11-10T22:46:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65K10",
      "15A80",
      "65K05",
      "90C48",
      "90B35"
    ],
    "keywords": [
      "tropical optimization problem",
      "explicit solution",
      "project scheduling",
      "application",
      "multidimensional optimization problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.5457K"
    }
  }
}