Publication detail

Fixed interval scheduling under uncertainty - A tabu search algorithm for an extended robust coloring formulation

NOVOTNÝ, J. BRANDA, M. OLSTAD, A.

English title

Fixed interval scheduling under uncertainty - A tabu search algorithm for an extended robust coloring formulation

Type

journal article in Web of Science

Language

en

Original abstract

We propose several formulations of the fixed interval scheduling problem under uncertainty, where the risk is represented by random delays in processing times. We employ various stochastic programming and robust coloring problems to deal with the uncertainty. Our main goal is to introduce equivalent deterministic reformulations of the stochastic programming problems. We show that the minimization of the expected number of overlaps is equivalent to the deterministic robust coloring problem under particular choice of the penalties. Moreover, we extend the robust coloring problem to obtain equivalence with the stochastic programming problem with the schedule reliability objective under multivariate distribution of delays represented by an Archimedean copula. We show that small simulated instances of this problem can be solved to optimality by available software tools and we propose a tabu search algorithm suitable for larger instances.

English abstract

We propose several formulations of the fixed interval scheduling problem under uncertainty, where the risk is represented by random delays in processing times. We employ various stochastic programming and robust coloring problems to deal with the uncertainty. Our main goal is to introduce equivalent deterministic reformulations of the stochastic programming problems. We show that the minimization of the expected number of overlaps is equivalent to the deterministic robust coloring problem under particular choice of the penalties. Moreover, we extend the robust coloring problem to obtain equivalence with the stochastic programming problem with the schedule reliability objective under multivariate distribution of delays represented by an Archimedean copula. We show that small simulated instances of this problem can be solved to optimality by available software tools and we propose a tabu search algorithm suitable for larger instances.

Keywords in English

Fixed interval scheduling; Uncertainty; Stochastic programming; Robust coloring problem; Archimedean copula; Tabu search

Released

01.03.2016

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

Location

OXFORD

ISSN

0360-8352

Volume

93

Number

March

Pages from–to

45–54

Pages count

10

BIBTEX


@article{BUT171078,
  author="Jan {Novotný} and Martin {Branda} and Asmund {Olstad} and Pavel {Popela},
  title="Fixed interval scheduling under uncertainty – A tabu search algorithm for an extended robust coloring formulation",
  year="2016",
  volume="93",
  number="March",
  month="March",
  pages="45--54",
  publisher="PERGAMON-ELSEVIER SCIENCE LTD",
  address="OXFORD",
  issn="0360-8352"
}