Tropical optimization problems in time-constrained project scheduling

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7 Scopus citations


We consider a project that consists of activities to be performed in parallel under various temporal constraints, which include start-start, start-finish and finish-start precedence relationships, release times, deadlines and due dates. Scheduling problems are formulated to find optimal schedules for the project with respect to different objective functions to be minimized, such as the project makespan, the maximum deviation from the due dates, the maximum flow-time and the maximum deviation of finish times. We represent these problems as optimization problems in terms of tropical mathematics, and then solve them by applying direct solution methods of tropical optimization. As a result, new direct solutions of the scheduling problems are obtained in a compact vector form, which is ready for further analysis and practical implementation. The solutions are illustrated by simple numerical examples.
Original languageEnglish
Pages (from-to)205-224
Issue number2
Early online date8 Dec 2016
StatePublished - 2017

Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Algebra and Number Theory


  • idempotent semifield
  • optimization problem
  • project scheduling
  • precedence relationship
  • scheduling objective

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