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Mathematical Methods of Operations Research

, Volume 52, Issue 3, pp 489–499 | Cite as

Solving the discrete-continuous project scheduling problem via its discretization

  • Joanna Józefowska
  • Marek Mika
  • Rafał Różycki
  • Grzegorz Waligóra
  • Jan Weglarz

Abstract.

In this paper a discrete-continuous project scheduling problem is considered. In this problem activities simultaneously require discrete and continuous resources. The processing rate of each activity depends on the amount of the continuous resource allotted to this activity at a time. All the resources are renewable ones. The activities are nonpreemtable and the objective is to minimize the makespan. Discretization of this problem leading to a classical (i.e. discrete) project scheduling problem in the multi-mode version is presented. A simulated annealing (SA) approach to solving this problem is described and tested computationally in two versions: with and without finding an optimal continuous resource allocation for the final schedule. In the former case a nonlinear solver is used for solving a corresponding convex programming problem. The results are compared with the results obtained using SA for the discrete-continuous project scheduling problem where the nonlinear solver is used for exact solving the continuous part in each iteration. The results of a computational experiment are analyzed and some conclusions are included.

Key words: multi-mode project scheduling, simulated annealing, discrete resources, continuous resources 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Joanna Józefowska
    • 1
  • Marek Mika
    • 1
  • Rafał Różycki
    • 1
  • Grzegorz Waligóra
    • 1
  • Jan Weglarz
    • 1
  1. 1.Poznań University of Technology, Institute of Computing Science, Piotrowo 3A, 60-965 Poznań, Poland (e-mail: Jan.Weglarz@cs.put.poznan.pl)PL

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