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Mathematical Methods of Operations Research

, Volume 53, Issue 3, pp 435–450 | Cite as

A steepest ascent approach to maximizing the net present value of projects

  • Christoph Schwindt
  • Jürgen Zimmermann

Abstract.

We study the scheduling of projects subject to general temporal constraints between activities such that the project net present value is maximized. The proposed algorithm is based on a first-order steepest ascent approach, where the steepest ascent directions are normalized by the supremum norm. In each iteration, the procedure ascends from a vertex of the feasible region to some non-adjacent vertex, which leads to a considerable speed-up compared to standard line-search. In an experimental performance analysis, we compare previous solution methods from literature to the algorithm presented in this paper. On the basis of two randomly generated test sets, the efficiency of the steepest ascent approach is demonstrated. Problem instances with up to 1000 activities can be solved in less than one second on a personal computer.

Key words: Project scheduling net present value temporal constraints steepest ascent algorithm 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Christoph Schwindt
    • 1
  • Jürgen Zimmermann
    • 1
  1. 1.Institute for Economic Theory and Operations Research, University of Karlsruhe, D-76128 Karlsruhe, Germany (e-mail: {schwindt,zimmermann}@wior.uni-karlsruhe.de)DE

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