Netzplantechnik bei knappen Kapazitäten — Lösungsverfahren der begrenzten Enumeration mit Hilfe disjunktiver Graphen und bewerteter Stufen-Netze

Conference paper
Part of the Proceedings in Operations Research book series (ORP, volume 1973)


Referring to Balas the problem of minimizing project duration under multiple resource constraints can be formulated by means of a disjunctive graph. In the following paper this graph is used to develop a new branch-and-bound algorithm, in which a sequence of feasible plans with decreasing project duration is generated by introducing supplementary arcs between unconnected nodes. Davis/Heidorn solved the same problem by finding the shortest path in a rank-ordered network with nodes representing subsets of unit-duration tasks. This procedure seems to be less efficient when applied to large projects. On the other hand rank networks can be employed to deal with the more general problem of minimizing project costs as a function of project duration and resource utilization.


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  1. 1).
    Balas, E., Project Scheduling with Resource Constraints, in: Beale, E.M.L. (Hrsg.), Applications of Mathematical Programming Techniques, London 1970, S. 187–200.Google Scholar
  2. 2).
    Davis, E.W./Heidorn, G.E., An Algorithm for Optimal Project Scheduling under Multiple Resource Constraints, in: Management Science, 17 (1971), S. B 803-B 816.CrossRefGoogle Scholar
  3. 3).
    Burgess, A.R./Killebrew, J.B., Variation in Activity level on a Cyclical Arrow agram. in: The Journal of Industrial Engineering, 13(1962), S. 76 ff.Google Scholar

Copyright information

© Physica-Verlag, Rudolf Liebing KG, Würzburg 1974

Authors and Affiliations

  1. 1.HamburgDeutschland

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