An algorithm for the general resource constrained scheduling problem by using of cutting planes

  • W. Krause
II Mathematical Programming II.2 Discrete Optimization
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)


We formulate the general resource constrained scheduling problem, including the fact that every job can be split at any time, as follows:

Every set Fj of jobs is called front, if these jobs can be processed simultaneously (from point of the precedence relations and the resource restrictions). xj describes the period, in which Fj is active in the schedule. Then the problem is a disjunctive-linear program in which the disjunctive constraints
mean, that the corresponding fronts FK1 ,..., FKr(k) cannot occur in the same schedule.

We intend to solve this program with a combined cutting plane and branch & bound technique. Two cut-constructions are used. The first is the intersection cut by Balas confined to a subspace. An additional cut-conception yields faces of the convex hull of the feasible solutions. A procedure is given, by which the dimension of these facecuts can be increased by one. To guarantee finiteness of the whole method, a branch & bound algorithm has to be incorporated. It is started, if by a determined number of cuts no optimal solution is found.


Valid Inequality Precedence Relation Feasible Domain Independent Point Disjunctive Programming 
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  1. [1]
    Balas, E.: Disjunctive programming, Annals of Discrete Math. 5 (1979) S. 3–52.zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Deweß, G., Krause, W.: Schnittebenenverfahren für ein verallgemeinertes Komplementaritätsproblem, 33. Intern. Wiss. Koll., R. Math. Optimierung, TH Ilmenau 1988.Google Scholar
  3. [3]
    Deweß, G.: Zur Weiterentwicklung des Frontenmodells der Optimierung ressourcenbeschränkter Netzplanabläufe, Wiss. Z. KMU Leipzig, Math.-Naturwiss. R. 37 (1988) 4.Google Scholar
  4. [4]
    Graham, R.L., Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G.: Optimization and approximation in deterministic sequencing and scheduling: a survay, Ann. of Discrete Math. 5 (1979).Google Scholar
  5. [5]
    Krause, W., Deweß, G.: Facets of the scheduling polytope, System Modelling and Optimization, Lect. Notes in Control and Inf. Sciences 143, Springer-Verlag (1990) S. 478–485.Google Scholar
  6. [6]
    Reinelt, G.: The linear ordering problem: algorithm and applications, Berlin 1985.Google Scholar
  7. [7]
    Sheraly, H.D., Shetty, C.M.: Optimization with disjunctive constraints, Springer-Verlag 1980.Google Scholar
  8. [8]
    Suchowitzki, S.I., Radtschik I.A.: Mathematische Methoden der Netzplantechnik, Moskau 1965.Google Scholar

Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • W. Krause
    • 1
  1. 1.Sektion MathematikUniversität LeipzigLeipzig

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