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

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

Abstract

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.

Keywords

Valid Inequality Precedence Relation Feasible Domain Independent Point Disjunctive Programming 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

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

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