Active and stable project scheduling |
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Authors: | K Neumann H Nübel C Schwindt |
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Institution: | (1) Institut für Wirtschaftstheorie und Operations Research, University of Karlsruhe, Kaiserstr. 12, 76128 Karlsruhe, Germany, DE |
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Abstract: | The paper proposes a new classification of schedules for resource-constrained project scheduling problems with minimum and
maximum time lags between project activities and regular and different types of nonregular objective functions. The feasible
region of the scheduling problems represents a (generally disconnected) union of polytopes. In addition to the well-known
concepts of active and semiactive schedules, pseudoactive and quasiactive as well as stable, semistable, pseudostable, and
quasistable schedules are introduced. The (quasi-, pseudo-, semi-)active schedules are related to different types of left-shifts
of sets of activities and correspond to minimal points of certain subsets of the feasible region. The (quasi-, pseudo-, semi-)stable
schedules do not allow oppositely directed shifts and correspond to extreme points of certain subsets of the feasible region.
The different sets of schedules contain optimal schedules for project scheduling problems which differ in their objective
functions. The correspondence between those sets of schedules and vertices of specific polyhedral subsets of the feasible
region can be exploited for analyzing schedule generation schemes which have been developed recently for finding solutions
to the different classes of project scheduling problems. |
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Keywords: | : Resource-constrained project scheduling active and stable schedules regular and nonregular objective functions generation schemes |
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