GERT Networks and the Time-Oriented Evaluation of Projects (Lecture Notes in Economics and Mathematical Systems, 172)

Neumann, K.; Steinhardt, U.

ISBN 10: 3540097058 / ISBN 13: 9783540097051

Editore: Springer, 1979

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Dati bibliografici

• Titolo: GERT Networks and the Time-Oriented Evaluation of Projects (Lecture Notes in Economics and Mathematical Systems, 172)
• Editore: Springer
• Data di pubblicazione: 1979
• Lingua: Inglese
• ISBN 10: 3540097058
• ISBN 13: 9783540097051
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

Towards the end of the fifties methods for planning, scheduling,and control of proj­ ects were developed on the basis that the evolution of a project can be associated with a special weighted directed graph, called activity network. In this association, the individual activities of the project correspond to the arcs, the so-called proj­ ect events (beginning or termination of activities) correspond to the nodes, and the durations of the activities correspond to the weights of the respective arcs of the directed graph. 1) Contiguous arcs are assigned to activities which succeed one another immediately. The event corresponding to a node occurs exactly at the time at which all activities which are associated with the arcs leading into the node are terminated. After the occurrence of an event all those activities are be­ gun which correspond to the arcs emanating from the respective node. This implies especially that the evolution of the project has to be uniquely determined before­ hand, that every activity and every event are realized exactly once during the exe­ cution of the project, and that "feedback" (corresponding to cycles in the asso­ ciated network) is not permitted. Many projects, for example most R&D projects and projects in the area of production p 1 anni ng, do not sa ti sfy the foregoi ng res tri cti ons.

Contenuti

Summary of Assumptions.- 1 Basic Concepts.- 1.1 Directed Graphs and Activity Networks.- 1.2 GERT Networks.- 1.3 Assumptions Required for GERT Networks.- 1.4 Evaluation of GERT Networks.- 1.5 Subnetworks of GERT Networks.- 2 STEOR Networks.- 2.1 Stochastic Processes Connected with STEOR Networks.- 2.1.1 STEOR Networks and MARKOV Renewal Processes.- 2.1.2 GERT Networks with Only EOR Nodes.- 2.2 The MRP Method for the Evaluation of STEOR Networks.- 2.2.1 The Activation Functions and Activation Numbers.- 2.2.2 Special Cases and Examples.- 2.3 The Numerical Implementation of the MRP Method.- 2.4 The MASON Rule.- 2.5 Earliest and Latest Times in STEOR Networks.- 2.6 Applications.- 2.6.1 Time Planning for R&D Projects.- 2.6.2 Production Planning.- 2.6.3 Legislation and Administration of Justice.- 2.6.4 Evaluation of Linear Transmission Systems.- 2.6.5 Description and Analysis of Queueing Models.- 3 GERT Networks with Basic Element Structures.- 3.1 Nodes Which Belong Together.- 3.2 Basic Elements.- 3.3 Basic Element Structures.- 3.3.1 Definition and Properties of a Basic Element Structure.- 3.3.2 BES Networks.- 3.3.3 Examples.- 3.4 Evaluation of Admissible Basic Element Structures.- 3.5 Determination of Admissible Interior Basic Element Structures.- 3.5.1 Determination of Nodes Belonging Together (Labeling Process).- 3.5.2 Construction of a Possible Interior Basic Element Structure.- 3.5.3 Testing of a Possible Interior Basic Element Structure.- 3.5.4 The BES Method.- 3.6 Applications.- 3.6.1 Rendezvous of Two Space Vehicles.- 3.6.2 Production of a Television Program.- 3.6.3 Introduction of a New Industrial Product.- 3.6.4 Reliability Problems.- 4 Evaluation of General GERT Networks.- 4.1 Cycle Reduction.- 4.2 Evaluation of an Acyclic GERT Network N.- 4.2.1 Construction of the Sequence (N?) of Subnetworks of N.- 4.2.2 Determination of the Conditional Probabilities in (4.2.2).- 4.2.3 Test of the Assumptions A6 and A7.- 4.2.4 Example.- 4.3 Applications.- 4.3.1 Construction of a Turbine.- 4.3.2 Development of a Camera.- 4.4 Replacement of Non-genuine IOR Nodes.- 5 Multiple Activations of Non-STEOR Nodes.- 5.1 Generalized GERT Networks and Closed Subnetworks.- 5.2 Assumptions Required for Generalized GERT Networks.- 5.3 Evaluation of Generalized GERT Networks.- 5.3.1 A Method for Evaluating Admissible Generalized GERT Networks.- 5.3.2 Test of the Assumptions for a Generalized GERT Network.- 5.4 Applications.- 5.4.1 Introduction of a New Product.- 5.4.2 Overhaul of a Generator.- 6 GERT Networks with Time-dependent Arc Weights.- 6.1 Basic Concepts.- 6.2 STE0R Networks.- 6.3 GERT Networks with Basic Element Structures.- 6.4 General GERT Networks.- 7 Simulation.- 7.1 GERTS Networks and Equivalent GERT Networks.- 7.2 GERTS Networks Which Do Not Have Corresponding GERT Networks.- 7.3 Simulation of GERTS Networks.- 7.4 Generalized GERTS Networks.- 7.5 A Universal Method for Evaluating Admissible GERT Networks.- A.1 Some Formulas from Probability Theory.- A.2 Stochastic Processes.- A.3 Precise Formulation of Assumption A3.- References.