GERT Networks and the Time-Oriented Evaluation of Projects

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.