Stochastic Project Networks

This book presents the state of the art of temporal analysis and cost minimization of projects, as well as project planning under limited resources where the projects are modelled by GERT networks. Basic concepts are summarized and the book is self-contained.

Contenu
1 Basic Concepts.- 1.1 Directed Graphs and Project Networks.- 1.2 GERT Networks.- 1.3 Assumptions and Structural Problems.- 1.4 Complete and GERT Subnetworks.- 2 Temporal Analysis of GERT Networks.- 2.1 Activation Functions and Activation Distributions.- 2.2 Evaluation of Admissible GERT Networks.- 2.3 Computation of Some Quantities Important to Time Planning.- 2.4 Evaluation Methods for Admissible GERT Networks.- 3 STEOR Networks and EOR Networks.- 3.1 Markov Chains and Markov Renewal Processes.- 3.2 STEOR Networks and Markov Renewal Processes.- 3.3 Basic Properties of Admissible EOR Networks.- 3.4 Coverings of Admissible EOR Networks.- 3.5 Properties and Computation of Activation Functions and Activation Numbers.- 3.6 The MRP Method.- 4 Reducible GERT Networks.- 4.1 STEORReducible Subnetworks.- 4.2 Cycle Reduction.- 4.3 Nodes Which Belong Together.- 4.4 Basic Element Structures.- 4.5 BES Networks.- 4.6 Evaluation Methods for BES Networks and General Admissible GERT Networks.- 5 Scheduling with GERT Precedence Constraints.- 5.1 Deterministic SingleMachine Scheduling.- 5.2 Stochastic SingleMachine Scheduling with GERT Precedence Constraints: Basic Concepts.- 5.3 Stochastic SingleMachine Scheduling with GERT Precedence Constraints: Optimality Criteria and Complexity.- 5.4 List Schedules and Sequences of Activity Executions.- 5.5 Minimum FlowTime Scheduling in FOR Networks.- 5.6 A FlowTime Scheduling Example.- 5.7 Minimizing the Maximum Expected Lateness in FOR Networks.- 5.8 Essential Histories and Scheduling Policies for MinSum Problems in General GERT Networks.- 5.9 Elements of Dynamic Programming.- 5.10 Determination of an Optimal Scheduling Policy for the General MinSum Problem.- 6 Cost Minimization for STEOR and FOR Networks.- 6.1 STEORNetworks with TimeDependent Arc Weights.- 6.2 Cost Minimization in STEOR Networks: Basic Concepts.- 6.3 A Dynamic Programming Approach.- 6.4 The ValueIteration and PolicyIteration Techniques.- 7 Cost and Time Minimization for Decision Project Networks.- 7.1 Decision Project Networks.- 7.2 Cost Minimization.- 7.3 Randomized Actions.- 7.4 Multiple Executions of Projects.- 7.5 Time Minimization.- References.