Stochastic Project Networks: Temporal Analysis, Scheduling and Cost Minimization

ISBN-13: 9783540526643 / Angielski / Miękka / 1990 / 237 str.

Klaus Neumann

Opis

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. These projects are characterized by a stochastic evolution structure and possible feedback. The temporal analysis exploits the fact that Markov renewal processes can be associated with so-called EOR networks (special GERT networks all of whose nodes have exclusive-or entrance). For single-machine min-sum and min-max scheduling problems with EOR precedence constraints, two polynomial algorithms are presented. General min-sum problems are solved by dynamic programming. The cost minimization of projects modeled by EOR networks leads to Markov renewal decision processes and can be reduced to a stochastic dynamic programming problem. Basic concepts from the theory of graphs and networks, Markov renewal processes, deterministic scheduling, and dynamic programming are summarized. This makes the book self-contained.

Spis treści

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 STEOR—Reducible 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 Single—Machine Scheduling.- 5.2 Stochastic Single—Machine Scheduling with GERT Precedence Constraints: Basic Concepts.- 5.3 Stochastic Single—Machine Scheduling with GERT Precedence Constraints: Optimality Criteria and Complexity.- 5.4 List Schedules and Sequences of Activity Executions.- 5.5 Minimum Flow—Time Scheduling in FOR Networks.- 5.6 A Flow—Time Scheduling Example.- 5.7 Minimizing the Maximum Expected Lateness in FOR Networks.- 5.8 Essential Histories and Scheduling Policies for Min—Sum Problems in General GERT Networks.- 5.9 Elements of Dynamic Programming.- 5.10 Determination of an Optimal Scheduling Policy for the General Min—Sum Problem.- 6 Cost Minimization for STEOR and FOR Networks.- 6.1 STEOR Networks with Time—Dependent Arc Weights.- 6.2 Cost Minimization in STEOR Networks: Basic Concepts.- 6.3 A Dynamic Programming Approach.- 6.4 The Value—Iteration and Policy—Iteration 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.