Stochastic Project Networks

Project planning, scheduling, and control are regularly used in business and the service sector of an economy to accomplish outcomes with limited resources under critical time constraints. To aid in solving these problems, network-based planning methods have been developed that now exist in a wide variety of forms, cf. Elmaghraby (1977) and Moder et al. (1983). The so-called "classical" project networks, which are used in the network techniques CPM and PERT and which represent acyclic weighted directed graphs, are able to describe only projects whose evolution in time is uniquely specified in advance. Here every event of the project is realized exactly once during a single project execution and it is not possible to return to activities previously carried out (that is, no feedback is permitted). Many practical projects, however, do not meet those conditions. Consider, for example, a production process where some parts produced by a machine may be poorly manufactured. If an inspection shows that a part does not conform to certain specifications, it must be repaired or replaced by a new item. This means that we have to return to a preceding stage of the production process. In other words, there is feedback. Note that the result of the inspection is that a certain percentage of the parts tested do not conform. That is, there is a positive probability (strictly less than 1) that any part is defective.

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 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.