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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Basic Concepts

Abstract
In chapter 1 we first summarize the most important concepts from the theory of graphs and project networks which are needed in what follows. For additional background we refer to Elmaghraby (1977), Lawler (1976), and Neumann (1987a, 1987b). After that, the concept of a GERT network is introduced and some basic assumptions and results are stated.
Klaus Neumann

Chapter 2. Temporal Analysis of GERT Networks

Abstract
In CPM and PERT network techniques, the temporal analysis includes the determination of the earliest and latest times of occurrence of the individual project events besides the computation of the (distribution of the) project duration. For GERT networks, it is also possible to introduce the concepts of earliest and latest times of activation of nodes. Their meaning, however, is different from that for CPM and PERT networks (because project events may occur several times) and their computation is in general much more complicated (cf. Delivorias (1979a, 1979b), Neumann and Steinhardt (1979a), section 2.5, and Wietek (1983)). Therefore, we will not deal with those concepts in this monograph.
Klaus Neumann

Chapter 3. STEOR Networks and EOR Networks

Abstract
STEOR networks are GERT networks with only STEOR nodes. STEOR networks represent that class of GERT networks whose evaluation is the easiest due to the fact that Markov renewal processes can be associated with those networks. In particular, STEOR networks satisfy the one-sink condition. Exploiting some results from the theory of Markov renewal processes, an efficient method for computing the activation functions Yij can be found.
Klaus Neumann

Chapter 4. Reducible GERT Networks

Abstract
We have seen in chapter 3 that STEOR networks can be evaluated in a relatively easy manner by means of the MRP method. Nodes with AND entrance or IOR entrance, however, cause some difficulties. Therefore, it suggests itself to investigate GERT networks all of whose AND nodes and IOR nodes lie inside special subnetworks which can be reduced to structures containing only STEOR nodes. Obviously, the reduction of those subnetworks to “STEOR subnetworks” should be done such that the “reduced” GERT network is equivalent to the original (“reducible”) GERT network.
Klaus Neumann

Chapter 5. Scheduling with GERT Precedence Constraints

Abstract
Scheduling can be loosely defined as the art of assigning resources to tasks in order to insure the termination of the tasks in a reasonable amount of time or to minimize a certain cost function. Since the terminology of scheduling theory arose in the processing and manufacturing industries, one generally speaks of “machines” instead of resources and of “jobs” instead of tasks that have to be “processed” by the machines.
Klaus Neumann

Chapter 6. Cost Minimization for STEOR and EOR Networks

Abstract
In this chapter we consider the case where different types of cost are incurred by the execution of activities and the occurrence of events of a project modelled by a STEOR network. We will see that the expected total cost of the project depends only on the activation functions Yj of the individual nodes j of the network. Since the activation function Yj of any node j in an admissible EOR network N coincides with the activation function of node j in each STEOR network from a covering of N that contains all nodes from S(j) and all arcs joining those nodes (cf. (3.5.10)), the cost minimization problem for admissible EOR networks of Markov degree d >1 can be solved in the same manner as for STEOR networks.
Klaus Neumann

Chapter 7. Cost and Time Minimization for Decision Project Networks

Abstract
In chapter 6 we have seen that the problem of minimizing the (expected) cost of a project described by a GERT network can be reduced to a stochastic dynamic programming problem. That approach, however, generally requires a great computational effort. In addition, it is only applicable if the GERT network represents an admissible EOR network (which includes the stipulation that the independence and Markov properties from assumptions A2b and A2d are satisfied).
Klaus Neumann

Backmatter

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