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.

Project management has become a key component for improving organizational performance and is applied in many business areas and industries. Resource-constrained stochastic project networks are quite common. Managing such projects to maximize resource utilization and reduce project duration simultaneously is difficult. Resource loading, assignment rules, and priorities significantly affect project performance, especially in shared-resource, multi-project environments. This thesis provides an approach for using discrete-event simulation to analyze the behavior and performance of project networks that use resource pools. A method to translate project networks into simulation models is developed. The translator is used to convert and evaluate a benchmark test set of resource constrained stochastic project networks. The effect of factors like project network complexity, resource availability and allocation strategies on project performance is analyzed using a completely randomized design with factorial arrangement of the aforementioned factors. The conversion process and results from the analysis are discussed.

Project management has become a key component for improving organizational performance and is applied in many business areas and industries. Resource-constrained stochastic project networks are quite common. Managing such projects to maximize resource utilization and reduce project duration simultaneously is difficult. Resource loading, assignment rules, and priorities significantly affect project performance, especially in shared-resource, multi-project environments. This thesis provides an approach for using discrete-event simulation to analyze the behavior and performance of project networks that use resource pools. A method to translate project networks into simulation models is developed. The translator is used to convert and evaluate a benchmark test set of resource constrained stochastic project networks. The effect of factors like project network complexity, resource availability and allocation strategies on project performance is analyzed using a completely randomized design with factorial arrangement of the aforementioned factors. The conversion process and results from the analysis are discussed.

Beginning with Jackson networks and ending with spatial queuing systems, this book describes several basic stochastic network processes, with the focus on network processes that have tractable expressions for the equilibrium probability distribution of the numbers of units at the stations. Intended for graduate students and researchers in engineering, science and mathematics interested in the basics of stochastic networks that have been developed over the last twenty years, the text assumes a graduate course in stochastic processes without measure theory, emphasising multi-dimensional Markov processes. Alongside self-contained material on point processes involving real analysis, the book also contains complete introductions to reversible Markov processes, Palm probabilities for stationary systems, Little laws for queuing systems and space-time Poisson processes.

This book deals with dynamic and stochastic methods for multi-project planning. Based on the idea of using queueing networks for the analysis of dynamic-stochastic multi-project environments this book addresses two problems: detailed scheduling of project activities, and integrated order acceptance and capacity planning. In an extensive simulation study, the book thoroughly investigates existing scheduling policies. To obtain optimal and near optimal scheduling policies new models and algorithms are proposed based on the theory of Markov decision processes and Approximate Dynamic programming. Then the book presents a new model for the effective computation of optimal policies based on a Markov decision process. Finally, the book provides insights into the structure of optimal policies.