The application of decomposition and condensation algorithms to the logical design of resource planning and management (RPM) networks Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/2801pk75s

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  • Resource Planning and Management (RPM) network is a graphical representation of input-output relationships among activities and resources within a system. Both resources (events) and activities (decisions) are explicitly represented as nodes in all RPM networks. Depending upon the relationships being depicted, RPM networks can be classified into Relational (R), Precedence (P) and Mathematical (M) models. This thesis focuses on M-network models. The purpose of this study was threefold: (1) to investigate properties and concepts of RPM M-network models, (2) to provide a decomposition algorithm for studying large and complex R- and Mnetwork models, and (3) to present an approach for M-network condensation. The rationale for the development of RPM network methodology is explained in Chapter I. Presently available management network models have been surveyed in Chapter II. These models include traditional project management networks, decision process networks, and simulation networks. Chapter III deals with the logical structure of RPM networks. Definitions, symbols, conventions, postulates and construction procedures of RPM networks have been investigated and established. RPM normative models (M-models) are presented in Chapter IV. A System Equation has been formulated to represent RPM M-network models. Applying the Kuhn-Tucker conditions of mathematical programming to this System Equation, necessary conditions for feasibility and optimality can be derived. Both linear and non-linear mathematical programming problems are used for illustration. McCormick, Schweitzer and White's Bond Energy Algorithm (BEA) is employed to decompose complex RPM networks in Chapter V. The concept of "sector" and a procedure to facilitate decomposition process have been introduced. Three decomposition examples are presented. The first two examples illustrate the decomposition of general RPM models using actual data from the Oregon State University Sea Grant Program. The third example demonstrates the decomposition of an RPM-LP model using Dantzig and Wolfe's decomposition algorithm. FORTRAN IV programs are presented in three appendices: Appendix I contains a flowchart for the BEA program, Appendix J contains descriptions of program options, Appendix K contains program listings as well as sample computer input and output. Chapter VI investigates the relation between Signal Flowgraph (SFG) theory and RPM network condensation. Condensation procedures similar to SFG reduction rules have been proposed. System behavior studies are also presented in this chapter. In addition, several theorems and observations have been established and recorded. Chapter VII summarizes the study, draws conclusions, and points out some possibilities for future research. The recommended activities include: (1) simulation modeling and studies through RPM network models, (2) studies of discrete mathematical programming problems using RPM network models, (3) development of management information systems utilizing RPM networks, and (4) further system behavior and sensitivity studies of RPM M-models. A simulation oriented S-network modelling may provide a heuristic tool to complete this Resource Planning and Management System (RPMS) and to solve problems for which there is currently no viable analytic solution procedure.
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