Stability and efficiency (i.e. derivative function evaluations per processor) are the two main considerations in deriving good numerical methods for ODE's. The underlying challenge is to increase the stability region while maintaining or even improving efficiency. To achieve this, some extensions of predictor-corrector based methods, which apply a fixed number of corrector iterations, are considered. This thesis studies two particular members of a family of methods called the Parallel Block Predictor-Corrector Family, which are based on these extensions. These two members are called PBPC/2 and PBPC/3. They are characterized by iterated corrector evaluations carried out in two adjacent blocks. Stability properties of these methods are analyzed and compared with some existing block-based parallel predictor-corrector methods. Performance of the PBPC/2 and PBPC/3 methods and these existing block-based parallel predictor-corrector methods is compared using solution formulas which extend over a range of integration orders and which use various number of processors. The results obtained from a stability analysis and from a collection of numerical experiments indicate that the proposed methods provide a potential opportunity to balance stability properties and efficiency in the parallel computer systems.

This thesis evaluates the benefit of meshing mathematical programming and expert systems for solving capital budgeting problems, using constraint logic programming methods. A review of modelling capabilities of mathematical programs for capital budgeting, and of financial expert systems leads to defining the respective role and potential of each method, and to the proposal of a two-tiered project selection approach: project evaluation and resource allocation. With emphasis placed on a tight coupling of the two tiers, logic programming is shown to be a language of choice to implement mathematical programming within an expert system shell. Prolog has the requisite properties to deal with both logical considerations and optimization problems. Although Prolog was not primarily designed to solve optimization problems, it is shown that the backtracking mechanism of the Prolog language is powerful enough for that purpose; it liberates the programmer from having to implement tree-search programs. A generate and test program is written in Turbo-Prolog, and compared to a more sophisticated test and generate implementation that uses methods of constraint satisfaction programming. Continuous capital budgeting problems are solved in CLP(${\cal R}$), an experimental extension of Prolog that enables the solution of simultaneous algebraic constraints, as required to solve linear programs.

The efficiency with which the numerical solution of ordinary differential equations (ODE) can be generated depends to a large extent on the effectiveness of the stepsize adjustment strategy that is used. In this thesis the relative performance of a family of stepsize adjustment strategies is examined. Included in this family is a new strategy. A distinctive feature of its formulation is the incorporation of a mechanism to correct for any persistent deviation of a prescribed solution quality measure from its desired value. The evaluation of the various strategies is undertaken through an extensive set of numerical experiments which use both single processor and multiple processor ODE solution procedures.

The objective of this thesis was to develop the required tools to solve a relatively comprehensive telecommunications network design optimisation problem. It can be summarised as a Minimum Cost-Flow Capacitated Network Design Problem with multiple facilities, multiple commodities and constrained by performance and survivability requirements. The resulting optimisation model is supported by one mixed-integer/linear mathematical programming formulation and implemented in a 32-bit GUI-based network design tool for automation purposes. Throughout its developmert, the model was tested and validated with randomly generated design problems. The base case application, from which the design requirements were derived, is the National Defence Headquarters (NDHQ) Metropolitan Area Network (MAN). The area of interest on the NDHQ MAN is the inter-building router backbone, where expensive leased facilities are installed to inter-connect buildings routers. As a result of this thesis, an interactive tool was developed, which provides network design and analysis capabilities. Its impact on the NDHQ MAN was lowered because of the limitations in the data available and significant changes to the network environment, but the results obtained proved very insightful in validating the performance and accuracy of the model.

The DP-constraints are a recently defined class of valid inequalities for the Symmetric Traveling Salesman Polytope (STSP) which includes the family of comb constraints. Moreover, there exists a polynomial-time exact separation algorithm for the DP-constraints for points whose support graph is planar. However, while the comb constraints are known to be facet-inducing, the same is not true in general of the DP-constraints. This thesis addresses the question of which DP-constraints are facet-inducing; some sufficient conditions are given for identifying DP-constraints which are not facet-inducing, and a family of facet-inducing DP-constraints, the twisted comb constraints, is described and shown to be distinct from other known families of facet-inducing inequalities. We also present a new formulation of the DP-constraints in terms of tripartitions of the node set, which allows easier recognition of equivalent DP-constraints.

Robustness analysis, a technique proposed by Jacobson, can be used in a use-case-driven process to help close this gap between requirements and design by examining in depth the requirements found in the narrative text of each use case and structuring it into a robustness diagram. In this thesis, we present a step by step procedure for performing robustness analysis. In particular, we describe how to construct and use robustness diagrams to discover analysis and design errors early in the process, and to verify the correctness of the use case text. Moreover, we propose a new metric, robustness analysis points , to estimate project size and effort and we compare our results to function points and use case points in three case studies. Finally, we assess and evaluate the RA technique and conclude by giving recommendations for future work.

The proton exchange membrane fuel cell (PEMFC) is the focus of modeling and simulation efforts in order to better understand this technology and improve its design and operation. Simulated polarization curves for PEMFCs duplicate the observed performance of PEMFCs with varying degrees of success. In order for modelling and simulation to be more widely used in this field and elsewhere, effective tools must be made available for non-programmers to apply their knowledge to simulation problems. GestCell (A modelling and simulation environment based on Gest) is a new modelling and simulation environment designed with non-programmers in mind, in particular scientists studying PEMFCs. A friendly graphical interface allows users who are knowledgeable in a non-programming field to enter information about a system into GestCell, which automatically constructs a Gest specification. The Gest specification is highly readable for the user, and the system is able to generate a C++ program with the specification in order to allow the user to carry out simulation with the model, with very little knowledge in the area of simulation. GestCell is very general in nature and could be used in a wide variety of fields. It has a great deal of potential to be a powerful modelling and simulation environment.

Polytopes $Q\sbsp{2E}{n}$ and $Q\sbsp{2N}{n}$, which are associated with the minimum cost 2-edge-connected subgraph problem and the minimum cost 2-node-connected subgraph problem, respectively, are studied in this thesis, and some new classes of facet-inducing inequalities are introduced for these polytopes. These classes of inequalities are related to the so-called clique tree inequalities for the travelling salesman polytope ($Q\sbsp{T}{n}$), and the relationships between $Q\sbsp{T}{n}$ and $Q\sbsp{2E}{n}, Q\sbsp{2N}{n}$ are exploited in obtaining these new classes of facets. Due to the use of problem specific facet-inducing inequalities instead of dominant cutting-planes, the linear programming cutting-plane method has proven to be quite successful for solving some NP-hard combinatorial optimization problems. We believe that our new classes of facet-inducing inequalities can be used to further improve the cutting-plane procedure for designing minimum cost survivable communication networks.

This study presents a reliability and availability analysis of human-machine systems with human errors and common-cause failures. The systems incorporate elements of several commonly used redundant configurations: standby, k-out-of-n, majority voting with imperfect voter, and parallel. The analysis considers systems with constant human error rates, increasing human error rates and general human error rates, and with arbitrarily distributed failed system repair times. The method of linear ordinary differential equations for general system failure rates is presented to obtain the general expressions of the steady state availability for various types of system repair time distributions, such as Gamma, Weibull, lognormal, exponential and Rayleigh distributions. A method which combines the inclusion supplementary variables technique and the method of stages is developed to perform time-dependent system availability analysis for systems with both time-dependent human error rates and failed system repair rates. Generalized expressions for such relevant system performance indices as the system reliability, steady state availability, time-dependent system availability, mean time to failure and system variance of time to failure are presented. The impact of human error, common-cause failure, failed system repair policy and the elements of redundant configurations on the values of the afore-said system performance indices is demonstrated by means of plots.

The thesis focuses on methods of mathematical optimization for logistic planning with applications to the location of facilities and inventory of products. Algebraic models of location on networks are presented in increasing order of complexity and realism emphasizing the presence of elemental models as building blocks of larger logistic systems. The thesis examines two small, well-known logistic problem formulations. For both applications, optimization programs are presented for which a classical solution approach is to find approximate optima because the representation encapsulates either combinatorial or functional complexities. Mathematical expressions of these approximations enable the calculation of their variations with the model parameters. Thus, constraint specifications of mathematical programs ease both the analysis of fast approximation and the analysis of variation of the optimal value as a function of each parameter of the model. Starting with the uncapacitated facility location model, a simple heuristic for the location of facilities is compared with previous heuristics and exact algorithms and shown to yield an acceptable level of accuracy with respect to previous measures of quality. In a study of capacity planning patterned after a traditional model of inventory control, a (Q,r) inventory system is analysed. The underlying mathematical model serves as a base for sensitivity analysis. As in the previous chapter, an approximation yields sufficient insight to predict the variation of optimal policies under varying conditions.