The presence of imprecision in parameter specification of water resources management problems leads to the formulation of fuzzy programming models. This thesis presents the formulation of a two-reservoir system problem as a fuzzy L.P. model. The aim is to determine if larger monetary benefits, over and above the usual benefits, can be obtained from the system. The other aim is to determine if desired industrial and domestic water allocations, as well as outflows for selected periods can be achieved. The problem is formulated as a conventional L.P. model. Then selected water allocations and outflows are fuzzified resulting in a fuzzy L.P. model. The alternative fuzzy L.P. model is also presented. Monetary benefits larger than those from the conventional L.P. were obtained through the fuzzy L.P. model. The desired water allocations and outflows were also realised for selected periods. Sensitivity information was obtained for fuzzy and non-fuzzy constraints. The alternative fuzzy L.P. model did not give additional valuable information than that obtained from the initial fuzzy L.P. model. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

The human gut microbiome exists as a community of microorganisms in symbiosis with its host. Prebiotics are functional compounds that modulate this microbial community, promoting the growth and activity of bacteria that are beneficial to human health. Resistant starches (RS), a subclass of prebiotics, are compounds linked to a number of host-beneficial effects when included in human diets. Understanding how RS shapes gut flora composition and function is crucial to understanding these effects; however, these effects are clouded by the complexity of the microbiome’s interactions. Comprehensively characterizing microbiome shifts as the result of prebiotics is an intriguing bioanalytical problem. In the thesis project, I hypothesize that: RS changes microbiome biochemical pathway expression community-wide and at different taxonomic levels; that RS forms will affect microbiome bacterial taxonomic distribution; and that a linear programming optimization approach can parsimoniously distribute ambiguous peptide abundances amongst their constituent species, leading to different interpretations of functional and structural characteristics in microbiome metaproteomics data. To address these hypotheses, the thesis project utilizes a combined metaproteomics and bioinformatics approach. The Figeys lab-developed RapidAIM bioanalytical assay is deployed to generate label-free mass spectrometry metaproteomics data, testing for these effects experimentally. Further, Cerberus, a bioinformatics platform for microbiome metaproteomics analyses, was developed to integrate workflows from different software sources into a unified pipeline. Cerberus also implements a novel linear optimization approach addressing the shared-peptide problem. Through experimental data analyses using Cerberus, microbiomes encountering RS showed concerted taxonomic shifts, general and specific functional modulations linked to these taxonomic changes, and a significantly variable pathway expression profile for host-beneficial microbiome processes. The peptide-species linear optimization procedure demonstrates how naïve approaches to the shared-peptide problem greatly skew downstream taxonomic and functional analyses in metaproteomics experiments, marking an important consideration for microbiome studies seeking to resolve taxon-specific alterations.

Gene regulatory networks analyze the relationships between genes allowing us to un- derstand the gene regulatory interactions in systems biology. Gene expression data from the microarray experiments is used to obtain the gene regulatory networks. How- ever, the microarray data is discrete, noisy and non-linear which makes learning the networks a challenging problem and existing gene network inference methods do not give consistent results. Current state-of-the-art study uses the average-ranking-based consensus method to combine and average the ranked predictions from individual methods. However each individual method has an equal contribution to the consen- sus prediction. We have developed a linear programming-based consensus approach which uses learned weights from linear programming among individual methods such that the methods have di↵erent weights depending on their performance. Our result reveals that assigning di↵erent weights to individual methods rather than giving them equal weights improves the performance of the consensus. The linear programming- based consensus method is evaluated and it had the best performance on in silico and Saccharomyces cerevisiae networks, and the second best on the Escherichia coli network outperformed by Inferelator Pipeline method which gives inconsistent results across a wide range of microarray data sets.

The design of a chilled water plant involves selecting the size and type of chillers to be employed and determining the operating strategy. The types may include both gas engine and electric motor driven chillers. The issues that have to be considered in the selection problem are to incorporate external and internal factors into the decision making. External factors may include the utility rate schedules, the cooling load profile, and the outdoor temperature profile. Internal factors may include the chiller performance characteristics, initial and maintenance costs, and the chiller(s) operating strategy. A mathematical model representing the chilled water plant design problem is developed. The problem is approached as a mixed integer linear programming problem where non-linear chiller performance curves are transformed into linear constraints through the use of integer variables. The optimization task is to select the best cooling plant configuration and operating strategy to minimize life cycle cost. A solution procedure is developed which decomposes the optimization problem to reduce extensive computation time. Two case studies are provided to investigate the implementation of the mathematical model. / Master of Science

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The purpose of this study was to develop and demonstrate an analytical framework to filter technical and economic information regarding alternative agricultural enterprises in order to enable farmers to make more informed diversification and adjustment decisions. This is particularly important for areas that need to adjust the structure of income sources as a result of dramatic changes in market demand and/or agricultural policy. Tobacco producing regions are currently facing such a problem in the United States. These regions need to consider a wide range of alternatives to maintain or enhance income and standards of living. The problem involved both strategic economic decisions and operational economic decisions. The method used combined information in the ArcView Geographic Information Systems (GIS) with Linear Programming (LP). Part of Pittsylvania County, Virginia, served as a case study example. A GIS database including soils and climatic conditions of the study area was created. Soils belonging to land capability classes 1 to 4 were considered for agricultural purposes. Agronomic requirements for specific yield levels of the enterprises considered were tabulated. An ArcView GIS analysis was conducted based on soil map unit symbols. Soil depth, soil series, soil texture, slope, flood potential and average summer temperature were factors associated with yield. Natural drainage, pH, natural fertility, content of organic matter and annual rainfall were factors that served for enterprise budget adjustments. The output of ArcView GIS analysis is maps of physically viable enterprise boundaries or enterprise reference units and tables of attributes for each field. Marketing of agricultural products that have prices that fluctuate seasonally is feasible only within the period of time called the "market window". When average historical prices were above total costs, a market window was identified. The optimal enterprise mix was addressed by LP from a whole farm planning perspective based on the results of ArcView GIS analysis and other constraints, including crop rotations, and irrigation limits. Various levels of tobacco production, vegetable enterprise activity levels, and limits on irrigation were employed to generate, ten scenarios. Results include the optimal enterprise mix, net revenue (above variable costs), shadow prices and sensitivity analysis. It is shown that specialty crops are not likely to replace tobacco income, at least in the near term. Developing a diversified farm plan could help farmers to make a smooth transition to other alternatives. / Ph. D.

This dissertation deals with a primal-dual conjugate subgradient-based algorithm for solving large-scale and/or specially structured linear programming problems. The proposed algorithm coordinates a Lagrangian dual function and a primal penalty function which satisfies a flexible set of specified properties, in order to generate a sequence of primal and dual iterates which can be shown to converge to an optimal pair of primal and dual solutions. Besides producing both primal and dual solutions, this coordination of primal and dual functions serves to guide the crucial choice of step-sizes in the iterative algorithm, and also provides a natural stopping criterion based on the duality gap. The generic algorithm maintains a considerable degree of flexibility which permits one to exploit any special structures inherent in the problem. Moreover, the algorithm admits a rich variety of admissible penalty functions and dual formulations in designing a particular implementation scheme. Other algorithmic strategies that can be gainfully employed to improve the performance of the algorithm include space-dilation and box step techniques, pattern search strategies and suboptimization based on complementary slackness conditions. The algorithm is tested on three different transportation problems with additional constraints which are faced by the Freight Equipment Management Program of the Association of American Railroads. Problem 1 is a maximin problem in which ∫(x) = minimum {∫,(x), r=1, ... , R} is maximized subject to the transportation constraints and a total cost constraint, where ∫, (·) is a savings function for the r^th railroad, for r=1, ... , R. Problem 2 minimizes weighted absolute deviations of ∫, (x); r=1, ... , R from its mean value subject to the Problem 1 constraint set. Problem 3, on the other hand, minimizes total cost subject to the transportation constraints and the constraint which requires each ∫, (x), r=1, ... , R to be at least at some desired level. Both theoretical issues concerning convergence properties and rates, as well as algorithmic design and computational performance issues are investigated. The results indicate that the algorithm is a viable strategy for these problems. In particular, a new conjugate gradient strategy emerges as a byproduct of this algorithm, which is shown to dominate other available strategies on standard test problems from the literature. / Ph. D.

Approved for public release, distribution is unlimited / .08B in shipping and redistribution costs of Not Ready for Issue (NRFI) materiel. This thesis models the NAVICP shipping of unserviceable but repairable (retrograde) Navy materiel or Depot Level Repairables (DLRs). It develops an integer linear program to prescribe minimum cost shipment recommendations of DLRs from fleet to repair locations within the NAVICP and Defense Logistics Agency (DLA) distribution system subject to constraints on average shipping time (AveTime). NAVICP provided data on DLR shipments for one year from which we construct six representative DLRs, 3 of aviation and 3 of maritime cognizance. We find a cost and time savings can be achieved for all representative DLRs by avoiding the use of DLA as storage prior to induction for repair. In this study we compare shipping costs for each of the six DLRs when we constrain AveTime, from 2 to 8 days. We find 2-day constrained AveTime shipping, on average, costs 18 times that of 7-day AveTime shipping, twice that of 3-day shipping and a minimum of 5 times and a maximum of 11 times that of the costs of 4 through 6-day shipping. / Lieutenant Commander, United States Navy