ANSWERS, an event-oriented, distributed parameter nonpoint source pollution model for simulating runoff and sediment transport was modified to develop a continuous nonpoint source model to simulate runoff, erosion, transport of dissolved and sediment-bound nutrients, and nutrient transformations. The model was developed for use by nonpoint source pollution managers to study the long-tenn effectiveness of best management practices (BMPs) in reducing runoff, sediment, and nutrient losses from agricultural watersheds. The Holtan's infiltration equation used in the original version of ANSWERS was replaced by the physically-based Green-Ampt infiltration equation. Soil evaporation and plant transpiration were modeled separately using the Ritchie equation. If soil moisture exceeds field capacity, the model computes percolation based on the degree of soil saturation. Nutrient losses include nitrate, sediment-bound and dissolved ammonium; sediment-bound TKN, and sediment-bound and dissolved phosphorus. A linear equilibrium is assumed between dissolved and sediment-bound phases of ammonium and phosphorus. Nutrient loss is assumed to occur only from the upper cm of the soil profile. The model simulates transformations and interactions between four nitrogen pools including stable organic N, active organic N, nitrate and ammonium. Transformations of nitrogen include mineralization simulated as a combination of ammonification and nitrification, denitrification, and plant uptake of ammonium and nitrate. The model maintains a dynamic equilibrium between stable and active organic N pools. / Ph. D.

Scheduling workers in a restaurant is a difficult and time consuming task that involves matching the needs of the restaurant with respect to filling various shifts for different positions, the varying availabilities of the workers, along with their seniority levels and qualifications, among other factors. The restaurant manager/scheduler must adhere to these individual workers' restrictions, while at the same time satisfy the restaurant's needs. Another issue that a manager tries to accommodate is to equitably assign shifts to workers, attempting to balance their expressed wishes with their relative merits and qualifications; although in practice, this goal is rarely achieved. In this thesis, a mathematical model is developed to solve the scheduling problem, with attention focused on maximizing worker satisfaction levels, considering their seniority levels and their qualifications, while meeting with the restaurant's needs of filling various required shifts for various positions with capable workers. We show that this model possesses a hidden network structure that can be revealed via some simple variable substitutions. Consequently, an efficient network-flow approach can be used to solve the model and derive an optimal (integer) solution. We illustrate the model and the proposed algorithmic approach by generating a schedule using real data obtained via specially designed surveys from the Cheddar's restaurant in Newport News, Virginia. Further results on a variety of test problems are used to evaluate the performance of the algorithm, and suitable pre- and post-processor considerations are addressed to permit the use of this technology in a productive environment. / Master of Science

The methodology and the appropriateness of adapting the linear programming model to the evaluation of timber harvest alternatives of a specific forest enterprise was examined. The use of linear programming to describe a program in which profit is maximum rather than one of several other economic allocation models was justified. The basic model, using 3 percent as the alternative rate, described the alternative thinning and harvesting opportunities for the Seward Forest at Triplett, Virginia. The optimum program had to satisfy the restrictions imposed by scarce resources and by personal management constraints. The solution of the model described a course of action for the forest manager for the next 50 years. The initiation of the optimum plan would result in maximizing total present worth to the fixed resources of the Forest. Changes were made in the constraints on the model to demonstrate their effect upon the combination of activities which comprise the optimum program and the effect of these constraints on present worth. Additional solutions at 6 percent and 10 percent alternative rates were made to demonstrate the change which occurs in the activities that describe the optimum program at successively higher alternative rates. / Master of Science

This thesis presents an approach for solving the problem of determining a near optimal number of machines in order to minimize total cost in a Cellular Manufacturing System. In addition, all aspects and design of a Cellular Manufacturing System are discussed along with other related topics such as Group Technology and Plant Layout as applied to Cellular Manufacturing. / Master of Science

Recognizing the complexity of coal mining management, e.g., the scarcity of financial resources and the high level of uncertainty, a mixed binary programming model has been developed as an aid for generating production schedules which maximize the associated net present value. Defining the mine layout as a precedence network, with the nodes representing mining blocks, a solution procedure is developed, based on Benders' partitioning scheme. That is, the procedure iterates between two problems, namely, the master (primal) problem, solved by a combination of heuristic and exact methods, and the subproblem (dual problem), solved partly by inspection and partly as a minimal cost network flow problem. The heuristic methods are based on improvements of existing algorithms for scheduling precedence-related jobs on m processors. Computational experiences are presented and the procedure is demonstrated on a mining case. / Ph. D.

Thesis (MSc)--University of Stellenbosch, 2002. / See article for abstract

This dissertation studies the pricing of Outside barrier call options, when their activation starts at a hitting time. The pricing of Outside barrier options when their activation starts at time zero, and the pricing of standard barrier options when their activation starts at a hitting time of a pre speci ed barrier level, have been studied previously (see [21], [24]). The new work that this dissertation will do is to price Outside barrier call options, where they will be activated when the triggering asset crosses or hits a pre speci ed barrier level, and also the pricing of Outside barrier call options where they will be activated when the triggering asset crosses or hits a sequence of two pre specifed barrier levels. Closed form solutions are derived using Girsanov's theorem and the re ection principle. Existing results are derived from the new results, and properties of the new results are illustrated numerically and discussed. / Mathematical Sciences / M. Sc. (Applied Mathematics)

Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: We consider the problem of portfolio's asset allocation characterised by risk and return. Prior to the 2007-2008 financial crisis, this important problem was tackled using mainly the Markowitz mean-variance framework. However, throughout the past decade of challenging markets, particularly for equities, this framework has exhibited multiple drawbacks. Today many investors approach this problem with a 'safety first' rule that puts risk management at the heart of decision-making. Risk-based strategies have gained a lot of popularity since the recent financial crisis. One of the 'trendiest' of the modern risk-based strategies is the Risk Parity model, which puts diversification in terms of risk, but not in terms of dollar values, at the core of portfolio risk management. Inspired by the works of Maillard et al. (2010), Bruder and Roncalli (2012), and Roncalli and Weisang (2012), we examine the reliability and relationship between the traditional mean-variance framework and risk parity. We emphasise, through multiple examples, the non-diversification of the traditional mean-variance framework. The central focus of this thesis is on examining the main Risk-Parity strategies, i.e. the Inverse Volatility, Equal Risk Contribution and the Risk Budgeting strategies. Lastly, we turn our attention to the problem of maximizing the absolute expected value of the logarithmic portfolio wealth (sometimes called the drift term) introduced by Oderda (2013). The drift term of the portfolio is given by the sum of the expected price logarithmic growth rate, the expected cash flow, and half of its variance. The solution to this problem is a linear combination of three famous risk-based strategies and the high cash flow return portfolio. / AFRIKAANSE OPSOMMING: Ons kyk na die probleem van batetoewysing in portefeuljes wat gekenmerk word deur risiko en wins. Voor die 2007-2008 finansiele krisis, was hierdie belangrike probleem deur die Markowitz gemiddelde-variansie raamwerk aangepak. Gedurende die afgelope dekade van uitdagende markte, veral vir aandele, het hierdie raamwerk verskeie nadele getoon. Vandag, benader baie beleggers hierdie probleem met 'n 'veiligheid eerste' reël wat risikobestuur in die hart van besluitneming plaas. Risiko-gebaseerde strategieë het baie gewild geword sedert die onlangse finansiële krisis. Een van die gewildste van die moderne risiko-gebaseerde strategieë is die Risiko- Gelykheid model wat diversifikasie in die hart van portefeulje risiko bestuur plaas. Geïnspireer deur die werke van Maillard et al. (2010), Bruder and Roncalli (2012), en Roncalli and Weisang (2012), ondersoek ons die betroubaarheid en verhouding tussen die tradisionele gemiddelde-variansie raamwerk en Risiko- Gelykheid. Ons beklemtoon, deur middel van verskeie voorbeelde, die niediversifikasie van die tradisionele gemiddelde-variansie raamwerk. Die sentrale fokus van hierdie tesis is op die behandeling van Risiko-Gelykheid strategieë, naamlik, die Omgekeerde Volatiliteit, Gelyke Risiko-Bydrae en Risiko Begroting strategieë. Ten slotte, fokus ons aandag op die probleem van maksimering van absolute verwagte waarde van die logaritmiese portefeulje welvaart (soms genoem die drif term) bekendgestel deur Oderda (2013). Die drif term van die portefeulje word gegee deur die som van die verwagte prys logaritmiese groeikoers, die verwagte kontantvloei, en die helfte van die variansie. Die oplossing vir hierdie probleem is 'n lineêre kombinasie van drie bekende risiko-gebaseerde strategieë en die hoë kontantvloei wins portefeulje.

Life-history traits in fish populations are highly correlated. A subset of these correlations are called allometric scaling, they refer to biological processes which can be described using body size as independent variable. Particularly, allometric scaling related with food consumption (Q) and biomass production (P) has gained the attention of ecologists for several decades. This thesis proposes a quantitative framework for food consumption, which allows both the identification of the mechanisms underlying the allometric scaling for Q and the development of a predictive model for consumption to biomass ratio (Q/B) in fish populations. This thesis is based on the fact that food consumption can be inferred from first principles underlying the von Bertalanffy growth model. In addition, it has been noticed in the literature that biomass production and food consumption show similar allometric scaling dependence, therefore, both can be derived from these first principles. Thus, a similar quantitative framework was used to produce models for P/B in fish populations. Once functional forms for production and food consumption were identified, a third model was developed for the ratio between production and consumption (P/Q). This ratio is usually named ecological efficiency because it determines how efficiently a population can transform ingested food into biomass. Several authors have noticed that P/Q remains invariant (independent of body size) across species. From a theoretical point of view, the results presented here allow the first quantitative explanation for the existence of the allometric scaling for Q/B and the invariance of P/Q across fish species. These results, together with the explanation for allometry in P/B reported in the literature, suggest that the regular across-species pattern for the trio {P/B,Q/B,P/Q} can be explained by basic principles that underpin life-history in fish populations. This quantitative framework for the trio {P/B,Q/B,P/Q} is based on an explicit dependence with body size, which simplifies the estimation of these quantities. Model complexity depends, in part, on which data are available. Models were applied to real data from commercially important species fished in Chile. Statistical properties of the new models were evaluated by an intensive resampling approach. The simplest possible model for the trio {P/B,Q/B,P/Q} rests on the assumption of a stable age distribution. These quantities have a key importance in ecosystem modelling because they determine population energetics in terms of food intake by predation and the transformation of this energy into population biomass of predators. Application of the new models produces results which were comparable to those given by standard methods. This thesis is a result of multidisciplinary research which attempts to make a contribution to the understanding of the mechanisms underlying the allometric scaling of food consumption and production in fish populations. It proposes models for the trio {P/B,Q/B,P/Q} and thus, has the potential to be widely applicable in fisheries science.

Agricultural economists have devoted considerable attention to the financial stress situation of agricultural producers. Many studies have been conducted in various regions of the U.S. in an attempt to better understand the causes of the problem. The costs associated with farm financial stress imply corresponding benefits to be realized by its reduction. Benefits of studying and resolving farm financial stress reach beyond the farms and ranches to many related sectors such as rural communities, agribusinesses, and lending institutions. The specific hypothesis tested in this thesis is as follows: some but not all farms and ranches which have undergone serious financial stress in the early part of the 1980's in Oregon can be assisted in withstanding fluctuations in economic conditions by adopting specific strategies which promote financial stability and profitability. One of the specific objectives of this thesis was to evaluate the level of financial stress for two different agricultural production units in Oregon under differing leverage positions, and macroeconomic conditions. The production units selected for study were a cattle ranch and a wheat farm, based on their relative importance to Oregon. This first objective was satisfied through analysis of a baseline scenario, which was essentially a continuation of current conditions. Debt levels and growth rates were then altered to reflect the desired study conditions. Changing and considering three leverage ratios (20%, 40%, and 70%) and three sets of macroeconomic conditions (baseline, pessimistic, and optimistic) allowed studying of nine alternative situations to the base firm type or a total of 18 alternatives. Analysis of these different alternative production units was accomplished through a deterministic computer-based simulation model. The model simulates the financial structure and performance of a farm business over a transition period of four years with emphasis placed on the financial transactions of the firm. These transactions include purchases and sales of farm assets, financing terms, debt management, cash flows, tax obligations, consumption levels, and growth rates. The computer-based model made necessary calculations of cash flows and changes in financial statements to derive the ratios used for financial analysis over the planning horizon of four years beyond the present input case and is deterministic in the sense that all essential variables are entered by the researcher. Output from this model includes a set of coordinated financial statements for the firm over the planning horizon: a balance sheet, an income statement, statements for changes in net worth, flow of funds statement, and a fund availability report. The model also calculates profitability, liquidity, and solvency ratios used in financial ratio analysis which are provided on a summary sheet. These statements and reports are provided on an annual basis; thus, financial information is provided on yearly changes in financial position over the four year horizon. Another objective of this thesis was to evaluate various policy and management strategies designed to reduce financial stress. This objective was achieved by analysis of various scenarios designed to reduce stress simultaneously with the baseline case, which served for comparison. The specific scenarios considered were: 35% reduction of debt, 35% reduction of interest rates, two year deferral of debt, sales of 35% of total assets with no lease back, sales of 35% of total assets with lease back arrangements, and an infusion of equity capital equal to 35% of total debt. Results from this analysis were intended to show what, if any, courses of action could be pursued by agricultural firm managers and policy makers to reduce farm financial stress. The best test of the ability of these scenarios to reduce financial stress occurred in application to the high leverage wheat farm situations, as these were the cases with the most financial stress. Appropriate programs could be adopted to strengthen the financial position of the farm; in the case of low liquidity, asset sales-lease back; in cases of low solvency, equity infusions; and in circumstances where profitability needs to be enhanced, interest reductions would be the best choice. The results also seemed to suggested that public programs can maintain current levels of financial performance for producers under financial stress but do little to improve those positions. / Graduation date: 1988