This study provides an environmental and economic analysis of the ability to reduce potential nitrogen loadings to water bodies through the implementation of nutrient management plans on livestock farms. Study results indicate that nutrient management plans do result in significant reductions while maintaining or increasing farm income. Nutrient management plans on the four case farms reduced mean nitrogen losses by 23 to 45 percent per acre while increasing net farm income from $395 to $7,249. While reducing excess nitrogen applications with the implementation of nutrient management plans achieved significant reductions in potential nitrogen losses, further reductions may be achieved through farm level planning. After achieving initial reductions through the elimination of excessive nutrient applications, variation in application rates of organic and inorganic fertilizers across soils may become important in achieving further reductions in nitrogen loss. Study results suggest that it may be beneficial to apply higher rates of manure on soils and slopes less susceptible to nitrogen losses in order to reduce applications elsewhere. Increased nutrient losses on such fields may be more than offset by reductions on soils more susceptible to nutrient losses. Linear programming results for the Shenandoah Valley Dairy show that nitrogen losses could be reduced up to 44 percent below pre-plan losses with no impact on farm net economic returns. However, if nitrogen loss restrictions were instituted beyond this level, the impact on farm income increases significantly. After-plan nitrogen losses can reduced up to 52 percent, but farm returns decrease by 56 percent. / Master of Science

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No description available.

No description available.

No description available.

Closed-loop supply chains (CLSC) though present for decades, have seen significant research in optimization only in the last five years. Traditional sustainable CLSCs have generally implemented a Carbon Cap Trading (CCT), Carbon Cap (CC), or Carbon Taxes methodology to set carbon emissions limits but fail to minimize these emissions explicitly. Moreover, the traditional CCT model discourages investment in greener technologies by favoring established logistics over eco-friendly alternatives. This research tackles the sustainable CLSC problem by proposing a mixed-integer linear programming (MILP) carbon-conscious textit{p}-hub location model having the objective of minimizing emissions subject to profit constraints. The model is then extended to incorporate multi-periodicity, transportation modes, and end-of-life periods with a bi-objective cost and emissions function. Additionally, the model accounts for long-term planning and optimization, considering changes in demand and returns over time by incorporating a time dimension. The model's robustness and solving capabilities were tested for the case of electric vehicle (EV) battery supply chains. Demand for EVs is projected to increase by 18% annually, and robust supply chain designs are crucial to meet this demand, making this sector an important test case for the model to solve. Two baseline cases with minimum cost and minimum emissions objectives were tested, revealing a significant gap in emissions and underlining the need for an emissions objective. A sensitivity analysis was conducted on key parameters focusing on minimizing emissions; the analysis revealed that demand, return rates, and recycling costs greatly impact CLSC dynamics. The results showcase the model's capability of tackling real-world case scenarios, thus facilitating comprehensive decision-making goals in carbon-conscious CSLC design. / Master of Science / Closed-loop supply chain (CLSC) is a supply chain that recycles used products back to the manufacturer. CLSCs have been around for decades, but significant progress in optimizing them has only emerged over the last five years. Sustainable CLSC models often include limits on carbon emissions but usually don't directly minimize them. Traditional CLSC models tend to prioritize established logistics over greener technologies, discouraging investment in eco-friendly options. This study addresses this problem by introducing a mathematical model designed to minimize emissions while considering profit constraints. The model is expanded to factor in different time periods, transportation methods, and end-of-use phases with two goals in mind: cost and emissions. Additionally, it incorporates long-term planning, accounting for shifts in customer demand and product returns. The model's effectiveness was tested with electric vehicle (EV) battery supply chains, which serve as an important example given the predicted annual 18% growth in EV demand and the crucial need for efficient supply chain design. Two baseline scenarios were examined: one aiming to minimize costs and the other to minimize emissions. The results showed a notable disparity in emissions between the two, underscoring the importance of an emissions-focused objective. Key parameters, such as demand, return rates, and recycling costs, demonstrated a significant impact on CLSC operations. The findings highlight the model's ability to handle real-world challenges, enabling informed decision-making for designing carbon-conscious CLSCs.

Firm growth and best management practice (BMP) adoption of a representative, diversified, southeastern Virginia, farrow to finishing hog farm is examined in a multi-period linear programming framework. Specific attention is focused on the acquisition of additional productive resources and the impact of BMP adoption on the optimal combinations of crop and livestock activities over a five year planning horizon. The maximization of after-tax net income was employed as the objective function of the model. Increases in terminal net worth were transferred to the objective function at the end of the planning period. Two sets of model solutions were obtained; one set with cost-share subsidies and the other without. Results indicate that farm growth potential exists with or without cost-share subsidies and that the current high costs of external capital tend farmers toward use of internal financing. The availability of labor during peak periods ultimately constrained the growth process. The specific direction of the modeled farm's growth led to the investment in a totally confined slatted-floor house means of hog production. The model demonstrated a decic;!ed preference for the use of investment tax credits over the direct expense deduction provision of the federal income tax code. In general, sod filter strips, grassed waterways and no-till cropping proved to be the most cost-effective BMPs in achieving nonpoint source pollution objectives. / M.S.

This research is primarily concerned with the development of a new algorithm for the general Bilinear Programming Problem (BlP). BLP's are a class of nonlinear, non convex problems that belong to a higher class known as Biconvex Programming Problems (BCP). These problems find numerous applications in engineering, industrial, and management environments. The new algorithm develops a novel Reformulation-Linearization Technique (RlT) that uses an enumeration of variable factors to multiply constraints, and uses constraints to multiply constraints, to generate new nonlinear constraints which are subsequently linearized by defining new variables. The motivation is to transform the nonconvex bilinear problem into a lower bounding linear program that closely approximates the (partial) convex hull of feasible solutions to the problem. when the objective function is accommodated into the constraints through an auxiliary variable. This is equivalent to implicitly constructing tight approximations for the convex envelope of the objective function. The characteristic transformation induced by the Rl T therefore intrinsically yields enhanced lower bounds for use in a branch-and-bound procedure. In particular, we show that this technique actually constructs the exact convex hull representation for special (triangular and quadrilateral) polytopes in R². Our results therefore generalize the convex envelope construction process over rectangular polytopes as done by AI-Khayyal and Falk [1983), and our approach significantly enhances the lower bounding capability of the underlying linear approximation, over that of the latter method. / Ph. D.

Three topics are developed: interval convex programming, and program generation techniques. The interval convex programming problem is similar to the convex programming problem of the real number system except that all parameters are specified as intervals of real numbers rather than as real scalars. The interval programming solution procedure involves the solution of a series of 2n real valued convex programs where n is the dimension of the space. The solution of an interval programming problem is an interval vector which contains all possible solutions to any real valued convex program which may be realized. Attempts to improve the efficiency of the interval convex programming problem lead to the eventual development of a new solution procedure for the real valued linear programming problem, Orthogonal linear programming. This new algorithm evolved from some heuristic procedures which were initially examined in the attempt to improve solution efficiency. In the course of testing these heuristics, which were unsuccessful, procedures were developed whereby it is possible to generate discrete and continuous mathematical programs with randomly chosen parameters, but known solutions. / Ph. D.

This research effort is concerned with a class of mathematical programming problems referred to as Mixed-Integer Bilinear Programming Problems. This class of problems, which arises in production, location-allocation, and distribution-application contexts, may be considered as a discrete version of the well-known Bilinear Programming Problem in that one set of decision variables is restricted to be binary valued. The structure of this problem is studied, and special cases wherein it is readily solvable are identified. For the more general case, a new linearization technique is introduced and demonstrated to lead to a tighter linear programming relaxation than obtained through available linearization methods. Based on this linearization, a composite Lagrangian relaxation-implicit enumeration-cutting plane algorithm is developed. Extensive computational experience is provided to test the efficiency of various algorithmic strategies and the effects of problem data on the computational effort of the proposed algorithm. The solution strategy developed for the Mixed-Integer Bilinear Programming Problem may be applied, with suitable modifications,. to other classes of mathematical programming problems: in particular, to the Zero-One Quadratic Programming Problem. In what may be considered as an extension to the work performed on the Mixed-Integer Bilinear Programming Problem, a solution strategy based on an equivalent linear reformulation is developed for the Zero-One Quadratic Programming Problem. The strategy is essentially an implicit enumeration algorithm which employs Lagrangian relaxation, Benders' cutting planes, and local explorations. Computational experience for this problem class is provided to justify the worth of the proposed linear reformulation and algorithm. / Ph. D.