Origin-Destination (O-D) trip tables represent the demand-supply information of each directed zonal-pair in a given region during a given period of time. The effort of this research is to develop a linear programming methodology for estimating O-D trip tables based on observed link volumes. In order to emphasize the nature of uncertainty in the data and in the problem, the developed model permits the user's knowledge of path travel time to vary within a band-width of values, and accordingly modifies the user-optimality principle. The data on the observed flows might also not be complete and need not be perfectly matched. In addition, a prior trip table could also be specified in order to guide the updating process via the model solution. To avoid excessive computational demands required by a total numeration of all possible paths between each O-D pair, a Column Generation Algorithm (CGA) is adopted to exploit the special structures of the model. Based on the known capacity of each link, a simple formula is suggested to calculate the cost for the links having unknown volumes. An indexed cost is introduced to avoid the consideration of unnecessary passing-through-zone paths, and an algorithm for solving the corresponding minimum-cost-path problem is developed. General principles on the design of an object-oriented code are presented, and some useful programming techniques are suggested for this special problem. Some test results on the related models are presented and compared, and different sensitivity analyses are performed based on different scenarios. Finally, several research topics are recommended for future research. / Master of Science

A profit maximizing linear programming model was developed. The model was fitted to a demonstration farm having a forage based livestock feeding system. Restraints where the resources of the McCoy farm in Rockbridge County, Virginia, which included limited pasture, labor, storage availability, and limited financial resources. Row crop production was an option not considered. Only variable costs of production were considered as fixed costs continue in the absence of production. Forage and livestock species used in the model were currently in existence on the farm. Estimated productivity levels were also based on actual farm data and were used to establish the upper limits of forage production. Results of the analysis indicate that alfalfa hay held for sale was the most profitable single enterprise. Grass hay was produced and fed to meet the livestock requirements during February and March. A fall calving cow-calf herd, with calves being marketed, at 634 pounds on September 30 was more profitable than marketing during July at lighter weights even though this system had higher forage requirements. Neither a spring calving cow herd or the purchase of stocker calves for summer grazing ensured the optimal farm plan as forage was better utilized by the fall herd. Seventy three fall calving cows and 152 winter lambing ewes were in the optimal plan. The ratio of fall calving cows to winter lambing ewes was 1 : 2. Stocking ratios between cows and ewes were dependent upon price relationships used and could vary with differing price relationships between feeder calves and slaughter lambs. Stocking rates were limited most by the availability of the improved and unimproved pastures. All available labor was used during November through May. Additional labor had to be hired to offset labor shortages during January through May. Financial resources of the farmer were adequate to meet the variable costs of production without additional use of borrowed capital. / M.S.

The incentives and policies spearheaded by the U.S. government have created abundant opportunities for renewable fuel production and commercialization. Bio-butanol is a very promising renewable fuel for the future transportation market. Many efforts have been made to improve its production process, but seldom has bio-butanol research discussed the integration and optimization of a cellulosic bio-butanol supply chain network. This study focused on the development of a physical supply chain network and the optimization of a green supply chain network for cellulosic bio-butanol. To develop the physical supply chain network, the production process, material flow, physical supply chain participants, and supply chain logistics activities of cellulosic bio-butanol were identified by conducting an onsite visit and survey of current bio-fuel stakeholders. To optimize the green supply chain network for cellulosic bio-butanol, the life cycle analysis was integrated into a multi-objective linear programming model. With the objectives of maximizing the economic profits and minimizing the greenhouse gas emissions, the proposed model can optimize the location and size of a bio-butanol production plant. The mathematical model was applied to a case study in the state of Missouri, and solved the tradeoff between the feedstock and market availabilities of sorghum stem bio-butanol. The results of this research can be used to support the decision making process at the strategic, tactical, and operational levels of cellulosic bio-butanol commercialization and cellulosic bio-butanol supply chain optimization. The results of this research can also be used as an introductory guideline for beginners who are interested in cellulosic bio-butanol commercialization and supply chain design. / Ph. D. / Renewable energy is one of the most effective tools to fight the threats of climate change, global warming, food price rising, and energy dependence. Cellulosic bio-butanol, a renewable alcohol-based biofuel, is a very promising energy candidate to support the fight for these threats. Due to its low water miscibility, similar energy content and octane number with gasoline, blending ability with gasoline in any proportions, and its directly utilization in gasoline engine, cellulosic bio-butanol is a potential candidate to replace gasoline. Unlike bioethanol, which only relies its fuel distribution on railway and tanker trucks, bio-butanol is compatible with not only railway and tanker trucks but also current pipeline based fuel distribution infrastructures. In order to increase the competitively of this promising energy candidate, the cellulosic bio-butanol is worth to be commercialized. An important step for the commercialization of cellulosic bio-butanol is the network design of its supply chain. In this research, the supply chain network of cellulosic bio-butanol was constructed and optimized. The supply chain network of cellulosic bio-butanol was constructed by identifying the three important aspects of a supply chain network structure: structure dimension, participants in supply chain, and supply chain business process links. A) The structure dimension was identified by understanding the production process of bio-butanol. A case study was used to study the production process of cellulosic bio-butanol. B) The supply chain business process links were identified by conducting a survey on the logistics activities in bio-butanol supply chain. C) The participants of cellulosic bio-butanol supply chain were identified by identifying the physical infrastructure of cellulosic bio-butanol supply chain. The results of the literature review, case study and survey were analyzed to identify the physical infrastructure and the participants in the supply chain. It was found out that the supply chain network structure of cellulosic bio-butanol includes 4 tiers of horizontal structure: suppliers, producers, distributors, and customers. The suppliers refer to the local farmers and feedstock aggregators. The producers are the cellulosic bio-butanol production plants. The distributors are the fuel logistics companies and fuel distributors. The customers are the fuel companies. The cellulosic bio-butanol producers use contracts to connect with biomass suppliers, fuel distributors, and bio-butanol customers. Based on the proposed network structure of cellulosic bio-butanol supply chain, the optimization of the green cellulosic bio-butanol supply chain network was conducted. A multi-objective linear integer programming model was developed to design the green cellulosic bio-butanol supply chain network. Life cycle analysis (LCA) and net present value techniques were used in the proposed model to formulate the environmental and economic objective function. With the objectives of maximizing the economic profits while minimizing the greenhouse gas (GHG) emissions, the proposed model can optimize the location and the size of bio-butanol production plant. The model was applied using data from the state of Missouri (MO). The results showed that the optimal location of cellulosic bio-butanol production plant is in the southeastern region of MO. And the production size of bio-butanol production plant is based on the tradeoff between the economic and environmental objectives. The lower GHG emissions results in a smaller size of production plant.

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 research project examined the ability to combine spatial data analysis and mathematical programming techniques in developing a multiple-use land management plan for a public forest in northeastern Virginia. Linear programming-based timber management scheduling models were constructed utilizing the Model I formulation of Johnson and Scheurman (1977). The models were formulated as mixed strata-based, area-based models (Johnson and Stuart 1987) that maximized present net worth subject to a fixed timberland base, an ending inventory requirement, workload control restrictions, and harvest volume control restrictions. The linear programming-based models which incorporated spatial data analysis capabilities were solved using mixed-integer programming. The model was used to assess the costs of implementing spatial restrictions designed to address forest resource management concerns, in particular, timber production and reserve status acreage for wildlife habitat purposes. The impact of imposing alternative spatial stand allocation requirements and different levels of reserve status acreage was evaluated by measuring the cost in terms of reductions in the present net value (PNV) of timber benefits and timber harvest volumes. The results indicate that the optimal solution value is more sensitive to the level of reserve status acreage imposed on the model than to the spatial restrictions for stand allocations placed on the model. / Master of Science

The traditional method for conducting sensitivity analysis is to repeatedly solve a model while varying the parameters. The solution is then obtained as some average of these optimal solutions under those different conditions or states of the world. The present work presents results of conducting sensitivity analysis using a method more firmly ground in mathematical programming theory. The present analysis models the investment decisions in a case with large uncertainty in demand: the steel industry in Argentina. Special emphasis is devoted to the recent history, where a recent shift in economic policy (1976-1981) towards allowing free competition with imported products resulted in a severe crisis for the steel industry and its trading partners. An increase in exports was observed during this period which is not likely to continue if there is a recovery process. In the first sections, the relation of steel production and economic growth is analyzed in the context of the world situation of the industry, setting the background for the analysis of the Argentinian industry as a case study. The results of the present model adequately describe the existence of unutilized capacity observed in the industry, as well as the recent increase in exports. The most important conclusion of the model is that the traditional method of conducting sensitivity analysis results in significant inefficiency of the reached decisions, involving large losses for a case such as the steel industry considered here. / Master of Arts / incomplete_metadata

This paper focuses on the Virginia Chesapeake Bay Preservation Act (the Act), the regulations promulgated thereunder and several questions arising from an examination of the Act and regulations. Specifically, the analysis examines the agricultural provisions within the regulations and asks whether the provisions are economically desirable, as well as legally enforceable. The provisions of the Act and the regulations constitute the major focus of Chapter One. Chapter One's discussion concludes with an analysis of the regulations’ main pollution prevention tool, the vegetative buffer strip, and a brief listing of various issues and controversies involving the Act and the regulations. Chapter Two introduces a linear programming model designed to determine the most cost-effective means of pollution control based on farmer profits under several regulatory scenarios. The results imply that the mandatory provisions of the regulation prevent farmers from achieving the desired level of pollution reduction in the least costly fashion. The takings issue, a major concern for all environmental legislation, forms the major focus of Chapter Three. This analysis considers the provisions of the Act and regulations within the historic context of the takings clause of the Fifth Amendment of the United States Constitution, as well as the takings clause of the Virginia Constitution, and determines the legal validity of the provisions. Finally, Chapter Four presents several criticisms of the regulations as presently constituted. Suggestions for a more cost effective regulatory scheme conclude the analysis. / Master of Science

There are hundreds of existing dams within the State of Virginia, and even thousands more specifically within the United States. A large portion of these dams do not meet the current safety standard of passing the Probable Maximum Flood. Likewise, many of the dams have reached or surpassed the original design lives, and are in need of rehabilitation. A standard protocol will assist dam owners in completing a dam rehabilitation analysis. The protocol provides the methods to complete the hydrologic, hydraulic, and economic analysis. Additionally, alternative augmentation techniques are discussed including the integration of GIS applications and linear programming optimization techniques. The standard protocol and alternative techniques are applied to a case study. The case study includes a set of flood control dams located in the headwaters of the South River watershed in Augusta County, VA. The downstream impacts of the flood control dams on the city of Waynesboro are demonstrated through the hydrologic and hydraulic analysis. / Master of Science

The United States is facing a rising average age of principal farm operators and a decline in number of beginning farmers. With numerous barriers and challenges resulting in many farm failures, a majority of beginning farmers are relying on off-farm income to support their households. Decision-making and farm business planning are difficult skills to develop and improve, and the ability to develop a plan to balance on- and off-farm labor could allow farmers to make more profitable decisions. In this study, a General Algebraic Modeling System (GAMS) is used to develop a labor management planning framework for use by Virginia's beginning vegetable farmers or service providers, such as extension agents, with the goal of improving total (on- and off-farm) profitability and farm viability. Study findings suggest that a willingness to work of 12 hours per day, 365 days per year and hired labor costs of $9.30 per hour, which is the national average for agricultural workers encourage a farmer to maintain an off-farm job, while a relatively lower off-farm wage or salary may encourage a farmer to work on the farm only. Lastly, higher hired labor costs may encourage a farmer to pursue his or her most profitable work opportunity, be it on- or off-farm, without hiring labor to maintain the farm. The model developed in this study may be used to plan multiple years of farm management to include anticipated changes in off-farm employment opportunities, land availability, product mix, and access to farm labor. The author suggests that beginning farmers who use this planning tool are able to make more informed decisions related to allocation of labor time and resources, resulting in lower failure rates for beginning farmers in Virginia. A user-friendly interface may be developed based on the study framework, to strengthen the results and increase the practicality of the tool. / Master of Science

A linear programming model for multiple use was developed for the High Knob Unit of the Jefferson National Forest. The model was intended to be a pilot study for the development of similar models for other units in the Appalachians. The model was developed to provide information about trade-offs between timber, recreational activities, and budgets during the 10 year planning period. Currently used estimates and "rules of thumb" were used as the means for relating the activities considered in the model. The objective function used was timber maximization and it was constrained by the activity and budget constraints. The maximum possible timber volume that could be cut was found for the High Knob Unit by using only acreage constraints on the objective function. Then the constraints for the other activities were added, each of which being tied to the timber variables. An initial optimal solution was found which not only gave values for the amounts of the activities that would be best to produce but also where they were to occur on the ground. To provide information about trade-offs, a sensitivity analysis was done to provide a series of solutions for the High Knob Unit. These solutions were evaluated and recommendations were made for the High Knob Unit. Benefits and limitations of the model were discussed as were the problems encountered in developing the High Knob LP. Suggestions for future study were also made. / Master of Science