This thesis focuses on combining data envelopment analysis (DEA) and multi-objective linear programming (MOLP) methods to set targets by referencing peers' performances and decision-makers' (DMs) preferences. A large number of past papers have proven the importance of a company having a target; however, obtaining a feasible but challenging target has always been a difficult topic for companies. Since DEA was proposed in 1978, it has become one of the most popular performance assessment tools. The performance possibility set and efficient frontier established by DEA provide solid and scientific reference information for managers to evaluate an individual's efficiency. Based on the successful experience of DEA in performance assessment, many scholars have mentioned that DEA can be used to set appropriate targets as well; however, traditional DEA models do not include DMs' preference information that is crucial to a target-setting process. Therefore, several MOLP methods have been introduced to include DMs' preferences in the target-setting process based on the DEA efficient frontier and performance possibility set. The trade-off-based method is one of the most popular interactive methods that have been incorporated with DEA. However, there are several gaps in the current research: (1) the trade-off-based method could take so many interactions that no DMs could finish the interactive process; (2) DMs might find it very difficult to provide the preference information required by MOLP models; and (3) DMs cannot have an intuitive view in terms of the efficient frontier. Regarding the gaps above, this thesis proposes three new trade-off-based interactive target-setting models based on the DEA performance possibility set and efficient frontier to improve DMs' experience when setting targets. The three models can work independently or can be combined during the decision-making process. The piecewise linear model uses a piecewise linear assumption to simulate DMs' real utility function. It gradually narrows down the region that could contain DMs' most-preferred solution (MPS) until it reaches an acceptable range. This model could help DMs who have limited time for interaction but want to have a global view of the entire efficient frontier. This model has also been proven very helpful when DMs are not sensitive to close efficient solutions. The prioritized trade-off model provides a new way for a DM to know about the efficient frontier, which allows the DM to explore the efficient frontier following the preferred direction with a series of trade-off tables and trade-off figures as visual aids. The stepwise trade-off model focuses on situations where the number of objectives (outputs/inputs for the DEA model) is quite large and DMs cannot provide all indifference trade-offs between all the objectives simultaneously. To release the DMs' burden, the stepwise model starts from two objectives and gradually includes new objectives in the decision-making process, with the assumption that the indifference trade-offs between previous objectives are fixed, until all objectives are included. All three models have been validated through numerical examples and case studies of a Chinese state-owned bank to help DMs to explore their MPS in the DEA production possibility set.

Linear programming is widely used to solve various complex problems with many variables, subject to multiple constraints. Expert systems are created to provide expertise on complex problems through the application of inference procedures and advanced expert knowledge on facts relevant to the problem. The diet problem is well-known for its contribution to the development of linear programming. Over the years many variations and facets of the diet problem have been solved by means of linear programming techniques and expert systems respectively. In this study the feasibility of combining expert system technology and linear programming techniques to solve a diet problem topical to South Africa, is examined. A computer application is created that incorporates goal programming- and multi-objective linear programming models as the inference engine of an expert system. The program is successfully applied to test cases obtained through knowledge acquisition. The system delivers an eating-plan for an individual that conforms to the nutritional requirements of a healthy diet, includes the personal food preferences of that individual, and includes the food items that result in the lowest total cost. It further allows prioritization of the food preference and least cost factors through the use of weights. Based on the results, recommendations and contributions to the linear programming and expert system fields are presented. / MSc (Computer Science), North-West University, Potchefstroom Campus, 2014

Linear programming is widely used to solve various complex problems with many variables, subject to multiple constraints. Expert systems are created to provide expertise on complex problems through the application of inference procedures and advanced expert knowledge on facts relevant to the problem. The diet problem is well-known for its contribution to the development of linear programming. Over the years many variations and facets of the diet problem have been solved by means of linear programming techniques and expert systems respectively. In this study the feasibility of combining expert system technology and linear programming techniques to solve a diet problem topical to South Africa, is examined. A computer application is created that incorporates goal programming- and multi-objective linear programming models as the inference engine of an expert system. The program is successfully applied to test cases obtained through knowledge acquisition. The system delivers an eating-plan for an individual that conforms to the nutritional requirements of a healthy diet, includes the personal food preferences of that individual, and includes the food items that result in the lowest total cost. It further allows prioritization of the food preference and least cost factors through the use of weights. Based on the results, recommendations and contributions to the linear programming and expert system fields are presented. / MSc (Computer Science), North-West University, Potchefstroom Campus, 2014

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.

Problems in the public policy decision-making environments are typically complex and continuously evolve. In a resource-constrained environment, several alternatives, criteria, and conflicting objectives must be considered. As a result, solutions to these types of problems cannot be modelled solely using single-criteria techniques. It has been observed that most techniques used to shape energy policy and planning either produce sub-optimal solutions or use strong assumptions about the preferences of decision-maker(s). This difficulty creates a compelling need to develop novel techniques that can handle several alternatives, multiple criteria and conflicting objectives to support public sector decision-making processes. First, the study presents a novel scenario-based multi-objective optimisation framework based on the augmented Chebychev goal programming (GP) technique linked to a value function for analysing a decision environment underlying energy choice among low-income households in isolated rural areas and informal urban settlements in South Africa. The framework developed includes a multi-objective optimisation technique that produced an approximation of a Pareto front linked to an a priori aggregation function and a value function to select the best alternatives. Second, the study used this model to demonstrate the benefits of applying the framework to a previously unknown subject in public policy: a dynamic multi-technology decision problem under uncertainty involving multiple stakeholders and conflicting objectives. The results obtained suggest that while it is cost-optimal to pursue electrification in conjunction with other short-term augmentation solutions to meet South Africa's universal electrification target, sustainable energy access rates among low-income households can be achieved by increasing the share of clean energy generation technologies in the energy mix. This study, therefore, challenges the South African government's position on pro-poor energy policies and an emphasis on grid-based electrification to increase energy access. Instead, the study calls for a portfolio-based intervention. The study advances interventions based on micro-grid electrification made up of solar photovoltaics (PV), solar with storage, combined cycle gas turbine (CCGT) and wind technologies combined with either bioethanol fuel or liquid petroleum gas (LPG). The study has demonstrated that the framework developed can benefit public sector decision-makers in providing a balanced regime of technical, financial, social, environmental, public health, political and economic aspects in the decision-making process for planning energy supply interventions for low-income households. The framework can be adapted to a wide range of energy access combinatorial problems and in countries grappling with similar energy access challenges.