The intersection form of production possibility set in DEA and its applications

2006-2007 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Domination and Decomposition in Multiobjective Programming

During the last few decades, multiobjective programming has received much attention for both its numerous theoretical advances as well as its continued success in modeling and solving real-life decision problems in business and engineering. In extension of the traditionally adopted concept of Pareto optimality, this research investigates the more general notion of domination and establishes various theoretical results that lead to new optimization methods and support decision making. After a preparatory discussion of some preliminaries and a review of the relevant literature, several new findings are presented that characterize the nondominated set of a general vector optimization problem for which the underlying domination structure is defined in terms of different cones. Using concepts from linear algebra and convex analysis, a well known result relating nondominated points for polyhedral cones with Pareto solutions is generalized to nonpolyhedral cones that are induced by positively homogeneous functions, and to translated polyhedral cones that are used to describe a notion of approximate nondominance. Pareto-oriented scalarization methods are modified and several new solution approaches are proposed for these two classes of cones. In addition, necessary and sufficient conditions for nondominance with respect to a variable domination cone are developed, and some more specific results for the case of Bishop-Phelps cones are derived. Based on the above findings, a decomposition framework is proposed for the solution of multi-scenario and large-scale multiobjective programs and analyzed in terms of the efficiency relationships between the original and the decomposed subproblems. Using the concept of approximate nondominance, an interactive decision making procedure is formulated to coordinate tradeoffs between these subproblems and applied to selected problems from portfolio optimization and engineering design. Some introductory remarks and concluding comments together with ideas and research directions for possible future work complete this dissertation

The Administrative Efficiency of Hospitals and the Effect of Electronic Data Interchange: A Critical Evaluation of the Stochastic Frontier and the Data Envelopment Analysis Models to Efficiency Measurement

The investigation and measurement of administrative efficiency is an issue of great concern for health care policy decision makers and has important implications for the efficiency of the overall health care sector itself as well as for the cost containment efforts and the restructuring of the health care system. The administrative cost efficiency of the United States health care system has received much attention during the last years, and has been under continuous criticism since it became widely known that the country\u27s administrative costs are higher than those of any other country in the world. As criticism on administrative inefficiency of the U.S. health care system has intensified, the need for detailed empirical studies has become imperative. To answer the question of administrative efficiency, this study undertakes an empirical investigation of the largest component of the health care sector; the hospital sector. The variety of proposed health care reform proposals that involve the reduction of administrative costs of hospitals consider the application of Electronic Data Interchange as the potential mechanism towards streamlined administration, cost efficiency and cost containment. Efficiency is the main concern of all economic sectors and a variety of models have been developed to examine every aspect of it. In this dissertation, the two leading approaches to efficiency measurement (Stochastic Frontier and Data Envelopment Analysis) are used and compared. To increase the reliability and comparability of estimates, a variety of models are estimated. In addition, an integrated model that incorporates the characteristics of the Stochastic Frontier with Data Envelopment Analysis techniques is developed. The model provides a new approach for incorporating Technologically Consistent information into DEA in the form of weight restrictions. In this integrated framework the extent of administrative efficiency of hospitals is evaluated. In a second stage analysis, the determinants of inefficient performance are assessed with special attention to the effect of Electronic Data Interchange. The results support the common belief that hospital administration is inefficient. Hospital administration appears to be the most significant determinant of hospital inefficiency. Furthermore, the results indicate that Electronic Data Interchange could be used as a mechanism of reducing administrative inefficiency

Inequity-averse decisions in operational research

This thesis is on inequity-averse decisions in operational research, and draws on concepts from economics and operational research such as multi-criteria decision making (MCDM) and mathematical modelling. The main focus of the study is developing systematic methods and modelling to help decision makers (DMs) in situations where equity concerns are important. We draw on insights from the economics literature and base our methods on some of the widely accepted principles in this area. We discuss two equity related concerns, namely equitability and balance, which are distinguished based on whether anonymity holds or not. We review applications involving these concerns and discuss alternative ways to incorporate such concerns into operational research (OR) models. We point out some future research directions especially in using MCDM concepts in this context. Specifically, we observe that research is needed to design interactive decision support systems. Motivated by this observation, we study an MCDM approach to equitability. Our interactive approach uses holistic judgements of the DM to refine the ranking of an explicitly given (discrete) set of alternatives. The DM is assumed to have a rational preference relation with two additional equity-related axioms, namely anonymity and the Pigou-Dalton principle of transfers. We provide theoretical results that help us handle the computational difficulties due to the anonymity property. We illustrate our approach by designing an interactive ranking algorithm and provide computational results to show computational feasibility. We then consider balance concerns in resource allocation settings. Balance concerns arise when the DM wants to ensure justice over entities, the identities of which might affect the decision. We propose a bi-criteria modelling approach that has efficiency (quantified by the total output) and balance (quantified by the imbalance indicators) related criteria. We solve the models using optimization and heuristic algorithms. Our extensive computational experiments show the satisfactory behaviour of our algorithms

Managing radiotherapy treatment trade-offs using multi-criteria optimisation and data envelopment analysis

Techniques for managing trade-offs between tumour control and normal tissue sparing in radiotherapy treatment planning are reviewed and developed. Firstly, a quality control method based on data envelopment analysis is proposed. The method measures the improvement potential of a plan by comparing the plan to other reference plans. The method considers multiple criteria, including one that represents anatomical variations between patients. An application to prostate cases demonstrates the capability of the method in identifying plans with further improvement potential. A multi-criteria based planning technique that considers treatment delivery is then proposed. The method integrates column generation in the revised normal boundary intersection method, which projects a set of equidistant reference points onto the non-dominated set to form a representative set of non-dominated points. The delivery constraints are considered in the column generation process. Essentially, the method generates a set of deliverable plans featuring a range of treatment trade-offs. Demonstrated by a prostate case, the method generates near-optimal plans that can be delivered with dramatically lower total fluence than the optimal ones post-processed for treatment delivery constraints. Finally, a navigation method based on solving interactive multi-objective optimisation for a discrete set of plans is developed. The method sets the aspiration values for criteria as soft constraints, thus allowing the planner to freely express his/her preferences without causing infeasibility. Navigation is conducted on planner-defined clinical criteria, including the non-convex dose-volume criteria and treatment delivery time. Navigation steps on a prostate case are demonstrated with a prototype implementation. The prostate case shows that optimisation criteria may not correctly reflect plan quality and can mislead a planner to select a “sub-optimal” plan. Instead, using clinical criteria provides the most relevant measure of plan quality, hence allowing the planner to quickly identify the most preferable plan from a representative set

WATER REFORMS IN KENYA: A HISTORICAL CHALLENGE TO ENSURE UNIVERSAL WATER ACCESS AND MEET THE MILLENNIUM DEVELOPMENT GOALS

Access to water is a key issue for developing countries. Kenya is one such country in which water scarcity and a poor water infrastructure compromise the health and standard of living of the population, and hinder its economic and social development. Despite a long history of attempts to reform the country's water sector and improve water resources management, a large proportion of Kenya's population is still not sufficiently served with water for consumptive, sanitation, and productive purposes. This dissertation examines aspects of water reform and access in the country, including the institutional and historical factors affecting the water sector, and the historical evolution of water resources management from the colonial to post-independence periods. The most recent reform (2002) is assessed in terms of its effectiveness in bringing about institutional reform, as well as the operating performance of water service providers in meeting the Millennium Development Goals (MDGs).The study adopts a case study approach using mixed methods. Specifically, a questionnaire was administered to the newly formed Water Service Providers (WSPs) as well as various water sectors. The performance efficiency of the WSPs was analyzed using data envelopment analysis. The results reveal that continuing duplication of functions across the water sectors, low levels of funding, and corruptions are inhibiting the effectiveness of the restructuring. The greatest challenge in executing the reforms relates to the financing of the whole process. While the relevant policies and institutions have been set up, they lack funds either to support the planned activities, and projects or, importantly, to raise the performance of existing WSPs. The study uncovered that, by pegging its initiatives on global targets and foreign aid, Kenya has changed its policies and institutions to reflect the global trends several times. This has led to weak or lack of continuity in policy, and reform process in the country. Furthermore, linkages among the several agencies dealing with water services remain weak, and water resource policy has not been harmonized with sanitation policy, irrigation policy, and environmental policy.The study has further shown that while the 2000 reforms have resulted in major gains in policy reforms, significant improvement in water access will not be achieved without addressing the systematic inequalities of water access caused by land alienation during the colonial rule. After independence, most of the land owned by the Europeans was not returned to the natives, but rather bought by the rich or converted to game reserves. In this case, the land tenure system that broadly disenfranchised the local population before independence continues to date.The study shows that the WSPs created to replace the government agencies in the provision of water services are not efficient and productive enough to meet the MDGs as envisioned by government plan. The implications and recommendations for water sector performance relate mainly to these WSPs. While the companies are still young and need time to mature, some challenges need to be addressed immediately. Many WSPs still lose more than 50% of water as unaccounted-for-water. This is mainly due to a dilapidated infrastructure most of which was developed during the colonial period. Most of the pipeline systems, especially in urban areas, need to be replaced before extending coverage to other areas. In the absence of more (e.g., private sector) funding, this is unlikely to happen. Possible solutions include amalgamating smaller WSPs to increase their scale of operation. The study further outlined how some of the inefficiencies could be mitigated through benchmarking process. Weaker companies should be encouraged to emulate their benchmarked peers within the country, while stronger companies should be benchmarked with stronger companies in eastern Africa