The dissertation deals with the allocation of resources, among profit producing elements within a company, to achieve satisfactory results over a planning horizon. The company is viewed as a confederation of profit making elements called Strategic Business Units (SBU) which are independent of each other and held together by a central authority. The dissertation uses a computerized simulation model of the deterministic type in a timesharing mode. The model is deterministic with some limited probabilistic The model is deterministic with some limited probabilistic effects. It is used to develop projected balance sheets and profit and loss statements for each period in a predetermined planning horizon and to evaluate the success of a set of alternative futures of the SBU. The set of SBU alternatives to be evaluated as the "company" may be arbitrarily chosen by the operator or chosen through the use of a near-optimal, integer programming algorithm for a variety of measurement criteria and subject to various restraints on the balance sheet. The research uses data generated by the long-range planning process at an intermediate sized, multinational corporation listed on the New York Stock Exchange. The data consist of assets, liabilities, and profit and loss statement items for each period in a planning horizon and for each of three alternatives of each SBU in the study. In addition, a beginning corporate balance sheet is required as are planned corporate expense items and the specification of operating restrictions. Research into the effect of several strategic policies, including dividend rate and debt to equity ratio, on the future prospects of the company in accordance with the optimal value of five different measurement criteria, is reported. The five measurement criteria are present value of shareholder equity, growth in earnings per share, growth in total assets, total assets and growth in sales. The appendix material contains listings of computer programs used in the model (written in the Basic computer language), the research data used, numerous computer printouts, and technical discussions on the model. Several tentative conclusions are listed, many areas for further research are suggested, and strengths and constraints of the model are discussed. It is concluded that the techniques developed have good potential for increasing cash generation and the efficiency of the investment process in a company; the dividend rate has a significant effect on how fast a company can grow; and the model is flexible and can be used for a number of investigative purposes to support company decision-makers. An interesting area for further research is the tentative conclusion that return on assets, when used as an optimization criterion, produces a significantly different set of SBU alternatives from the one which results from using the other measurement criteria.

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An adequate health care resource allocation in a hospital is directly dependent upon the ability to estimate the hospital's patient census accurately. Efforts to estimate hospital's patient census are classified into two general methods: estimating from historical data, and demographic analysis. This paper takes the position that the estimate from the historical data is more economic and convenient for understanding than the estimate from the demographic analysis. Seven models that predict hospital's patient census by using the hospital's historical data are evaluated to fit the characteristics of each pattern shown in historical information. Where a microcomputer is available, this forecasting system provides detailed prediction of patient census with the comparable percentage of forecasting error among each model. Data from a ten-unit hospital in Florida is analyzed and provides a predicted patient census for the hospital's short-term plan. Results of this patient census estimating system and its advantage over the other forecasting method are discussed.

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Two complex resource allocation problems motivate the algorithms and applications discussed in this dissertation. The Public Broadcasting Service (PBS), a cooperative of television stations with independent budgets, must decide which programs to purchase from various producers and at what cost to its member stations. The airports of America must decide how to allocate limited takeoff and landing slots to competing airlines. Both problems are recognized as zero/one decision problems with multiple resource constraints. A computer aided allocation mechanism is proposed as an alternative to the currently practiced decision procedures. Bid information, solicited in an auction phase, provides values to parameterize a mathematical model. An optimization phase is then used to generate the best solution for the given information. The integer programming algorithms required to solve the particular models suggested are explored in detail. A best bound enumeration strategy which uses a surrogate knapsack relaxation is developd. Computer storage requirements are curtailed by using a new greedy heuristic for general integer programming problems. The PBS model has a structure closely related to certain fixed charge problems. This allows the use of necessary conditions for the existence of a solution of capacitated transportation problems to test the feasibility of candidate solution vectors. In the SLOT model feasibility testing is a trivial matter of maintaining running row sums. The bound provided by the knapsack relaxation is further enhanced with the addition of a set of generalized choice constraints. An efficient polynomial algorithm and proof of optimality are given for the linear relaxation of this problem. A procedure for generating a set of generalized choice constraints from any set of logical constraints is also given. The viability of the approach developed and the effects of parameter variation are computationally tested in both PBS and SLOT contexts. Some further computational results for project selection, set covering, and multiple knapsack problems are reported. A broad class of mixed integer linear programming problems is defined (e.g., capital expenditure and network design problems) and a suitable relaxation for a similar approach is developed. Finally, several new directions for research in algorithmic development and application are proposed.

Nie Xiaofeng. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 52-56). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- A Minimax Model and Its CAPM --- p.9 / Chapter 2.1 --- Model Formulation --- p.9 / Chapter 2.2 --- Efficient Frontier --- p.11 / Chapter 2.3 --- Market Portfolio --- p.15 / Chapter 2.4 --- CAPM of Minimax Model --- p.22 / Chapter 3 --- "A Revised Minimax Model with Downside Risk, and Its CAPM" --- p.28 / Chapter 3.1 --- Model Formulation --- p.28 / Chapter 3.2 --- Efficient Frontier --- p.30 / Chapter 3.3 --- Market Portfolio and CAPM --- p.38 / Chapter 4 --- Numerical Analysis --- p.43 / Chapter 4.1 --- Efficient Frontiers --- p.43 / Chapter 4.1.1 --- Input Data --- p.45 / Chapter 4.1.2 --- Efficient Frontiers --- p.45 / Chapter 4.2 --- Monthly Rate of Return Comparison --- p.47 / Chapter 5 --- Summary --- p.50 / Bibliography --- p.52

This thesis addresses the problem of setting up a surface mount placement machine for production. The objective is to minimize the number of machine changeovers made during a production run consisting of a number of circuit cards. The solution to the problem involves two separate decisions. The first decision considers determining how to combine feeders together in "bays" or groups of feeders, and how to assign the bays to the circuit cards. The second decision considers the circuit card production sequence. A mathematical programming formulation is given, however, its solution is very difficult for problems of a realistic size. Several heuristic approaches are suggested and used to solve actual and test problems. The heuristic for bay design uses clustering techniques used in Group Technology while the sequencing problem is solved using heuristics based on solution techniques for the Traveling Salesman problem.

This study explores the possible role of mathematical system theory in integrating existing ecological knowledge within the existing concepts of the structure of the biosphere. The objective of this integration is a theory of ecosystems which must include interactions. The basic unit of the biosphere is the biogeocoenose; similar to the ecosystem, but homogeneous with respect to topographic, microclimatic, vegetation, animal, pedalogical, hydrological and geochemical conditions. The role of the biogeocoenose in a theory of ecosystems based on system theory is discussed. The biogeocoenose may serve as the building block for modeling watersheds as ecosystems. The fundamentals of system theory are reviewed. As an example, an analysis and synthesis of the arid zone water balance follows. The water balance is resolved into twenty components which represent the water balance of (1) the canopy, (2) the mulch, (3) the soil surface, (4) the soil, and (5) the plant, including interactions. The twenty components were modeled as separate systems which were later coupled into one overall, complex, well defined ecosystem water balance system. The example illustrates the role of system theory in integrating ecological knowledge. Further discussion indicates the need for explicitly including plant behavior in the water balance model.

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy