Mathematical Programming And The Analysis Of Capital Budgeting Problems

Capital budgeting problems are linear or non-linear programming models that address the solution of the level of investment in projects by considering basically budget limits. Additional constraints such as borrowing limit constraint or scarce resource constraint are also possible. In this thesis, we study the uncertainty in different capital rationing and capital budgeting problems by considering fuzzy and robust optimization approaches. Fuzzy mathematical programming includes the defuzzification of a fuzzy model by using a fuzzy relation, and analysis and solution of the model by using deterministic mathematical programming techniques. On the other hand, robust optimization approach includes the best solution of the model by considering the worst realization of the uncertain parameters. Although both approaches are devoted to the solution of the models by considering uncertainty , a model solved by fuzzy mathematical programming does not necessarily have to be robust. In this thesis, we. first examine the fuzzy mathematical programming approaches to the Lorie-Savage capital rationing model in the literature, and illustrate the models with the numerical examples. In the other sections devoted to the fuzzy optimization, we propose the defuzzification of Weingartner's pure capital rationing model by triangular norm (t-norm) fuzzy relation and Bernhard's model by t-norm and triangular conorm (t-conorm) fuzzy relations and their detailed analysis. We also propose the decision rules for intemal rate of retum (IRR) in case of cash flow uncertainty .In the chapters devoted to robust optimization, we extend the robust optimization approach to W eingartner' s pure capital rationing and horizon capital budgeting models proposed in the literature by considering additional parameters as uncertain. We also redefine the decision rules of investment appraisal techniques for simple projects analogous to robust optimization. All model propositions are accompanied by computation analysis, which proves the applicability and practicality of the proposed models.

Part of an annual series dedicated to the discussion of the studies in the application of management science to the solution of significant managerial decision making problems. This volume deals with the applications of mathematical programming to Multi-criteria decision making, Supply chain management, Performance management, and Risk analysis.