Mathematical programming models for capital budgeting

Abstract

This thesis deals with analytical techniques to be utilized during the various decision making phases of the capital budgeting process. This thesis begins with the attempt to solve the capital budgeting problem in which both the following conditions hold: (1) the borrowing interest rate varies from period to period in close relation to the size of debt and (2) projects are indivisible, i.e., fractional projects are not allowed. The problem can be formulated in a mixed integer non-linear programming model. Generally, this model is difficult to solve because the constraints are not linear and solution set is not convex. In order to solve the model, we characterized the dominance properties of the solution of the model. This special property reduces the solution space and the binary variables make the solution space finite. Thus we only need to search the finite points of the solution space. That is, this model could be solved by explicit enumeration. After that, we derived the equivalent model to solve the problem more efficiently. This equivalent model enables us to develop an implicit enumeration algorithm which requires much less computation than the explicit enumeration algorithm. The other model developed in this thesis is to provide the optimal combinations of investment at each level of capital budget. This is important especially for a decision maker when he examines the possibilities for revising the underlying budget limits. This model is studied to answer the following question. Is it worthwhile to relax the current budget limits for a given set of projects? In linear programming framework, dual variables do work as an accurate shadow price evaluator of the theoretical payoff from very small continuous budget relaxation. Under project indivisibility condition, however, dual variables fail to work as an indicator of attractiveness of additional funds. So we employed the modified internal rate of return method to provide incremental rate of return on dif...