Generating the Discrete Efficient Frontier to the Capital Budgeting Problem

Abstract

In this paper, we characterize the capital budgeting problem by two objective functions. One is maximizing the present value of accepted projects and the other is minimizing their risk. As we assume that the weights assigned to these objectives are unspecified, we utilize a Discrete Efficient Frontier (DEF) approach to represent all the efficient combinations. We found an optimality range for each efficient combination covering the entire possible range of weights (zero to one). Furthermore, we present different properties and characteristics of the DEF, and develop two algorithms for constructing the DEF. The first one is a simple heuristic and the second one is an optimal algorithm. We conducted experiments measuring the effectiveness of the heuristic algorithm and the effect of terminating the optimal algorithm before its completion. We have shown that the heuristic algorithm, which is the first phase of the branch-and-bound algorithm, has an average error of about 2%. Furthermore, we have shown that this average error can be reduced by applying only part of the optimal algorithm and terminating it before its actual completion.