Generating the Discrete Efficient Frontier to the capital budgeting problem

In this paper, the authors 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 the authors assume that the weights assigned to these objectives are unspecified, they utilize a Discrete Efficient Frontier (DEF) approach to represent all the efficient combinations. The authors found an optimality range for each efficient combination covering the entire possible range of weights (zero to one). Furthermore, they 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. The authors conducted experiments measuring the effectiveness of the heuristic algorithm and the effect of terminating the optimal algorithm before its completion. They 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, the authors have shown that this average error can be reduced by applying only part of the optimal algorithm and terminating it before its actual completion.