Finding the Integer Efficient Frontier for Quadratic Capital Budgeting Problems

This paper shows that the integer efficient frontier for capital budgeting problems can be computed using a modified Markowitz approach. It is shown that if the quadratic integer capital budgeting problem is reformulated as a parametric programming problem on the right-hand side of the return constraint, the problem indicated by Baum, Carlson, and Jucker [1] is eliminated. The traditional Markowitz approach is to formulate the problem as an objective function parametric programming problem. Baum, Carlson, and Jucker [1] show that the traditional approach cannot generally be applied to solve quadratic zero-one integer capital budgeting problems. They show that this approach may fail to identify some efficient points. The failure results from the objective function parametric programming approach. Even though the objective function and the right-hand side parametric programming approaches are equivalent in the continuous case, they may not be equivalent in the integer case.