Application of chance-constrained programming to capital rationing problems with asymmetrically distributed cash flows and available budget

Most applications of chance-constrained programming are based on either normally distributed random variables or random variables with symmetric distributions such as uniform, which can be approximated rather accurately by the normal distribution. In this paper we study pure capital rationing with selection of the best project mix when cash flows and available budget are random variables with asymmetric distributions. We show that solutions obtained by chance-constrained programming using normality approximation for asymmetrically distributed random variables fail to satisfy budget constraints when cash outflows are skewed to the left, indicating that realized cash outflows are more likely to be higher than expected.