Optimizing the Capital Rationing Decision with Uncertain Returns

In this article, we develop a new optimization model for capital rationing with uncertain project returns. Our model maximizes the probability of meeting a pre-defined target return by selecting a feasible set of projects subject to budget constraints in multiple time periods. We employ a mixed-integer nonlinear algorithm recently developed in the optimization field to solve the resulting non-convex optimization problem to optimality. Our model and solution methods are tested and validated through a comprehensive computational experiment. Several managerial insights are obtained about the impact of available budget and target return on the optimal solutions. Notably, we have found that increasing target return may not necessarily result in increase of optimal total expected return of the selected projects. Our model and solution method offer a unified and computationally tractable approach to precisely quantify the tradeoff between project returned and risk.