In many managerial situations it is important to consider both risk and reward simultaneously. This is a challenging task using standard techniques that are applied for solving sequential stochastic optimization problems since these techniques are designed to consider only one objective at a time—either maximizing reward or minimizing risk. In applications such as operational decisions for start-ups, this can be particularly restricting, since managers need to make trade-offs between profitability driven growth and the risk of bankruptcy. We extend in several ways prior work that has addressed the inventory issue for start-ups to minimize the risk of bankruptcy. The primary contribution of this paper is to present a novel approach to track mean as well as variance of a set of policies in a dynamic stochastic programming model and using the mean-variance solutions in a simple heuristic for creating efficient risk-reward frontiers. This is a challenging task from an implementation standpoint, since this requires carrying information on both risk and reward simultaneously for each state, which standard stochastic programming solution methods are not designed to do. We also illustrate the use of our methodology in a richer model of start-up operations where, in addition to inventory issues, advertising decisions are also considered. 
Analyzing operational risk-reward trade-offs for start-ups