A value-at-risk, or quantile, is widely used as an appropriate investment selection measure for risk-conscious decision makers. We present two quantile-based sequential procedures—with and without consideration of equivalency between alternatives—for selecting the best alternative from a set of simulated alternatives. These procedures asymptotically guarantee a user-defined target probability of correct selection within a prespecified indifference zone. Experimental results demonstrate the trade-off between the indifference-zone size and the number of simulation iterations needed to render a correct selection while satisfying a desired probability of correct selection.

We propose two sequential, indifference-zone procedures for the comparison of simulated systems. Comparisons and selection of the best system are based on the mean and variance of a performance metric estimated by simulation. The mean represents the central tendency while the variance is the surrogate for the system’s inherent systematic risk. The first procedure identifies the system(s) with the largest expected value and smallest variance. The second procedure uses the variance of a reference system as a risk threshold, and selects the system with the largest mean from among those with an acceptable level of risk not above the threshold. Numerical experiments demonstrate the validity and efficacy of the proposed procedures. The online appendix is available at https://doi.org/10.1287/ijoc.2018.0808 .

Foundations, models, and algorithms are provided for identifying optimal mean and variance bounds of an ill-specified random variable. A random variable is ill-specified when at least one of its possible realizations and/or its respective probability mass is not restricted to a point but rather belongs to a set or an interval. We show that a nonexhaustive sensitivity-analysis approach does not always identify the optimal bounds. Also, a procedure for determining the mean and variance bounds of an arithmetic function of ill-specified random variables is presented. Estimates of pairwise correlation among the random variables can be incorporated into the function. The procedure is illustrated in the context of a case study in which exposure to contaminants through the inhalation pathway is modeled.

Evidence theory is a powerful tool for modeling ambiguity. Ambiguity is prevalent in the description of most alternatives and it arises from the existence of many-to-many relations between outcomes and probabilities of outcomes. We present procedures for determining bounds for the mean and variance of alternatives under conditions of ambiguity. The mean and variance, for example, can be used for identifying the set of non-dominated alternatives.