A deficiency of prescriptive analytics—No perfect predicted value or predicted distribution exists

Researchers and industrial practitioners are now interested in combining machine learning (ML) and operations research and management science to develop prescriptive analytics frameworks. By and large, a single value or a discrete distribution with a finite number of scenarios is predicted using an ML model with an unknown parameter; the value or distribution is then fed into an optimization model with the unknown parameter to prescribe an optimal decision. In this paper, we prove a deficiency of prescriptive analytics, i.e., that no perfect predicted value or perfect predicted distribution exists in some cases. To illustrate this phenomenon, we consider three different frameworks of prescriptive analytics, namely, the predict-then-optimize framework, smart predictthen- optimize framework and weighted sample average approximation (w-SAA) framework. For these three frameworks, we use examples to show that prescriptive analytics may not be able to prescribe a full-information optimal decision, i.e., the optimal decision under the assumption that the distribution of the unknown parameter is given. Based on this finding, for practical prescriptive analytics problems, we suggest comparing the prescribed results among different frameworks to determine the most appropriate one.