Practical Considerations When Using Predictive Models Within Optimization Problems: Issues, Options, and Applications

Abstract

This research highlights important practical considerations when incorporating predictive models within prescriptive optimization models. We provide a scholarly research stream and suggest industry best practices by identifying novel modeling considerations that can reduce decision support risk. Specifically, we provide a practical two-stage predictive to prescriptive decision support modeling framework where the analyst creates a model for predicting some quantity in the first stage, then optimizes some business performance measure in the second stage using the estimated predictive model from the first stage.

We propose and demonstrate novel methods to detect and account for data regions in the decision model formulation where the predictive model is not supported (or is weakly supported) by the data, unwittingly leading to more risky business decisions. We provide examples where the predictive model features are numeric, which are most common in prediction-type problems, as well as optimization problems where decision variables are real-numbered variables.

We posit that current practices integrating a predictive model into a prescriptive model solution are potentially leading to risky decision recommendations. We provide an example from carpet manufacturing focused on achieving a specified quality level along with financial cost considerations. In this real-world case, the prediction problem contains features that are controllable decisions in the decision model.

We demonstrate how the modeler could effectively consider decisions that fall "inside the box" of historical data. Subsequently, we provide a novel approach to identify and assess solutions "outside the box" of historical solutions, which might occur from a new process, product, or situation where the decision maker wants to take risker decisions for the chance of a potentially greater outcome. Next, we demonstrate how the decision maker may want to "push the envelope" to solutions that exceed the historical observations in a structured fashion.

Lastly, we summarize our findings and identify new avenues for research when predictive models are integrated within optimization models.