Smart Predict-then-Optimize for Two-Stage Linear Programs with Side Information

Abstract

We study two-stage linear programs with uncertainty in the right-hand side in which the uncertain parameters of the problem are correlated with a variable called the side information, which is observed before an action is made. We propose an approach in which a linear regression model is used to provide a point prediction for the uncertain parameters of the problem. We use an approach called smart predict-then-optimize. Rather than minimizing a typical loss function for regression, such as squared error, we approximately minimize the objective value of the resulting solutions to the optimization problem. We conduct computational tests that compare our method with other approaches for optimization problems with side information. The results indicate that our method can provide better objective values in situations where the true model is reasonably close to a linear model. Although the procedure we propose requires a longer time for fitting than existing methods, it requires less time to produce a decision for each given observation of the side information. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoo.2023.0088 .