Integration of machine learning and optimization models for a data-driven lot sizing problem with random yield

Abstract

We investigate a data-driven lot sizing problem under random yield. Motivated by semi-conductor production, we focus on the case where the random yield rate of a manufacturing process depends on a large number of features that can be observed before the lot sizing decision is made. Similarly, demand may also be random and may depend on a number of features. The lot sizing problem in this setting is challenging because the optimal decision depends on a large number of observed features for which there is limited data. To address this challenge, we propose estimation and optimization methods that combine tools from machine learning with tools from stochastic optimization. Using a publicly available data set for semi-conductor yield data and an additional synthetic data set, we compare the performance of different estimation and optimization approaches. We show that there is significant value of taking feature information into account for cost minimization. We also find that the best method for this problem combines tools from estimation with theoretical optimization properties of the random yield inventory problem.