Integration of machine learning and optimization models for data-driven decisions: Applications to lot sizing problem with random yield

In recent years, significant advancements in data collection, analytical techniques, and data-driven methodologies have transformed the landscape of addressing complex decision-making and production planning challenges. Building on these innovations, this thesis introduces novel data-driven approaches to manage uncertainty and variability across diverse applications. The core focus of this research is to leverage big data in uncertain environments to derive effective decision-making rules for policymakers by integrating machine learning techniques with optimization methods. The thesis encompasses three primary studies: decision-making problems under uncertainty, a single-stage lot sizing problem, and a multi-period lot sizing problem with random yields. First, we address a challenge in decision-making and classification problems where actions must be taken prior to observing an uncertain event, and incorrect decisions result in asymmetric costs. We propose some novel methods that integrate machine learning and optimization techniques to derive decision rules from limited observations, particularly in scenarios where frequent features have a significant impact on outcomes. Our methods aim to minimize the costs associated with incorrect decisions in both binary and multi class classification problems. Experimental results using publicly available data sets show that our approaches significantly outperform traditional benchmarks, reducing costs by up to 95% with respect to naive benchmarks. Second, 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. Finally, we extend the single-period lot sizing problem to a multi-period setting. Given the realized variability in yields across periods, there are numerous potential scenarios by the end of the production horizon. The main objective is to develop a data-driven rule for determining optimal lot sizes under unknown yield distributions, unlike conventional approaches in the literature that assume known distributions. This rule aims to minimize the expected underage and overage costs at the end of the final period plus holding cost of intermediate periods and variable production cost while ensuring that total customer demand is met. This study advances the literature by introducing reinforcement learning to address the multi-period lot sizing problem with stochastic yields and unknown distribution for the first time. To assess the effectiveness of our approach, we compare results against established static and dynamic optimization methods. Our method provides a flexible and adaptive framework for decision-making in complex production systems characterized by stochastic yields.