Data, models and decisions for large-scale stochastic optimization problems

Abstract

Modern business decisions exceed human decision making ability: often, they are of a large scale, their outcomes are uncertain, and they are made in multiple stages. At the same time, firms have increasing access to data and models. Faced with such complex decisions and increasing access to data and models, how do we transform data and models into effective decisions? In this thesis, we address this question in the context of four important problems: the dynamic control of large-scale stochastic systems, the design of product lines under uncertainty, the selection of an assortment from historical transaction data and the design of a personalized assortment policy from data. In the first chapter, we propose a new solution method for a general class of Markov decision processes (MDPs) called decomposable MDPs. We propose a novel linear optimization formulation that exploits the decomposable nature of the problem data to obtain a heuristic for the true problem. We show that the formulation is theoretically stronger than alternative proposals and provide numerical evidence for its strength in multi-armed bandit problems. In the second chapter, we consider to how to make strategic product line decisions under uncertainty in the underlying choice model. We propose a method based on robust optimization for addressing both parameter uncertainty and structural uncertainty. We show using a real conjoint data set the benefits of our approach over the traditional approach that assumes both the model structure and the model parameters are known precisely. In the third chapter, we propose a new two-step method for transforming limited customer transaction data into effective assortment decisions. The approach involves estimating a ranking-based choice model by solving a large-scale linear optimization problem, and solving a mixed-integer optimization problem to obtain a decision. Using synthetic data, we show that the approach is scalable, leads to accurate predictions and effective decisions that outperform alternative parametric and non-parametric approaches. In the last chapter, we consider how to leverage auxiliary customer data to make personalized assortment decisions. We develop a simple method based on recursive partitioning that segments customers using their attributes and show that it improves on a "uniform" approach that ignores auxiliary customer information.