Prescriptive analytics in operations problems : a tree ensemble approach

Abstract

The main contributions of this thesis concern addressing challenges in the field of prescriptive optimization, and how machine learning techniques can be incorporated into solving data-driven operational optimization problems. In chapter 2, we provide a data-driven study of the secondary ticket market. In particular we are primarily concerned with accurately estimating price sensitivity for listed tickets. We propose a semi-parametric model for measuring heterogeneous treatment effects using the concept of orthogonalization in the classification setting, and derive a novel loss function which can be solved using a range of off-the-shelf machine learning methods. Over a wide range of synthetic data experiments, we show how this approach beats state-of-the-art machine learning and causal inference methods for estimating treatment effects in classification tasks.

In chapter 3, we show how to solve optimization problems with random forest objective functions and general polyhedral constraints. We show how to formulate this problem using MIO techniques and show this formulation can be decomposed and solved iteratively using Pareto-optimal Benders cuts. We also provide analytical guarantees on an approach that approximates a large scale random forest optimization problem by optimizing over a smaller forest, and develop heuristics based on ideas from cross validation. In chapter 4, we study a new problem where nurse practitioners need to be dynamically routed to patients' houses as service requests are received. We show how to solve using Approximate Dynamic Programming and develop methods to solve ADP's with combinatorial action spaces and non-linear cost-to-go functions approximated using a tree or tree ensemble approximation.

In chapter 5, we propose a Markov Decision Process (MDP) model for the tramp shipping that captures the dynamic and stochastic nature of spot cargo availability. We propose a novel methodology for solving this MDP in a tractable way, by introducing a ranking algorithm which is equivalent to solving the DP. We show that our ranking algorithm outperforms several benchmarks and the average performance of ships operating on the spot market in practice by between 4% and 32%.