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Problem definition: We present a data-driven study of the secondary ticket market. In particular, we are primarily concerned with accurately estimating price sensitivity for listed tickets. In this setting, there are many issues including endogeneity, heterogeneity in price sensitivity for different tickets, binary outcomes, and nonlinear interactions between ticket features. Our secondary goal is to highlight how this estimation can be integrated into a prescriptive trading strategy for buying and selling tickets in an active marketplace. Academic/practical relevance: We present a novel method for demand estimation with heterogeneous treatment effect in the presence of confounding. In practice, we embed this method within an optimization framework for ticket reselling, providing the ticket reselling platform with a new framework for pricing tickets on its platform. Methodology: We introduce a general double/orthogonalized machine learning method for classification problems. This method allows us to isolate the causal effects of price on the outcome by removing the conditional effects of the ticket and market features. Furthermore, we introduce a novel loss function that can be easily incorporated into powerful, off-the-shelf machine learning algorithms, including gradient boosted trees. We show how, in the presence of hidden confounding variables, instrumental variables can be incorporated. Results: Using a wide range of synthetic data sets, we show this approach beats state-of-the-art machine learning and causal inference approaches for estimating treatment effects in the classification setting. Furthermore, using National Basketball Association ticket listings from the 2014–2015 season, we show that probit models with instrumental variables, previously used for price estimation of tickets in the resale market, are significantly less accurate and potentially misspecified relative to our proposed approach. Through pricing simulations, we show our proposed method can achieve an 11% return on investment by buying and selling tickets, whereas existing techniques are not profitable. Managerial implications: The knowledge of how to price tickets on its platform offers a range of potential opportunities for our collaborator, both in terms of understanding sellers on their platform and in developing new products to offer them. History: This paper has been accepted as part of the 2019 Manufacturing & Service Operations Management Practice-Based Research Competition. Funding: This work was supported by the National Science Foundation [Grant CMMI-1563343]. Supplemental Material: The online appendices are available at https://doi.org/10.1287/msom.2021.1065 .

This paper is motivated from a collaboration with a start-up delivering on-demand health care services. In this setting, nurse practitioners need to be dynamically routed to patients' houses as service requests are received. We solve this problem using approximate dynamic programming and machine learning techniques. At every stage, an optimization problem needs to be solved to assign nurse practitioners to patients. We capture the future cost of having nurse practitioners positioned at certain locations around the city by estimating a cost-to-go function. Many previous approaches treat the cost-to-go function as a black box, which requires the enumeration of all possible actions to make a routing decision at each stage. This is an intractable problem in the reoptimization setting. Our approach overcomes this issue by approximating the cost-to-go function using a tree or tree ensemble, and leverages formulation techniques from Mixed Integer Optimization to solve the optimization problem at each stage sufficiently fast. Furthermore, this approach has the advantage of being more accurate relative to separable approximations used in the literature. We also apply this approach to several other online optimization problems in operations management which can be modeled through an underlying optimization formulation that needs to be solved at each stage, and show improvements relative to state-of-the-art methods.

We study the problem of optimizing a tree-based ensemble objective with the feasible decisions lie in a polyhedral set. We model this optimization problem as a Mixed Integer Linear Program (MILP). We show this model can be solved to optimality efficiently using Pareto optimal Benders cuts. For large problems, we consider a random forest approximation that consists of only a subset of trees and establish analytically that this gives rise to near optimal solutions by proving analytical guarantees. The error of the approximation decays exponentially as the number of trees increases. Motivated from this result, we propose heuristics that optimize over smaller forests rather than one large one. We present case studies on a property investment problem and a jury selection problem. We show this approach performs well against benchmarks, while providing insights into the sensitivity of the algorithm's performance for different parameters of the random forest.