The purpose of this paper is to provide a new framework for evaluating education programs that ration excess demand by admission lotteries when selective attrition cannot be ignored. Differential attrition arises in these models because students that lose the lottery are more likely to pursue educational options outside the school district. When students leave the district, important outcome variables are often not observed. We provide conditions that allow us to identify the proportions of latent student types and, thereby, the extent of differential attrition. We provide estimators of the proportions of the these latent types and their characteristics. We apply our methods to study the effectiveness of magnet programs in a mid-sized urban school district. We show that the students that cause the differential attrition have very different observed characteristics than the other students. Selective attrition implies that treatment effects are not point identified. We discuss how to construct informative bounds when point identification is not feasible. Our findings show that magnet programs help the district to attract and retain students. The bound estimates also demonstrate that magnet programs offered by the district improve behavioral outcomes such as offenses, timeliness, and attendance.

We study stochastic optimization problems with objective function given by the expectation of the maximum of two linear functions defined on the component random variables of a multivariate Gaussian distribution. We consider random variables that are arbitrarily correlated, and we show that the problem is NP-hard even if the space of feasible solutions is unconstrained. We exploit a closed-form expression for the objective function from the literature to construct a cutting-plane algorithm for a highly nonlinear function, which includes the evaluation of the cumulative distribution function and probability density function of a standard normal random variable with decision variables as part of the arguments. To exhibit the model’s applicability, we consider two featured applications. The first is daily fantasy sports, where the algorithm identifies entries with positive returns during the 2018–2019 National Football League season. The second is a special case of makespan minimization for two parallel machines and jobs with uncertain processing times; for the special case where the jobs are uncorrelated, we prove the equivalence between its deterministic and stochastic versions and show that our algorithm can deliver a constant-factor approximation guarantee for the problem. The results of our computational evaluation involving synthetic and real-world data suggest that our discretization and upper bounding techniques lead to significant computational improvements and that the proposed algorithm outperforms suboptimal solutions approaches. History: Andrea Lodi, Area Editor for Design & Analysis of Algorithms-Discrete. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.1259 .

We examine the characteristics of schools preferred by parents in New Orleans, Louisiana, where a “portfolio” of school choices is available. This tests the conditions under which school choice induces healthy competition between public and private schools through the threat of student exit. Using unique data from parent applications to as many as eight different schools (including traditional public, charter, and private schools), we find that many parents include a mix of public and private schools among their preferences, often ranking public schools alongside or even above private schools on a unified application. Parents who list both public and private schools show a preference for the private sector, all else equal, and are willing to accept lower school performance scores for private schools than otherwise equivalent public options. These parents reveal a stronger preference for academic outcomes than other parents and place less value on other school characteristics such as sports, arts, or extended hours. Public schools are more likely to be ranked with private schools and to be ranked higher as their academic performance scores increase.

In this paper, an analytical approach to National Football League (NFL) survival pools is investigated. This paper introduces into the literature NFL survival pools and presents optimization models for determining strategies. Computational results indicate that planning only partway through the season yields the highest survival probabilities, which dominate millions of randomly generated strategies.

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