research

Assignment mechanisms for many-to-one matching markets with preferences revolve around the key concept of stability. Using school choice as our matching market application, we introduce the problem of jointly allocating a school capacity expansion and finding the best stable allocation for the students in the expanded market. We theoretically analyze the problem, focusing on the trade-off behind the multiplicity of student-optimal assignments, the incentive properties, and the problem’s complexity. Due to the impossibility of efficiently solving the problem with classical methods, we generalize existent mathematical programming formulations of stability constraints to our setting, most of which result in integer quadratically-constrained programs. In addition, we propose a novel mixed-integer linear programming formulation that is exponentially-large on the problem size. We show that its stability constraints can be separated in linear time, leading to an effective cutting-plane method. We evaluate the performance of our approaches in a detailed computational study, and we find that our cutting-plane method outperforms MIP solvers applied to the formulations obtained by extending existing approaches. We also propose two heuristics that are effective for large instances of the problem. Finally, we use the Chilean school choice system data to demonstrate the impact of capacity planning under stability conditions. Our results show that each additional school seat can benefit multiple students. Moreover, our methodology can prioritize the assignment of previously unassigned students or improve the assignment of several students through improvement chains. These insights empower the decision-maker in tuning the matching algorithm to provide a fair application-oriented solution.

We study the behavioral effects of process automation on human workers interacting with automated tasks. We introduce a stylized model with two workers who complete their tasks sequentially, working toward a joint project to obtain a fixed payment plus a variable bonus that depends on how early the project is completed. We show that workers will complete their tasks as soon as possible if the early completion bonus is high enough. Following the literature, we hypothesize that workers will suboptimally delay project completion. In addition, we predict that automation will alleviate this problem by reducing the uncertainty about task completion, leading to a higher project completion rate and worker productivity. To test these predictions, we conduct an experiment replicating the theoretical model, varying whether a worker collaborates with a coworker or robot. First, we find that workers largely deviate from the optimal policy, as they take longer than what the theory prescribes to complete their tasks or do not complete the project. Second, process automation increases the project completion rate and reduces the project completion time, confirming the benefits of process automation. Interestingly, workers who collaborate with robots take longer to complete their tasks, contradicting our initial hypothesis that process automation has a positive effect on the productivity of human workers. An additional treatment shows that the reduced uncertainty derived from process automation cannot be leveraged to improve workers’ productivity in the same way as in a human-human setting and that social preferences are an important driver of this result.

We study settings in which a centralized clearinghouse organizes a market where agents sequentially search among different options under competition. We introduce a stylized model of sequential search, whereby agents are exogenously prioritized by the clearinghouse and must decide when to stop their search to maximize the chosen option’s value. We focus on the effect of two market design choices that are motivated in the context of kidney transplants: (i) transparency, i.e., whether agents know their priority relative to the other agents searching; and (ii) the mechanism to collect decisions, namely, whether all agents make their decisions simultaneously or sequentially in decreasing order of priority. In each case, we characterize the optimal policy, which defines a sequence of thresholds that determine when each agent should accept an option depending on the information available. We find that, although the mechanism to collect agents’ decisions does not affect the optimal policy, providing information about agents’ priorities reduces the overall welfare and fairness of the allocation. We design and conduct a lab experiment that replicates our theoretical model to test these predictions. We find that agents significantly deviate from their corresponding optimal policies. Moreover, we find that the mechanism has a significant effect on their decisions, due primarily to two drivers: (i) saliency of competition and (ii) frustration in regard to accepting but not obtaining an option. Finally, we find that the benefits of opaqueness do not translate to practice, mainly because agents do not incorporate relevant information about the amount of competition.

We study how online platforms can leverage the behavioral considerations of their users to improve their assortment decisions. Motivated by dating markets, we consider a platform that must select an assortment of potential partners to show to each user in each day. Users can like/not like each potential partner presented to them, and a match is formed if two users (eventually) like each other. The platform’s objective is to maximize the expected number of matches in a time horizon. Using data from a dating company, we estimate the main inputs of our model, namely, the like and log in probabilities, and find that the number of matches obtained in the recent past has a negative effect on the like behavior of users. Leveraging this finding, we propose a family of heuristics that decide the assortment to show to each user on each day. We show that these heuristics considerably improve the number of matches generated by the platform in markets simulated based on the real data and further identify the sources of improvement. Finally, we implemented a field experiment that confirms that the improvement achieved by our algorithms also translates into our partner’s platform.

Centralized school admission mechanisms are an attractive way of improving social welfare and fairness in large educational systems. In this paper we report the design and implementation of the newly established school choice mechanism in Chile, where over 274,000 students applied to more than 6,400 schools. The Chilean system presents unprecedented design challenges that make it unique. On the one hand, it is a simultaneous nationwide system, making it one of the largest school admission problems worldwide. On the other hand, the system runs at all school levels, from Pre-K to 12th grade, raising at least two issues of outmost importance; namely, the system needs to guarantee their current seat to students applying for a school change, and the system has to favor the assignment of siblings to the same school. As in other systems around the world, we develop a model based on the celebrated Deferred Acceptance algorithm. The algorithm deals not only with the aforementioned issues, but also with further practical features such as soft-bounds and overlapping types. In this context we analyze new stability definitions, present the results of its implementation and conduct simulations showing the benefits of the innovations of the implemented system.

In this paper we present the design and implementation of a new system to solve the Chilean college admissions problem. We develop an algorithm that obtains all stable allocations when preferences are not strict and when all tied students in the last seat of a program (if any) must be allocated. We use this algorithm to determine which mechanism was used to perform the allocation, and we propose a new method to incorporate the affirmative action that is part of the system and correct the inefficiencies that arise from having double-assigned students. By unifying the regular admission with the affirmative action, we have improved the allocation of approximately 3% of students every year since 2016. From a theoretical standpoint, we show that some desired properties, such as strategy-proofness and monotonicity, cannot be guaranteed under flexible quotas. Nevertheless, we show that the mechanism is strategy-proof in the large, and therefore truthful reporting is approximately optimal.

Motivated by recent initiatives to increase transparency in procurement, we study the effects of disclosing information about previous purchases in a setting where an organization delegates its purchasing decisions to its employees. When employees can use their own discretion-which may be influenced by personal preferences—to select a supplier, the incentives of the employees and the organization may be misaligned. Disclosing information about previous purchasing decisions made by other employees can reduce or exacerbate this misalignment, as peer effects may come into play. To understand the effects of transparency, we introduce a theoretical model that compares employees’ actions in a setting where they cannot observe each other’s choices, to a setting where they can observe the decision previously made by a peer before making their own. Two behavioral considerations are central to our model: that employees are heterogeneous in their reciprocity towards their employer, and that they experience peer effects in the form of income inequality aversion towards their peer. As a result, our model predicts the existence of negative spillovers as a reciprocal employee is more likely to choose the expensive supplier (which gives him a personal reward) when he observes that a peer did so. A laboratory experiment confirms the existence of negative spillovers and the main behavioral mechanisms described in our model. A surprising result not predicted by our theory, is that employees whose decisions are observed by their peers are less likely to choose the expensive supplier than the employees in the no transparency case. We show that observed employees’ preferences for compliance with the social norm of "appropriate purchasing behavior" explain our data well.

We describe how to build a stochastic programming model from scratch, starting with the formulation of a deterministic prototype and then progressively incorporating uncertainty. We use a stylized harvesting management problem to illustrate the approach. The deterministic prototype is a linear program that determines multi-period harvesting schedules. We then extend this model to handle uncertainty in growth and prices, resulting in a dynamic stochastic program. We show how to generate scenarios using time series methods and discuss how to solve the resulting stochastic program. The paper is intended as a tutorial for practitioners who want to understand the modeling and computational challenges involved in stochastic programming.

We consider the problem of generating scenarios for multistage stochastic programs when historical data is limited. We focus on the special case where data is available for aggregate quantities but not for individual components, and propose a method that combines historical aggregate data with expert opinion about the components. The method constructs scenarios that are consistent with the aggregate data while respecting the expert’s beliefs about the individual components. We illustrate the approach using electricity load forecasting, where aggregate load data is plentiful but data for individual customer segments may be limited. The method can be applied to other contexts where limited data is a constraint, such as forecasting demand for new products or estimating the impact of rare events.

We propose a framework for modeling commodity prices that captures key stylized facts observed in commodity markets, including mean reversion, stochastic volatility, and occasional price spikes. The model uses a regime-switching process to represent different market states (normal, high volatility, and spike) and allows for transitions between states. We develop estimation procedures based on maximum likelihood and show how to apply them to historical price data. The model is flexible enough to capture the diverse behavior of different commodities while being parsimonious enough to be estimated with limited data. We illustrate the approach using copper and oil price data and show that the model fits the data well and produces realistic scenarios for use in stochastic optimization.

The unit commitment problem determines which generating units to start up and shut down, and how much power to generate from each unit, to meet anticipated electricity demand at minimum cost while respecting operational constraints. Renewable energy sources introduce significant uncertainty in both supply and demand, making stochastic unit commitment increasingly important. However, solving stochastic unit commitment at the scale of real power systems is computationally challenging. This paper, the first in a two-part series, focuses on scenario generation for load forecasting. We develop methods to generate scenarios that capture the spatial and temporal correlations in electricity demand across multiple regions and time periods. The scenarios are designed to be used in large-scale stochastic unit commitment models. We validate the approach using data from a real power system and show that the generated scenarios accurately represent the statistical properties of the load process while being computationally tractable for use in optimization.

We study the impact of including high school grades (GPA) in the Chilean university admission process, which was previously based solely on standardized test scores. Using detailed administrative data, we analyze how different weighting schemes for GPA and test scores affect the composition of admitted students and their subsequent academic performance. We find that including GPA increases socioeconomic diversity among admitted students, as GPA is less correlated with family income than test scores. Moreover, GPA is a strong predictor of college success, even after controlling for test scores. We simulate alternative admission policies with different weights on GPA and show that increasing the weight on GPA would admit more students from disadvantaged backgrounds without sacrificing academic quality. Our findings inform ongoing debates about fair and effective college admissions policies in Chile and other countries facing similar equity-efficiency trade-offs.

We present the first implementation of stochastic unit commitment at independent system operator (ISO) scale. The unit commitment problem determines the on/off status and generation levels of power plants to meet electricity demand at minimum cost. Traditional approaches solve this problem deterministically, potentially leading to inefficient or infeasible solutions when faced with uncertain renewable generation and load. We develop a scalable stochastic programming framework that accounts for uncertainty through scenario trees and can handle problem instances with hundreds of generators and thousands of time periods. The framework combines progressive hedging decomposition with specialized heuristics and parallelization strategies to solve large-scale problems in reasonable time. We test the approach on realistic problems based on actual ISO systems and show that the stochastic solution provides significant operational and economic benefits compared to deterministic approaches, including reduced reserve costs and improved reliability.