### About

I am currently assistant professor at the department of Industrial Engineering in University of Chile (UCH). I graduated from a PhD in – Operations Research at MIT. Previously, I obtained a Master in Operations Management and an undergraduate degree in Industrial Engineering at University of Chile.

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**Research**

My research focuses on problems in the intersection of operations research and data analytics, in applied fields of study such as revenue management, political science, services, and racing.

**Publications**

**1. Optimizing Pit Stop Strategies in Formula 1 with Dynamic Programming and Game Theory**

Aguad, F., and Thraves, C.*To come in European Journal of Operations Research (2024)*

Optimization of pit stop strategies in motorsports is not trivial. Most existing studies neglect competition, or account for it using simulation or historical data, but not in a game theory sense. In this work, we present a model, based on Formula 1, in which two drivers optimize their pit stop strategies. Each car decides at each lap whether to continue on-track, or to take a pit stop to change tires to one of the three tire compounds available. Since the drivers’ decisions affect each other due to interactions such as overtaking, the problem is formulated as a zero-sum feedback Stackelberg game using Dynamic Programming, in which in each lap the race leader (follower) decides first (second). In addition, drivers decide simultaneously their starting tire compounds. The formulation allows for the inclusion of uncertain events, such as yellow flags, or randomness in lap times. We show the existence of the game equilibrium, and provide an algorithm to find it. Then, we solve numerical instances of the problem with hundreds of millions of states. We observe how drivers’ different objective functions induce different race strategies. In particular, if players maximize the probability of winning, instead of the time-gap with their opponent, their actions tend to be more risk taking. Our instances show that a strategic driver who faces another who ignores competition, increases the winning odds by more than 15% compared to when both race strategically. Finally, yellow flags tend to increase the winning chances of the driver with the worst performance.

##### 2. Analytics Saves Lives During the COVID-19 Crisis in Chile

*Informs Journal on Applied Analytics*

*(2023)*

During the COVID-19 crisis, the Chilean Ministry of Health and the Ministry of Sciences, Technology, Knowledge and Innovation partnered with the Instituto Sistemas Complejos de Ingeniería (ISCI) and the telecommunications company ENTEL, to develop innovative methodologies and tools that placed operations research (OR) and analytics at the forefront of the battle against the pandemic. These innovations have been used in key decision aspects that helped shape a comprehensive strategy against the virus, including tools that (1) provided data on the actual effects of lockdowns in different municipalities and over time; (2) helped allocate limited intensive care unit (ICU) capacity; (3) significantly increased the testing capacity and provided on-the-ground strategies for active screening of asymptomatic cases; and (4) implemented a nationwide serology surveillance program that significantly influenced Chile’s decisions regarding vaccine booster doses and that also provided information of global relevance. Significant challenges during the execution of the project included the coordination of large teams of engineers, data scientists, and healthcare professionals in the field; the effective communication of information to the population; and the handling and use of sensitive data. The initiatives generated significant press coverage and, by providing scientific evidence supporting the decision making behind the Chilean strategy to address the pandemic, they helped provide transparency and objectivity to decision makers and the general population. According to highly conservative estimates, the number of lives saved by all the initiatives combined is close to 3,000, equivalent to more than 5% of the total death toll in Chile associated with the pandemic until January 2022. The saved resources associated with testing, ICU beds, and working days amount to more than 300 million USD.

##### 3. On the Optimization of Pit Stop Strategies via Dynamic Programming

Carrasco, F., and Thraves, C.*Central European Journal of Operations Research **(2022)*

Pit stops are a key element of racing strategy in several motor sports. Typically, these stops involve decisions such as in which laps to stop, and which type of tire, of three possible compounds, to set at each of these stops. There are several factors that increase the complexity of the task: the impact of lap times depending on the tire compound, the wear of the tires, unexpected events on the track such as safety cars and the weather, among others. This work presents a Dynamic Programming formulation that addresses the pit-stop strategy problem in order to optimize the laps in which to stop, and the tire changes that minimize the total race time. We show the relative performance of the optimal strategies for starting with tires of different compounds with different yellow-flag scenarios. Then, we extend the Dynamic Program (DP) to a Stochastic Dynamic Programming (SDP) formulation that incorporates random events such as yellow flags or rainy weather. We are able to visualize and compare these optimal pit-stop strategies obtained with these models in different scenarios. We show that the SDP solution, compared to the DP solution, tends to delay pit stops in order to benefit from a possible yellow flag. Finally, we show that the SDP outperforms the DP, especially in races in which yellow flags are likely to be waved more frequently.

##### 4. On the Resource Allocation for Political Campaigns

Morales, S., and Thraves, C.*Production and Operations Management (2021)*

In an election campaign, candidates must decide how to optimally allocate their efforts/resources optimally among the regions of a country. As a result, the outcome of the election will depend on the players’ strategies and the voters’ preferences. In this work, we present a zero-sum game where two candidates decide how to invest a fixed resource in a set of regions, while considering their sizes and biases. We explore the two voting systems, the Majority System (MS) and the Electoral College (EC). We prove equilibrium existence and uniqueness under MS in a deterministic model; in addition, their closed form expressions are provided when fixing the subset of regions and relaxing the non-negative investing constraint. For the stochastic case, we use Monte Carlo simulations to compute the players’ payoffs. For the EC, given the lack of equilibrium in pure strategies, we propose an iterative algorithm to find equilibrium in mixed strategies in a subset of the simplex lattice. We illustrate numerical instances under both election systems, and contrast players’ equilibrium strategies. We show that polarization induces candidates to focus on larger regions with negative biases under MS, whereas candidates concentrate on swing states under EC. Finally, we calibrate the analyzed models with real data from the US 2020 presidential election.

**5. On a Variation of Two-part Tariff Pricing of Services: A Data-Driven Approach**

Perakis, G., and Thraves C.*Manufacturing and Service Operations Management (2021)*

We present a data-driven pricing problem motivated from our collaboration with a satellite service provider. In particular, we study a variant of the two-part tariff pricing scheme. The firm offers a set of data plans consisting of a bundle of data at a fixed price plus additional data at a variable price. Most literature on two-part tariff problems focuses on models that assume full information. However, little attention has been devoted to this problem from a data-driven perspective without full information. One of the main challenges when working with data comes from missing data. First we develop a new method to address the missing data problem, which comes from different sources: (i) the number of unobserved customers, (ii) customers’ willingness to pay (WTP), and (iii) demand from unobserved customers. We introduce an iteration procedure to maximize the likelihood by combining the EM algorithm with a gradient ascent method. We also formulate the pricing optimization problem as a dynamic program (DP) using a discretized set of prices. From applying SAA, the DP obtains a solution within 3.8% of the optimal solution of the sampled instances, on average, and within 18% with 95% confidence from the optimal solution of the exact problem. By extending the DP formulation, we show it is better to optimize on prices rather than bundles, obtaining revenues close to optimizing jointly on both. The sensitivity analysis of the problem parameters is key for decision-makers to understand the risks of their pricing decisions. Indeed, assuming a higher variability of customers’ WTP induces higher revenue risks. In addition, revenues are barely (highly) sensitive to the customers’ assumed WTP variability when considering a high (low) number of unobserved customers. Finally, we extend the model to incorporate price dependent consumption.

**6. Consumer Surplus Under Demand Uncertainty**

Coehn, M., Perakis, G., and Thraves, C.*Production and Operations Management (2021)*

Consumer Surplus is traditionally defined for the case where demand is a deterministic function of the price. However, demand is usually stochastic and hence stock-outs can occur. Policy makers who consider the impact of different regulations on Consumer Surplus often ignore the impact of demand uncertainty. We present a definition of the Consumer Surplus under stochastic demand. We then use this definition to study the impact of demand and supply uncertainty on consumers in several cases (additive and multiplicative demand noise). We show that, in many cases, demand uncertainty hurts consumers. We also derive analytical bounds on the ratio of the Consumer Surplus relative to the deterministic setting under linear demand. Our results suggest that ignoring uncertainty may severely impact the Consumer Surplus value.

**7. The effect of correlation and false negatives in pool testing strategies for COVID-19**

Basso, J. L., Salinas, V., Saure, D., Thraves, C., and Yankovic, N. *Health Care Management Science (2021)*

During the current COVID-19 pandemic, active testing has risen as a key component of many response strategies around the globe. Such strategies have a common denominator: the limited availability of diagnostic tests. In this context, pool testing strategies have emerged as a means to increase testing capacity. The efficiency gains obtained by using pool testing, derived from testing combined samples simultaneously, vary according to the spread of the SARS-CoV-2 virus in the population being tested. Motivated by the need for testing closed populations, such as long-term care facilities (LTCFs), where significant correlation in infections is expected, we develop a probabilistic model for settings where the test results are correlated, which we use to compute optimal pool sizes in the context of two-stage pool testing schemes. The proposed model incorporates the specificity and sensitivity of the test, which makes it possible to study the impact of these measures on both the expected number of tests required for diagnosing a population and the expected number and risk of false negatives. We use our experience implementing pool testing in LTCFs managed by SENAMA (Chile’s National Service for the Elderly) to develop a simulation model of contagion dynamics inside LTCFs, which incorporates testing and quarantine policies implemented by SENAMA. We use this simulation to estimate the correlation in infections among tested samples when following SENAMA’s testing guidelines. Our results show that correlation estimates are high in settings representative of LTCFs, which validates the use of the proposed model for incorporating correlation in determining optimal pool sizes for pool testing strategies. Generally, our results show that settings in which pool testing achieves efficiency gains, relative to individual testing, are likely to be found in practice. Moreover, the results show that incorporating correlation in the analysis of pool testing strategies both improves the expected efficiency and broadens the settings in which the technique is preferred over individual testing.

##### 8. Contingent Preannounced Pricing Policies with Strategic Consumers

Correa, J. R., Montoya, R., and Thraves C.*Operations Research (2016)*

Companies in diverse industries must decide the pricing policy of their inventories over time. This decision becomes particularly complex when customers are forward looking and may defer a purchase in the hope of future discounts and promotions. With such uncertainty, many customers may end up not buying or buying at a significantly lower price, reducing the firm’s profitability. Recent studies show that a way to mitigate this negative effect caused by strategic consumers is to use a posted or preannounced pricing policy. With that policy, firms commit to a price path that consumers use to evaluate their purchase timing decision. In this paper, we propose a class of preannounced pricing policies in which the price path corresponds to a price menu contingent on the available inventory. We present a two-period model, with a monopolist selling a fixed inventory of a good. Given a menu of prices specified by the firm and beliefs regarding the number of units to be sold, customers decide whether to buy upon arrival, buy at the clearance price, or not to buy. The firm determines the set of prices that maximizes revenues. The solution to this problem requires the concept of equilibrium between the seller and the buyers that we analyze using a novel approach based on ordinary differential equations. We show existence of equilibrium and uniqueness when only one unit is on sale. However, if multiple units are offered, we show that multiple equilibria may arise. We develop a gradient-based method to solve the firm’s optimization problem and conduct a computational study of different pricing schemes. The results show that under certain conditions the proposed contingent preannounced policy outperforms previously proposed pricing schemes. The source of the improvement comes from the use of the proposed pricing policy as a barrier to discourage strategic waiting and as a discrimination tool for those customers waiting. testing.

**Working Papers**

**1. **A Fast Ecological Inference Algorithm for the R×C case

Thraves C. and Ubilla P.

It is known the difficulty to address the R×C ecological inference problem. In the past, researchers have approached this problem from various angles, including parametric probability models, entropy-maximization, and mathematical programming. In this work, the ecological inference problem is based in an election context where at each ballot box we observe candidates’ votes and the number of voters from each demographic groups. Employing a non-parametric model, we use the EM algorithm to maximize the likelihood given the observed data. We show that the M-Step can be solved in a closed-form solution, while the E-Step requires an exponential number of steps to be solved exactly. To address this, we evaluate several approximation methods to compute the E-Step in polynomial time. Through simulated instances, we observe that the resulting estimations of probabilities using these methods are very close to the real values. Furthermore, some of these methods exhibit running times of less than a thousandth of a second. Then, we introduce a methodology to perform group aggregation in cases where there are insufficient samples, i.e., ballot boxes in this case, to accurately estimate voting probabilities. We apply this technique to the Chilean Presidential election of 2021, obtaining estimates of voting probabilities with bounded errors for each resulting group aggregation within each district. We note that, in general, the number of aggregated groups obtained increases with the number of ballot boxes. Finally, we show how these methods can also be used to detect outlier ballot boxes.

**2. **Parametric Estimation Under Diffuse Observations: An Application On Election Polls

Morales S. and Thraves C.

Most techniques to estimate distributions consider observations as a single-point. However, there are several applications in which observations have some degree of uncertainty which is known by the researcher. We propose a method in which Maximum Likelihood Estimation (MLE) methods can incorporate this noise dimension of the observed data. In this context, classical MLE can be seen as a particular case. In this more general setting, we show how the likelihood can be written as a product integral, while the log-likelihood can be expressed as a tractable expression, i.e., a function with sums and integrals. We show how the introduced technique can be used as a novel methodology to aggregate polls for election forecasting. In addition, this can also account for state biases and house effects, while also consider a time-decay weight factor for polls depending on how afar are these with respect to the prediction date. We apply the presented method in the US President Election of 2020, in which polls at each state are used to estimate the probability distribution of votes during the election period. In particular, each poll’ distribution, due to its sampling error, is considered as a noisy observation represented by a known probability density function. States biases and house effects are estimated from the US presidential election of 2016. The results obtained by the proposed method outperforms the ones obtained with a classical MLE in terms of achieving a higher log-likelihood value. In addition, the distributions estimated by the former method have more variability than those obtained with the latter one. The proposed framework can be applied to several other applications in which observations can be considered as known probability distribution.

**3. Own Brand: Who benefits from it?**

Thraves C.*Submitted*

Own brand has been increasing on the last years in several product categories. This work analyses the impact of the introduction of own brand products. We introduce a modelling framework capturing suppliers, retailers, and consumption decisions under a non-own brand as well as with. An IP is formulated to provide a certificate that complex analytical expressions are non-negative. We then study the impact on the social welfare and all their agents as a result of the introduction of own-brand products. We conclude that own brand products are not beneficial for competing suppliers, however the opposite is true for the retailer and consumers.

**Teaching**

- Probability [IN3141-1] [UCH, undergraduate] – Fall 2024
- Operations Management [IN75R-2/DPDIIGDE05-1] [UCH, MBA] – Spring 2023
- Management in Data Analytics [IN7121-2] [UCH, MBA] – Spring 2023
- Probability [IN3141-1] [UCH, undergraduate] – Spring 2023
- Applications Workshop in R and Python [UCH-MIT, Certificate] – Spring 2023
- Probability [IN3141-1] [UCH, undergraduate] – Fall 2023
- Implementing Strategy through Business Operations [B63 MGT 560Q] [WASHU, MBA] – Spring 2022
- Operations Management [IN75R-2/DPDIIGDE05-1] [UCH, MBA] – Spring 2022
- Probability [IN3141-1] [UCH, undergraduate] – Spring 2022
- Probability [IN3141-1] [UCH, undergraduate] – Fall 2022
- Operations Management [IN75R-1/DPDIIGDE05-1] [UCH, MBA] – Spring 2021
- Probability [IN3141-1] [UCH, undergraduate] – Spring 2021
- Data Driven Decision Making [UCH-MIT, Certificate] – Spring 2021
- Probability [IN3141-1] [UCH, undergraduate] – Fall 2021
- Operations Management [IN75R-1/DPDIIGDE05-1] [UCH, MBA] – Spring 2020
- Data Driven Decision Making [UCH-MIT, Certificate] – Spring 2020
- Operations Management I [IN4703-1] [UCH, undergraduate] – Spring 2020
- Operations Management I [IN4703-2] [UCH, undergraduate] – Fall 2020
- Data Driven Decision Making [UCH-MIT, Certificate] – Spring 2019
- Operations Management [IN75R-1] [UCH, MBA] – Spring 2019
- Operations Management I [IN4703-2] [UCH, undergraduate] – Spring 2019
- Applied Methods for Data Analyses [IN5724-1] [UCH, master/PhD] – Fall 2019
- Operations Management I [IN4703-2] [UCH, undergraduate] – Fall 2019
- Operations Management [IN75R-1/IN7A6-1] [UCH, MBA] – Spring 2018
- Operations Management I [IN4703-1] [UCH, undergraduate] – Fall 2018
- Operations Management I [IN4703-1] [UCH, undergraduate] – Fall 2018

**Awards**

- Franz Edelman Award: «
*Analytics Saves Lives During the Covid Crisis in**Chile*» – 2022 - POMS Best Student Paper Award: College of Supply Chain Management – 2015
- Gold medal Chilean National Math Olympics – 2003