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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, and education.

Publications

1.  On the Optimization of Pit Stop Strategies via Dynamic Programming

Carrasco, F., and Thraves, C.
Forthcoming – 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.

2.   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.

3.  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.

4.  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.

5.  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.

6.  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 Game Theory Model for Pit-Stop  Optimization Strategies

Thraves C.

Paper

2.  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 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

Contact

Info

Industrial Engineering Department, University of Chile
Beauchef 851 Santiago, Chile
8370456
cthraves@dii.uchile.cl

About      Research      Publications   Working Papers      Teaching      Contact

Charles Thraves