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In this paper, we examine a data‐driven optimization approach to making optimal decisions as evaluated by a trained random forest, where these decisions can be constrained by an arbitrary polyhedral set. We model this optimization problem as a mixed‐integer linear program. We show this model can be solved to optimality efficiently using pareto‐optimal Benders cuts for ensembles containing a modest number of trees. We consider a random forest approximation that consists of sampling a subset of trees and establish that this gives rise to near‐optimal solutions by proving analytical guarantees. In particular, for axis‐aligned trees, we show that the number of trees we need to sample is sublinear in the size of the forest being approximated. Motivated by this result, we propose heuristics inspired by cross‐validation that optimize over smaller forests rather than one large forest and assess their performance on synthetic datasets. We present two case studies on a property investment problem and a jury selection problem. We show this approach performs well against other benchmarks while providing insights into the sensitivity of the algorithm's performance for different parameters of the random forest.

 

We study strategic capacity investment problems in joint ventures (JVs) with fixed‐rate revenue‐sharing contracts. We adopt a game‐theoretical approach to study two types of JVs depending on how individual resources determine the effective capacity of a JV. Withcomplementaryresources, the effective capacity of a JV is constrained by the most scarce resource. We show that multiple Nash equilibria could exist. Nevertheless, there exists a unique Strong Nash equilibrium. We show that there is an efficient and fair fixed‐rate revenue‐sharing contract which induces the system optimal outcome in the Strong Nash equilibrium. On the other hand, withsubstitutablea resource, the effective capacity of a JV is measured by aggregating individual contributions. We show that there does not exist a fixed‐rate revenue‐sharing contract that induces the system optimum. We quantify that the efficiency of a JV which decreases with the number of participants, the cost asymmetry and the cost margin of the JV. We propose provably‐good fixed‐rate revenue‐sharing contracts with performance guarantees. We also propose a simple modified contract to achieve the channel coordination. Finally, we fit our model with historical data to shed some insights on two JV examples in the motion picture industry.

 

Abstract Academic researchers, government agencies, industry groups, and individuals have produced forecasts at an unprecedented scale during the COVID-19 pandemic. To leverage these forecasts, the United States Centers for Disease Control and Prevention (CDC) partnered with an academic research lab at the University of Massachusetts Amherst to create the US COVID-19 Forecast Hub. Launched in April 2020, the Forecast Hub is a dataset with point and probabilistic forecasts of incident cases, incident hospitalizations, incident deaths, and cumulative deaths due to COVID-19 at county, state, and national, levels in the United States. Included forecasts represent a variety of modeling approaches, data sources, and assumptions regarding the spread of COVID-19. The goal of this dataset is to establish a standardized and comparable set of short-term forecasts from modeling teams. These data can be used to develop ensemble models, communicate forecasts to the public, create visualizations, compare models, and inform policies regarding COVID-19 mitigation. These open-source data are available via download from GitHub, through an online API, and through R packages. 

Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub ( https://covid19forecasthub.org/ ) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multimodel ensemble forecast that combined predictions from dozens of groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naïve baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-wk horizon three to five times larger than when predicting at a 1-wk horizon. This project underscores the role that collaboration and active coordination between governmental public-health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks.