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This study presents a new risk-averse multi-stage stochastic epidemics-ventilator-logistics compartmental model to address the resource allocation challenges of mitigating COVID-19. This epidemiological logistics model involves the uncertainty of untested asymptomatic infections and incorporates short-term human migration. Disease transmission is also forecasted through a new formulation of transmission rates that evolve over space and time with respect to various non-pharmaceutical interventions, such as wearing masks, social distancing, and lockdown. The proposed multi-stage stochastic model overviews different scenarios on the number of asymptomatic individuals while optimizing the distribution of resources, such as ventilators, to minimize the total expected number of newly infected and deceased people. The Conditional Value at Risk (CVaR) is also incorporated into the multi-stage mean-risk model to allow for a trade-off between the weighted expected loss due to the outbreak and the expected risks associated with experiencing disastrous pandemic scenarios. We apply our multi-stage mean-risk epidemics-ventilator-logistics model to the case of controlling COVID-19 in highly-impacted counties of New York and New Jersey. We calibrate, validate, and test our model using actual infection, population, and migration data. We also define a new region-based sub-problem and bounds on the problem and then show their computational benefits in terms of the optimality and relaxation gaps. The computational results indicate that short-term migration influences the transmission of the disease significantly. The optimal number of ventilators allocated to each region depends on various factors, including the number of initial infections, disease transmission rates, initial ICU capacity, the population of a geographical location, and the availability of ventilator supply. Our data-driven modeling framework can be adapted to study the disease transmission dynamics and logistics of other similar epidemics and pandemics.

We derive a nested risk measure for a maximization problem and implement it in a scenario-based formulation of a multi-stage stochastic mixed-integer programming problem. We apply the risk-averse formulation to the surveillance and control of a non-native forest insect, the emerald ash borer (EAB), a wood-boring beetle native to Asia and recently discovered in North America. Spreading across the eastern United States and Canada, EAB has killed millions of ash trees and cost homeowners and local governments billions of dollars. We present a mean-Conditional Value-at-Risk (CVaR), multi-stage, stochastic mixed-integer programming model to optimize a manager’s decisions about surveillance and control of EAB. The objective is to maximize the benefits of healthy ash trees in forests and urban environments under a fixed budget. Combining the risk-neutral objective with a risk measure allows for a trade-off between the weighted expected benefits from ash trees and the expected risks associated with experiencing extremely damaging scenarios. We define scenario dominance cuts (sdc) for the maximization problem and under the decision-dependent uncertainty. We then solve the model using the sdc cutting plane algorithm for varying risk parameters. Computational results demonstrate that scenario dominance cuts significantly improve the solution performance relative to that of CPLEX. Our CVaR risk-averse approach also raises the objective value of the least-benefit scenarios compared to the risk-neutral model. Results show a shift in the optimal strategy from applying less expensive insecticide treatment to more costly tree removal as the manager becomes more risk-averse. We also find that risk-averse managers survey more often to reduce the risk of experiencing adverse outcomes.

This paper presents a new and general approach, named “Stage-t Scenario Dominance,” to solve the risk-averse multi-stage stochastic mixed-integer programs (M-SMIPs). Given a monotonic objective function, our method derives a partial ordering of scenarios by pairwise comparing the realization of uncertain parameters at each time stage under each scenario. Specifically, we derive bounds and implications from the “Stage-t Scenario Dominance” by using the partial ordering of scenarios and solving a subset of individual scenario sub-problems up to stage t. Using these inferences, we generate new cutting planes to tackle the computational difficulty of risk-averse M-SMIPs. We also derive results on the minimum number of scenario-dominance relations generated. We demonstrate the use of this methodology on a stochastic version of the mean-conditional value-at-risk (CVaR) dynamic knapsack problem. Our computational experiments address those instances that have uncertainty, which correspond to the objective, left-hand side, and right-hand side parameters. Computational results show that our “scenario dominance"-based method can reduce the solution time for mean-risk, stochastic, multi-stage, and multi-dimensional knapsack problems with both integer and continuous variables, whose structure is similar to the mean-risk M-SMIPs, with varying risk characteristics by one-to-two orders of magnitude for varying numbers of random variables in each stage. Computational results also demonstrate that strong dominance cuts perform well for those instances with ten random variables in each stage, and ninety random variables in total. The proposed scenario dominance framework is general and can be applied to a wide range of risk-averse and risk-neutral M-SMIP problems.

In this paper, we address the controversies of epidemic control planning by developing a novel Simulation-Deep Reinforcement Learning (SiRL) model. COVID-19 reminded constituents over the world that government decision-making could change their lives. During the COVID-19 pandemic, governments were concerned with reducing fatalities as the virus spread but at the same time also maintaining a flowing economy. In this paper, we address epidemic decision-making regarding the interventions necessary given of the epidemic based on the purpose of the decision-maker. Further, we intend to compare different vaccination strategies, such as age-based and random vaccination, to shine a light on who should get priority in the vaccination process. To address these issues, we propose a simulation-deep reinforcement learning (DRL) framework. This framework is composed of an agent-based simulation model and a governor DRL agent that can enforce interventions in the agent-based simulation environment. Computational results show that our DRL agent can learn effective strategies and suggest optimal actions given a specific epidemic situation based on a multi-objective reward structure. We compare our DRL agent's decisions to government interventions at different periods of time during the COVID-19 pandemic. Our results suggest that more could have been done to control the epidemic. In addition, if a random vaccination strategy that allows super-spreaders to get vaccinated early were used, infections would have been reduced by 32% at the expense of 4% more deaths. We also show that a behavioral change of fully quarantining 10% of the risky individuals and using a random vaccination strategy leads to a reduction of the death toll by 14% and 27% compared to the age-based vaccination strategy that was implemented and the New Jersey reported data, respectively. We have also demonstrated the flexibility of our approach to be applied to other locations by validating and applying our model to the COVID-19 case in the state of Kansas.

Battery Asset Management problem determines the minimum cost replacement schedules for each individual asset in a group of battery assets that operate in parallel. Battery cycle life varies under different operating conditions including temperature, depth of discharge (DOD), charge rate, etc., and a battery deteriorates due to usage, which cannot be handled by current asset management models. This paper presents a new battery asset management methodology where battery cycle life prognosis is integrated with parallel asset management to reduce lifecycle cost of the Battery Energy Storage Systems (BESS). For the battery failure time prognosis, a nonlinear physics-based battery capacity fade model is developed and incorporated in parallel asset management model to update battery capacity over time. Experiment results have shown that the developed battery asset management methodology can be conveniently used to facilitate BESS asset management decision making thereby decreasing asset lifecycle costs.