COVID-19: Optimal Allocation of Ventilator Supply under Uncertainty and Risk

AbstractThis 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 the 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. The 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.

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Risk-Averse Multi-Stage Stochastic Programming to Optimizing Vaccine Allocation and Treatment Logistics for Effective Epidemic Response

10.1101/2021.05.28.21258003 ◽

2021 ◽

Author(s):

Xuecheng Yin ◽

Esra Buyuktahtakin

Keyword(s):

Value At Risk ◽

Virus Disease ◽

Risk Measure ◽

Adverse Outcomes ◽

Mixed Integer ◽

Conditional Value At Risk ◽

Risk Averse ◽

Expected Number ◽

Multi Stage ◽

Stochastic Mixed Integer Programming

Existing compartmental-logistics models in epidemics control are limited in terms of optimizing the allocation of vaccines and treatment resources under a risk-averse objective. In this paper, we present a data-driven, mean-risk, multi-stage, stochastic epidemics-vaccination-logistics model that evaluates various disease growth scenarios under the Conditional Value-at-Risk (CVaR) risk measure to optimize the distribution of treatment centers, resources, and vaccines, while minimizing the total expected number of infections, deaths, and close contacts of infected people under a limited budget. We integrate a new ring vaccination compartment into a Susceptible-Infected-Treated-Recovered-Funeral-Burial epidemics-logistics model. Our formulation involves uncertainty both in the vaccine supply and the disease transmission rate. Here, we also consider the risk of experiencing scenarios that lead to adverse outcomes in terms of the number of infected and dead people due to the epidemic. Combining the risk-neutral objective with a risk measure allows for a trade-off between the weighted expected impact of the outbreak and the expected risks associated with experiencing extremely disastrous scenarios. We incorporate human mobility into the model and develop a new method to estimate the migration rate between each region when data on migration rates is not available. We apply our multi-stage stochastic mixed-integer programming model to the case of controlling the 2018-2020 Ebola Virus Disease (EVD) in the Democratic Republic of the Congo (DRC) using real data. Our results show that increasing the risk-aversion by emphasizing potentially disastrous outbreak scenarios reduces the expected risk related to adverse scenarios at the price of the increased expected number of infections and deaths over all possible scenarios. We also find that isolating and treating infected individuals are the most efficient ways to slow the transmission of the disease, while vaccination is supplementary to primary interventions on reducing the number of infections. Furthermore, our analysis indicates that vaccine acceptance rates affect the optimal vaccine allocation only at the initial stages of the vaccine rollout under a tight vaccine supply.

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Convex approximations for two-stage mixed-integer mean-risk recourse models with conditional value-at-risk

Mathematical Programming ◽

10.1007/s10107-019-01428-6 ◽

2019 ◽

Vol 181 (2) ◽

pp. 473-507 ◽

Cited By ~ 1

Author(s):

E. Ruben van Beesten ◽

Ward Romeijnders

Keyword(s):

At Risk ◽

Error Bounds ◽

Value At Risk ◽

Risk Measure ◽

Mixed Integer ◽

Conditional Value At Risk ◽

Two Stage ◽

Special Cases ◽

Integer Recourse ◽

Mean Risk

Abstract In traditional two-stage mixed-integer recourse models, the expected value of the total costs is minimized. In order to address risk-averse attitudes of decision makers, we consider a weighted mean-risk objective instead. Conditional value-at-risk is used as our risk measure. Integrality conditions on decision variables make the model non-convex and hence, hard to solve. To tackle this problem, we derive convex approximation models and corresponding error bounds, that depend on the total variations of the density functions of the random right-hand side variables in the model. We show that the error bounds converge to zero if these total variations go to zero. In addition, for the special cases of totally unimodular and simple integer recourse models we derive sharper error bounds.

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Risk Constrained Short Term Hydro Scheduling using Two Point estimate method and conditional value at risk

2016 IEEE 6th International Conference on Power Systems (ICPS) ◽

10.1109/icpes.2016.7584039 ◽

2016 ◽

Author(s):

Prakash Chand Sharma ◽

A.R. Abhyankar

Keyword(s):

At Risk ◽

Value At Risk ◽

Conditional Value At Risk ◽

Point Estimate ◽

Short Term ◽

Point Estimate Method ◽

Estimate Method

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Comparison of new conditional value-at-risk-based management models for optimal allocation of uncertain water supplies

Water Resources Research ◽

10.1029/2006wr005210 ◽

2007 ◽

Vol 43 (7) ◽

Cited By ~ 30

Author(s):

Ghina M. Yamout ◽

Kirk Hatfield ◽

H. Edwin Romeijn

Keyword(s):

At Risk ◽

Value At Risk ◽

Optimal Allocation ◽

Conditional Value At Risk ◽

Water Supplies ◽

Management Models

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Portfolio Optimization with Metaheuristics

Finance and Market ◽

10.18686/fm.v2.1048 ◽

2017 ◽

Vol 2 (2) ◽

Author(s):

Georgios Mamanis

Keyword(s):

Portfolio Optimization ◽

Portfolio Selection ◽

Value At Risk ◽

Optimal Allocation ◽

Optimization Problems ◽

Objective Functions ◽

Cardinality Constraints ◽

Risk Optimization ◽

Measures Of Risk ◽

Mean Risk

<p>Portfolio optimization is the problem ofsearching foran optimal allocation of wealth to put in the available assets. Since the seminalworkdoneby Markowitz, the problem is codifiedas a two-objective mean-risk optimization problem where the best trade-off solutions (portfolios) between risk (measured by variance) and mean are hunted. Complex measures of risk (e.g., value-at-risk, expected shortfall, semivariance), addedobjective functions (e.g., maximization of skewness, liquidity, dividends) and pragmatic, real-worldconstraints (e.g., cardinality constraints, quantity constraints, minimum transaction lots, class constraints) that are included in recent portfolio selection models, provide many optimization challenges. The resulting portfolio optimizationproblem becomes very hard to be tackledwith exact techniquesas it displaysnonlinearities, discontinuities and high dimensional efficient frontiers. These characteristics prompteda lot ofresearchers to explorethe use of metaheuristics, which are powerful techniquesfor discoveringnear optimal solutions (sometimes the real optimum) for hard optimization problems in acceptable computationaltime. This report provides a briefnoteon the field of portfolio optimization with metaheuristics and concludes that especially Multiobjectivemetaheuristics (MOMHs) provide a natural background for dealing with portfolio selection problems with complex measures of risk (which define non-convex, non-differential objective functions), discrete constraints and multiple objectives.</p>

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Study on Single Cycle Production Allocation and Supply Strategy for DCEs Based on the CVaR Criterion

Discrete Dynamics in Nature and Society ◽

10.1155/2018/7840264 ◽

2018 ◽

Vol 2018 ◽

pp. 1-14

Author(s):

Leiyan Xu ◽

Zhiqing Meng ◽

Gengui Zhou ◽

Yunzhi Mu ◽

Minchao Zheng

Keyword(s):

Value At Risk ◽

Optimal Allocation ◽

Approximate Algorithm ◽

Conditional Value At Risk ◽

Total Production ◽

Single Cycle ◽

Expected Return ◽

Allocation Model ◽

Production Allocation ◽

The Given

Direct chain enterprises (DCEs) face a decision-making issue as to how to allocate and supply their products to their stores for sales with the minimum losses and maximum profits for the manufacturers. This paper presents a single-cycle optimal allocation model for DCEs under the given total production amount and conditional value at risk loss. The optimal strategy for production allocation and supply is derived. Subsequently, an approximate algorithm for solving the optimal total production amount is presented. The optimal allocation and supply strategy, the minimum total production amount, the minimum allocation strategy, and the discount pricing strategy are obtained for the single cycle. Finally, with the sales data of a food DCE, numerical results corroborate that adopting different production and supply strategies reduces the risk of expected losses and increases the expected return. It is of an important theoretical significance in guiding the production and operation of direct chain enterprises.

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Mean-risk stochastic electricity generation expansion planning problems with demand uncertainties considering conditional-value-at-risk and maximum regret as risk measures

International Journal of Electrical Power & Energy Systems ◽

10.1016/j.ijepes.2015.05.003 ◽

2015 ◽

Vol 73 ◽

pp. 309-317 ◽

Cited By ~ 13

Author(s):

Hatice Tekiner-Mogulkoc ◽

David W. Coit ◽

Frank A. Felder

Keyword(s):

At Risk ◽

Value At Risk ◽

Electricity Generation ◽

Risk Measures ◽

Conditional Value At Risk ◽

Expansion Planning ◽

Generation Expansion ◽

Planning Problems ◽

Mean Risk ◽

Maximum Regret

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Multi-stage stochastic model in portfolio selection problem

Filomat ◽

10.2298/fil1803991b ◽

2018 ◽

Vol 32 (3) ◽

pp. 991-1001

Author(s):

Shokoofeh Banihashemi ◽

Ali Azarpour ◽

Marziye Kaveh

Keyword(s):

At Risk ◽

Portfolio Selection ◽

Value At Risk ◽

Risk Measures ◽

Risk Measure ◽

Selection Problem ◽

Conditional Value At Risk ◽

Expected Return ◽

Portfolio Selection Problem ◽

Multi Stage

This paper is a novel work of portfolio-selection problem solving using multi objective model considering four parameters, Expected return, downside beta coefficient, semivariance and conditional value at risk at a specified confidence level. Multi-period models can be defined as stochastic models. Early studies on portfolio selection developed using variance as a risk measure; although, theories and practices revealed that variance, considering its downsides, is not a desirable risk measure. To increase accuracy and overcoming negative aspects of variance, downside risk measures like semivarinace, downside beta covariance, value at risk and conditional value at risk was other risk measures that replaced in models. These risk measures all have advantages over variance and previous works using these parameters have shown improvements in the best portfolio selection. Purposed models are solved using genetic algorithm and for the topic completion, numerical example and plots to measure the performance of model in four dimensions are provided.

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