Pragmatic convex approaches for risk-averse and distributionally robust mixed-integer recourse models

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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Robust SCUC considering continuous/discrete uncertainties and quick-start units: A two-stage robust optimization with mixed-integer recourse

2016 IEEE Power and Energy Society General Meeting (PESGM) ◽

10.1109/pesgm.2016.7741375 ◽

2016 ◽

Cited By ~ 1

Author(s):

Lei Wu

Keyword(s):

Robust Optimization ◽

Mixed Integer ◽

Two Stage ◽

Integer Recourse

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Optimizing Disruption Tolerance for Rail Transit Networks Under Uncertainty

Transportation Science ◽

10.1287/trsc.2021.1040 ◽

2021 ◽

Author(s):

Lei Xu ◽

Tsan Sheng (Adam) Ng ◽

Alberto Costa

Keyword(s):

Robust Optimization ◽

Optimization Model ◽

Optimization Problem ◽

Mixed Integer ◽

Rail Transit ◽

Distributionally Robust Optimization ◽

Performance Function ◽

Transit Networks ◽

Disruption Tolerance ◽

Distributionally Robust

In this paper, we develop a distributionally robust optimization model for the design of rail transit tactical planning strategies and disruption tolerance enhancement under downtime uncertainty. First, a novel performance function evaluating the rail transit disruption tolerance is proposed. Specifically, the performance function maximizes the worst-case expected downtime that can be tolerated by rail transit networks over a family of probability distributions of random disruption events given a threshold commuter outflow. This tolerance function is then applied to an optimization problem for the planning design of platform downtime protection and bus-bridging services given budget constraints. In particular, our implementation of platform downtime protection strategy relaxes standard assumptions of robust protection made in network fortification and interdiction literature. The resulting optimization problem can be regarded as a special variation of a two-stage distributionally robust optimization model. In order to achieve computational tractability, optimality conditions of the model are identified. This allows us to obtain a linear mixed-integer reformulation that can be solved efficiently by solvers like CPLEX. Finally, we show some insightful results based on the core part of Singapore Mass Rapid Transit Network.

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Technical Note—Time Inconsistency of Optimal Policies of Distributionally Robust Inventory Models

Operations Research ◽

10.1287/opre.2019.1932 ◽

2020 ◽

Vol 68 (5) ◽

pp. 1576-1584 ◽

Cited By ~ 1

Author(s):

Alexander Shapiro ◽

Linwei Xin

Keyword(s):

Decision Making ◽

Large Class ◽

Risk Measures ◽

Technical Note ◽

Time Inconsistency ◽

Base Stock ◽

Risk Averse ◽

Inventory Models ◽

Optimal Policies ◽

Distributionally Robust

The authors extend previous studies of time inconsistency to risk averse (distributionally robust) inventory models and show that time inconsistency is not unique to robust multistage decision making, but may happen for a large class of risk averse/distributionally robust settings. In particular, they demonstrate that if the respective risk measures are not strictly monotone, then there may exist infinitely many optimal policies which are not base-stock and not time consistent. This is in a sharp contrast with the risk neutral formulation of the inventory model where all optimal policies are base-stock and time consistent.

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Data-Driven Optimization of Reward-Risk Ratio Measures

INFORMS Journal on Computing ◽

10.1287/ijoc.2020.1002 ◽

2020 ◽

Author(s):

Ran Ji ◽

Miguel A. Lejeune

Keyword(s):

Optimization Problems ◽

State Of The Art ◽

Convergence Property ◽

Computational Study ◽

Data Driven ◽

Mixed Integer ◽

Finite Convergence ◽

Integer Nonlinear Programming ◽

Distributionally Robust ◽

Risk Ratios

We investigate a class of fractional distributionally robust optimization problems with uncertain probabilities. They consist in the maximization of ambiguous fractional functions representing reward-risk ratios and have a semi-infinite programming epigraphic formulation. We derive a new fully parameterized closed-form to compute a new bound on the size of the Wasserstein ambiguity ball. We design a data-driven reformulation and solution framework. The reformulation phase involves the derivation of the support function of the ambiguity set and the concave conjugate of the ratio function. We design modular bisection algorithms which enjoy the finite convergence property. This class of problems has wide applicability in finance, and we specify new ambiguous portfolio optimization models for the Sharpe and Omega ratios. The computational study shows the applicability and scalability of the framework to solve quickly large, industry-relevant-size problems, which cannot be solved in one day with state-of-the-art mixed-integer nonlinear programming (MINLP) solvers.

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