Value-at-Risk and Conditional Value-at-Risk Minimization for Hazardous Materials Routing

Bi-level chance constraint programming model for hazardous materials distribution

“…From the table, we can know, when the chance level (α, β, χ, γ) is to be (0.75, 0.75, 0.75, 0.75) , the minimum cost and minimum risk are only 66592612 and 13.6107, with the growing of chance level, the cost and risk is also increasing. This trend is in accordance with the VaR model and CVaR model proposed in the paper [18]. Although the risk and the cost is high, the credibility measure and probability is also growing, this means a lot to the decision maker.…”

An optimization method for sustainable traffic control in urban areas

“…The VaR and CVaR model, as mentioned above, was implemented by Toumazis et al (2013) for minimization of hazmat routing. This paper presents an adjusted application of those models as a method for optimizing sustainable traffic control in urban areas.The VaR of a network loading solution l is defined as the critical value b such that the value of the risk measure R exceeding that value b has probability less than or equal to (1 À a), where a is the confidence level (e.g.…”

“…In particular, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) models have been widely used in financial applications. Over the past years, VaR and CVaR have also been used in many engineering research fields, such as transportation of hazardous materials (Toumazis et al, 2013), network resilience (Cheliotis and Kenyon, 2002;Mastroeni and Naldi, 2011), network design and location problems (Sun and Gao, 2012;Wang et al, 2009), water management (Shao et al, 2011) and many others. In the framework of estimating the dynamic traffic conditions with DTA models, we define risk as the potential loss induced to travelers by exceeding their budgeted travel time as a result of the selected network control strategy, demand distribution and parameters setup for the simulation horizon.…”

Locating Direction Finders Optimally under Risk of Detection

“…Although VaR is a popular measure of risk, it has shortcomings in optimization problems; in particular, it is not a convex measure. CVaR, an alternative measure of risk that satisfies convexity (Artzner et al, [3]), has been applied successfully in a number of areas, including investment portfolios (Rockafellar et al, [12]), target assignment to weapons (Krokhmal et al, [9]), and hazardous material transportation (Toumazis et al, [14]). In many military applications, a decision must not only be effective on average, but also safe enough under a wide range of possible scenarios.…”