Chance-constrained stochastic programming under variable reliability levels with an application to humanitarian relief network design

•Study individual chance-constrained optimization models with variable reliability.•Balance the trade-off between the actual cost and the cost of reliability.•Hybrid stochastic approach with qualitative and quantitative aspects of risk.•Develop effective mixed-integer programming formulations.•Intro...

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Vydané v:	Computers & operations research Ročník 96; s. 91 - 107
Hlavní autori:	Elçi, Özgün, Noyan, Nilay, Bülbül, Kerem
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Elsevier Ltd 01.08.2018 Pergamon Press Inc
Predmet:	Accessibility Bonferroni approximation Chance constraints Constraint modelling Design optimization Disaster relief Equity Humanitarian logistics Integer programming Linear programming Mathematical programming Network design Network reliability Operations research Post-disaster Probabilistic constraints Reliability Risk aversion Risk levels Risk-averse Stochastic models Stochastic programming Studies Tolerances Value-at-risk Variable reliability Bonferroni approximation Humanitarian logistics Network design Probabilistic constraints Accessibility Equity Chance constraints Risk-averse Variable reliability Stochastic programming Value-at-risk Post-disaster
ISSN:	0305-0548, 1873-765X, 0305-0548
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Abstract	•Study individual chance-constrained optimization models with variable reliability.•Balance the trade-off between the actual cost and the cost of reliability.•Hybrid stochastic approach with qualitative and quantitative aspects of risk.•Develop effective mixed-integer programming formulations.•Introduce a new risk-averse stochastic last mile relief network design problem. We focus on optimization models involving individual chance constraints, in which only the right-hand side vector is random with a finite distribution. A recently introduced class of such models treats the reliability levels / risk tolerances associated with the chance constraints as decision variables and trades off the actual cost / return against the cost of the selected reliability levels in the objective function. Leveraging recent methodological advances for modeling and solving chance-constrained linear programs with fixed reliability levels, we develop strong mixed-integer programming formulations for this new variant with variable reliability levels. In addition, we introduce an alternate cost function type associated with the risk tolerances which requires capturing the value-at-risk (VaR) associated with a variable reliability level. We accomplish this task via a new integer linear programming representation of VaR. Our computational study illustrates the effectiveness of our mathematical programming formulations. We also apply the proposed modeling approach to a new stochastic last mile relief network design problem and provide numerical results for a case study based on the real-world data from the 2011 Van earthquake in Turkey.
AbstractList	We focus on optimization models involving individual chance constraints, in which only the right-hand side vector is random with a finite distribution. A recently introduced class of such models treats the reliability levels / risk tolerances associated with the chance constraints as decision variables and trades off the actual cost / return against the cost of the selected reliability levels in the objective function. Leveraging recent methodological advances for modeling and solving chance-constrained linear programs with fixed reliability levels, we develop strong mixed-integer programming formulations for this new variant with variable reliability levels. In addition, we introduce an alternate cost function type associated with the risk tolerances which requires capturing the value-at-risk (VaR) associated with a variable reliability level. We accomplish this task via a new integer linear programming representation of VaR. Our computational study illustrates the effectiveness of our mathematical programming formulations. We also apply the proposed modeling approach to a new stochastic last mile relief network design problem and provide numerical results for a case study based on the real-world data from the 2011 Van earthquake in Turkey. •Study individual chance-constrained optimization models with variable reliability.•Balance the trade-off between the actual cost and the cost of reliability.•Hybrid stochastic approach with qualitative and quantitative aspects of risk.•Develop effective mixed-integer programming formulations.•Introduce a new risk-averse stochastic last mile relief network design problem. We focus on optimization models involving individual chance constraints, in which only the right-hand side vector is random with a finite distribution. A recently introduced class of such models treats the reliability levels / risk tolerances associated with the chance constraints as decision variables and trades off the actual cost / return against the cost of the selected reliability levels in the objective function. Leveraging recent methodological advances for modeling and solving chance-constrained linear programs with fixed reliability levels, we develop strong mixed-integer programming formulations for this new variant with variable reliability levels. In addition, we introduce an alternate cost function type associated with the risk tolerances which requires capturing the value-at-risk (VaR) associated with a variable reliability level. We accomplish this task via a new integer linear programming representation of VaR. Our computational study illustrates the effectiveness of our mathematical programming formulations. We also apply the proposed modeling approach to a new stochastic last mile relief network design problem and provide numerical results for a case study based on the real-world data from the 2011 Van earthquake in Turkey.
Author	Elçi, Özgün Bülbül, Kerem Noyan, Nilay
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Keywords	Bonferroni approximation Humanitarian logistics Network design Probabilistic constraints Accessibility Equity Chance constraints Risk-averse Variable reliability Stochastic programming Value-at-risk Post-disaster
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Snippet	•Study individual chance-constrained optimization models with variable reliability.•Balance the trade-off between the actual cost and the cost of... We focus on optimization models involving individual chance constraints, in which only the right-hand side vector is random with a finite distribution. A...
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SubjectTerms	Accessibility Bonferroni approximation Chance constraints Constraint modelling Design optimization Disaster relief Equity Humanitarian logistics Integer programming Linear programming Mathematical programming Network design Network reliability Operations research Post-disaster Probabilistic constraints Reliability Risk aversion Risk levels Risk-averse Stochastic models Stochastic programming Studies Tolerances Value-at-risk Variable reliability
Title	Chance-constrained stochastic programming under variable reliability levels with an application to humanitarian relief network design
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