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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Bibliographic Details
Published in:Computers & operations research Vol. 96; pp. 91 - 107
Main Authors: Elçi, Özgün, Noyan, Nilay, Bülbül, Kerem
Format: Journal Article
Language:English
Published: New York Elsevier Ltd 01.08.2018
Pergamon Press Inc
Subjects:
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
Online Access:Get full text
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Summary:•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.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2018.03.011