A chance-constrained two-stage stochastic programming model for humanitarian relief network design

Two-stage stochastic programming under multivariate risk constraints with an application to humanitarian relief network design

“…A recent study Elçi (2016) proposes a more elaborate risk-averse extension, which features a mean-risk objective function on the random total cost with CVaR being the risk measure (as in Noyan, 2012), and enforces a joint chance constraint on the feasibility of the second-stage problem (as in Hong et al, 2015). In contrast to the other variants, the model of Elçi (2016) relies on an alternative formulation of the second-stage problem, which focuses on assigning the demand points to the facilities instead of determining the detailed arc-flow decisions. In our study, we follow this practically meaningful assignment-based modeling approach for the second-stage problem, and develop a new risk-averse variant of the widely-cited model of Rawls and Turnquist (2010).…”

“…The majority of the existing studies focus on pre-disaster relief network design and develop risk-neutral two-stage stochastic programs (e.g., Balcik and Beamon, 2008;Rawls and Turnquist, 2010;Salmerón and Apte, 2010;Döyen et al, 2012). However, this extensive literature includes only a few studies (e.g., Rawls and Turnquist, 2011;Noyan, 2012;Hong et al, 2015;Elçi, 2016) that provide risk-averse stochastic models, and lacks models with multivariate risk constraints. Here, we mainly discuss the studies that are most closely related to ours.…”

“…There also exist chance-constrained variants (Rawls and Turnquist, 2011;Hong et al, 2015). A recent study Elçi (2016) proposes a more elaborate risk-averse extension, which features a mean-risk objective function on the random total cost with CVaR being the risk measure (as in Noyan, 2012), and enforces a joint chance constraint on the feasibility of the second-stage problem (as in Hong et al, 2015). In contrast to the other variants, the model of Elçi (2016) relies on an alternative formulation of the second-stage problem, which focuses on assigning the demand points to the facilities instead of determining the detailed arc-flow decisions.…”

“…Their approach randomly identifies the link degradation and node damage levels depending on the proximity to the center of the disaster, and generates the realizations of the random input parameters accordingly. Elçi (2016) follows this elaborate scenario generation approach, but makes the necessary modifications according to their assignment-based formulation of the second-stage problem. More specifically, the author ignores 55 links of the original network and introduces the links according to the coverage-based responsiveness requirement.…”

“…The majority of the existing studies extend a univariate stochastic preference relation, based on second-order stochastic dominance (SSD) or a coherent risk measure such as CVaR, to the multivariate case by considering a family of scalarization functions. While multivariate SSD-constrained problems are more frequently studied (see, e.g., Dentcheva and Ruszczyński, 2009;Homem-de-Mello and Mehrotra, 2009;Dentcheva and Wolfhagen, 2015;2016), there is an increasing interest in risk measure-constrained variants (see, e.g., Noyan and Rudolf, 2013;Liu et al, 2015), which provide natural relaxations to overly demanding and conservative SSD-based models. More recently, studies focusing on both multivariate SSD-and risk measure-constrained models also appear in literature (Küçükyavuz and Noyan, 2016;Noyan and Rudolf, 2016).…”