A note on second-order stochastic dominance constraints induced by mixed-integer linear recourse

New Formulations for Optimization under Stochastic Dominance Constraints

“…We expect that when D is small it will be possible to significantly increase the number of possible realizations, N , of the random vector appearing in the constraints. Another setting in which to test the new formulations is in two-stage stochastic programming with stochastic dominance constraints, as has been recently studied in [11,12], where they use the previous, less compact, formulations for the stochastic dominance constraints.…”

“…Then, D k=1 π ik = 1 because w i ≥ y 1 for all i, and so π satisfies (12). It is also immediate by the definition of π ik that w i ≥ D k=1 y k π ik and so π satisfies (11). Finally, note that w i < y k if and only if…”

“…In addition, dose-volume restrictions appearing in radiation treatment planning problems [18] can be formulated as a firstorder stochatic dominance constraint. Stochastic programming under stochastic dominance constraints has recently been studied in [4,5,6,8,11,12,24,25,26].…”

Risk aversion for an electricity retailer with second-order stochastic dominance constraints

“…Rather than heading for "best" members of (5), we want to identify "acceptable" members of (5), and optimize over them. This leads to a recently introduced class of stochastic integer programs featuring stochastic dominance constraints induced by mixed-integer linear recourse (Drapkin and Schultz 2008;Gollmer et al 2007Gollmer et al , 2008. Stochastic dominance provides a possibility to formalize the desired "acceptability".…”

“…To that end, we impose that the profit variable must dominate a prespecified profit benchmark profile that is just acceptable to the decision maker. This approach is based on an established concept in decision theory named stochastic dominance (Dentcheva et al 2007;Ruszczyński 2003, 2004;Gollmer et al 2007Gollmer et al , 2008. In this paper stochastic dominance constraints are included in the problem faced by an electricity retailer presented in Carrión et al (2007a).…”