Two-stage stochastic optimization problems with stochastic ordering constraints on the recourse

• DOI: 10.1016/j.ejor.2011.11.044
• Publication Date: 2011-12-14T03:20:59Z
• Authors: Darinka Dentcheva; Gabriela Martinez
• Keywords: Quantile

Abstract We consider two-stage risk-averse stochastic optimization problems with a stochastic ordering constraint on the recourse function. Two new characterizations of the increasing convex order relation are provided. They are based on conditional expectations and on integrated quantile functions: a counterpart of the Lorenz function. We propose two decomposition methods to solve the problems and prove their convergence. Our methods exploit the decomposition structure of the risk-neutral two-stage problems and construct successive approximations of the stochastic ordering constraints. Numerical results confirm the efficiency of the methods.