From scenarios to conditional scenarios in two-stage stochastic MILP problems

The conditional scenario (CS) approach was introduced as an effective approximation to the two-stage stochastic mixed-integer linear programming problem. Although the original definition of CS is general, in practice it is basically suitable for the multivariate normal distribution. In this paper, we propose a new definition of CS that is suitable for approximating any multivariate distribution (continuous or discrete). This definition allows the approximation of a potentially large set of scenarios using a small set of CSs, unlike the previous definition. In the computational study, dedicated to solving the portfolio optimization problem with hard real-world constraints, the CS approach has clearly outperformed the sample average approximation approach in terms of solution time.