Two-Stage Stochastic Linear Programming: The Conditional Scenario Approach

In this paper we consider the Two-stage Stochastic Linear Programming (TSLP) problem with continuous random parameters. A common way to approximate the TSLP problem, generally intractable, is to discretize the random parameters into scenarios. Another common approximation only considers the expectation of the parameters, that is, the expected scenario. In this paper we introduce the conditional scenario concept which represents a midpoint between the scenario and the expected scenario concepts. The message of this paper is twofold: a) The use of scenarios gives a good approximation to the TSLP problem. b) However, if the computational effort of using scenarios results too high, our suggestion is to use conditional scenarios instead because they require a moderate computational effort and favorably compare to the expected scenario in order to model the parameter uncertainty.