Two-stage stochastic linear programs with incomplete information on uncertainty

Two-stage stochastic linear programming is a classical model in operations research. The usual approach to this model requires detailed information on distribution of the random variables involved. In this paper, we only assume the availability of the first and second moments information of the random variables. By using duality of semi-infinite programming and adopting a linear decision rule, we show that a deterministic equivalence of the two-stage problem can be reformulated as a second-order cone optimization problem. Preliminary numerical experiments are presented to demonstrate the computational advantage of this approach.