Abstrakt
Many practical problems involve solving stochastic optimization problems. As the number of scenarios increases, even in the linear case the necessity for specialized algorithms and software arises.
This is especially true for the polyhedral case, among which minimization of several risk measures belongs, namely conditional value at risk, mean absolute deviation and others. In this paper we deal with investment problem minimizing conditional value at risk.
This model is solved using several algorithms, namely deterministic equivalent, L-shaped algorithm, both in basic and multicut versions, furthermore we present hot start method. Regarding software, we present the comparison of specialized two stage programming software SLP-IOR with general purpose optimization software GAMS.
For large scale problems, the best performance is obtained with the L-shaped method solved in C# using GAMS solver CPLEX.