  Systematic scenario generation (SG) methods have emerged as an invaluable
tool to handle uncertainty towards the efficient solution of stochastic
programming (SP) problems. The quality of SG methods depends on their
consistency to generate scenario sets which guarantee stability on solving SPs
and lead to stochastic solutions of good quality. In this context, we delve
into the optimisation-based Distribution and Moment Matching Problem (DMP) for
scenario generation and propose a game-theoretic approach which is formulated
as a Mixed-Integer Linear Programming (MILP) model. Nash bargaining approach is
employed and the terms of the objective function regarding the statistical
matching of the DMP are considered as players. Results from a capacity planning
case study highlight the quality of the stochastic solutions obtained using
MILP DMP models for scenario generation. Furthermore, the proposed
game-theoretic extension of DMP enhances in-sample and out-of-sample stability
with respect to the challenging problem of user-defined parameters variability.
