Optimal scenario reduction framework based on distance of uncertainty distribution and output performance: I. Single reduction via mixed integer linear optimization

• Proposed a novel scenario reduction algorithm considering both input and output space probabilistic distance and output performance of decision making.
• Minimizes the differences on the best, worst and expected performance of the output measure of the original and the reduced scenario distributions.
• Developed a novel mixed integer linear optimization based problem formulation.
• A number of case studies demonstrating and comparing the performance of the proposed method with existing tools.

Realistic decision making involves consideration of uncertainty in various parameters. While large number of scenarios brings significant challenge to computations, the scenario reduction aims at selecting a small number of representative scenarios that can capture the wide range of possible scenarios. A novel scenario reduction algorithm is proposed in this paper to incorporate the consideration of both input data and output performance of decision making. The proposed optimal scenario reduction algorithm, OSCAR, is formulated as a mixed integer linear optimization problem. It minimizes not only the probabilistic distance between the original and reduced input scenario distribution, but also minimizes the differences between the best, worst and expected performances of the output measure of the original and the reduced scenario distributions. The proposed method leads to reduced distribution not only closer to the original distribution in terms of the transportation distance, but also captures the performance of the output.