# Two-stage Combinatorial Optimization Problems under Risk

arXiv: https://arxiv.org/abs/1812.07826 · HTML: https://mlsanity.com/paper/1812.07826/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2018.

## Built on by (most cited first, 1 of 1)

- [A Two-stage Framework and Reinforcement Learning-based Optimization Algorithms for Complex Scheduling Problems](https://mlsanity.com/paper/2103.05847/) (2021)

## Abstract (arXiv)

In this paper a class of combinatorial optimization problems is discussed. It is assumed that a solution can be constructed in two stages. The current first-stage costs are precisely known, while the future second-stage costs are only known to belong to an uncertainty set, which contains a finite number of scenarios with known probability distribution. A partial solution, chosen in the first stage, can be completed by performing an optimal recourse action, after the true second-stage scenario is revealed. A solution minimizing the Conditional Value at Risk (CVaR) measure is computed. Since expectation and maximum are boundary cases of CVaR, the model generalizes the traditional stochastic and robust two-stage approaches, previously discussed in the existing literature. In this paper some new negative and positive results are provided for basic combinatorial optimization problems such as the selection or network problems.