# Questions tagged [chance-constraints]

For questions on constraints over random variables that need to be satisfied with a given probability.

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### Chance constrained optimization - interpretation

Suppose that we have a stochastic vector $\psi$ and $S$ realisations of $\psi$ given by $\psi_1,\dots,\psi_S$ with equal probability of occurrence. In addition, we have constraints of the form \begin{...
390 views

### How can I approximate a chance constraint in a computationally tractable way?

I want to solve an optimization model that contains a constraint like $$\Pr[F(x,\xi)\leq0]\geq1-\varepsilon$$ where $x$ are my decision variables, $\xi$ is a random vector, and $\varepsilon\in(0,1)$ ...
258 views

### Decomposition methods for two-stage stochastic program with integer variables

In a stochastic programming problem, I have binary variables in the second stage. As an example, consider that the optimization problem is given by: \begin{align} &\text{minimize} &\gamma\\ &...
116 views

### Scenario based approach to value-at-risk optimization using mixed-integer programming

For a discrete set of scenarios, minimising value at risk can be formulated as a mixed integer linear programming problem. If each scenario has equal probability then this can be written as \begin{...
123 views

### Software for multi-objective optimization

I am looking to solve a multi-objective chance-constrained blending problem. Are there any suggestions about the software to use to try and solve a problem like this?
42 views

### Best method to optimise the blending of different types of coal to ensure all quality parameters are met at the lowest possible price?

I am looking to optimise the blending of different types of coal for the coke making process of a steel plant. I want to take into account the statistical variation of each coal’s qualities, so for ...
In the static stochastic knapsack problem (SSKP) the weights $w_i$ of the items are distributed according to a probability distribution. Each item $i \in I$ can be selected at most once. So, ...