Questions tagged [chance-constraints]
For questions on constraints over random variables that need to be satisfied with a given probability.
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questions
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Joint, two-sided chance constraint of MILP reformulation of a logical constrain
I reformulated the logical constraint $x = \min\{y,z\}$ as this MILP problem
$$
\begin{array}{ll}
x &\leq y \\
x &\leq z \\
x &\geq y-M(1-w) \\
x &\geq z-Mw
\end{array}
$$
in which $...
- 1
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Create constraint only for a recourse problem in stochastic linear programming
Question1: Northam Airlines is trying to decide how to partition a new plane for its Chicago–
Detroit route. The plane can seat $200$ economy class, passengers. A section can be partitioned off for ...
- 157
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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{...
- 1,143
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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\\
&...
- 161
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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{...
- 161
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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?
- 171
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Best method to optimize the blending of different types of coal to ensure all quality parameters are met at the lowest possible price?
I am looking to optimize 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 ...
- 171
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Static stochastic knapsack problem: unbounded version
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, ...
- 937
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votes
2
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Difference between Chance constraints and logical constraints
A logical constraint combines linear constraints using
logical operators, such as logical-and, logical-or, negation (that is, not), conditional statements (that is, if ... then ...) to express complex ...
- 9,068
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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 $\varepsilon\in(0,1)$ ...
- 2,117