Questions tagged [chance-constraints]

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

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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 $...
al b's user avatar
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2 votes
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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 ...
falamiw's user avatar
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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{...
Djames's user avatar
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3 votes
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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\\ &...
Sam's user avatar
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2 votes
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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{...
Sam's user avatar
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4 votes
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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?
danielcharters's user avatar
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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 ...
danielcharters's user avatar
9 votes
1 answer

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, ...
Libra's user avatar
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7 votes
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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 ...
A.Omidi's user avatar
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14 votes
2 answers

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 $\varepsilon\in(0,1)$ ...
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