Questions tagged [stochastic-programming]

For questions about optimization problems in which one or more parameters are stochastic, with known probability distributions or discrete scenarios. The goal is often, but not always, to minimize or maximize the expected value of the objective function.

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Solving large-scale stochastic mixed integer program

What are some methods or algorithms for solving a large-scale stochastic mixed-integer optimization problem that runs on an hourly dataset for a year? Do we employ some kind of decomposition? (the ...
6
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0answers
177 views

Airline revenue management re-solving problem

I am considering a bid prices (shadow price of the capacity constraint) problem (from Chen, L. and Homem-de Mello, T. (2009)., page 14) where the acceptable classes for booking requests for ...
6
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0answers
73 views

Sample Average Approximation vs. Numerical Integration

In the sense of the calculation of the expected value of objective functions, we have two choices to evaluate the value; 1. Sample Average Approximation (SAA): $$ \frac{1}{N}\sum_{i=1}^N f(x,\xi^i). $$...
5
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105 views

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{...
3
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0answers
60 views

Derivative of sup(max) functions in distributionally robust optimization

In the distributionally robust optimization problem \begin{aligned} \min_{x\in X}\sup_{P\in\mathfrak{P}}\mathbb{E}_P[f(x,\xi)], \end{aligned} where $f:\mathbb{R}^n\to\mathbb{R}$ and $P$ is a ...
3
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0answers
47 views

How to find range of values for the first-stage decisions resulting in the same cuts in two-stage stochastic programming?

Suppose we have a two-stage stochastic program as follows: \begin{equation} \begin{split} \min \ & c^Tx + \mathbb{E}_\xi[Q(x,\xi)] \\ & \text{where}\\ &Q(x,\xi)=\min q(\xi)^Ty\\ &Tx+...
2
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0answers
49 views

Two-stage stochastic with non-linear recourse

I am working on a two-stage facility location problem as I described in this question. I am solving it with the L-shaped method (Benders decomposition). The cost value between each $(i,j)$ is a ...
2
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0answers
76 views

What is the intuition behind Progressive hedging algorithm?

I am reading some papers about PHA to solve multi-stage stochastic programming, but I think it is not still clear to me. This is my understanding and I would be thankful to know if it is correct or ...
2
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0answers
141 views

How to write nonanticipativity constraints?

In Multi-stage stochastic programming, we write the constraints that for scenarios $s$ and $s^{\prime}$ which have the same trajectory up to time $t$, should take the same value. That is, $$ x_{t,s} =...
2
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0answers
48 views

Decision-making algorithm for dynamic load balancing

I'm researching a subject of balancing the load between two black-box systems (with some twists). I thought that I could record latest response time log from each of those systems and process such a ...
1
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38 views

Scenario Tree Construction in Multi-Stage Stochastic Programming

I gonna use the approach used in this document. Suppose there are $T$ stages and uncertain parameter is $\xi_{t}, \quad t \in \{1,2,\dots,T\}$. In this algorithm, it is required to calculate the ...
1
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93 views

How do I find the extreme rays and points for a stochastic programming problem

I have the following 2 stage Stochastic Programming program: \begin{align}\min_x& \quad x+\sum_{s=1}^{3}p_sQ_s(x)\\\text{s.t.}&\quad x\in\Bbb R\\&\quad Q_s(x)=\min\left[\begin{pmatrix}1&...