Unanswered Questions
28 questions with no upvoted or accepted answers
9
votes
0
answers
230
views
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 ...
- 1,687
6
votes
0
answers
226
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 ...
- 165
6
votes
0
answers
94
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):
$$
\frac{1}{N}\sum_{i=1}^N f(x,\xi^i).
$$...
- 155
5
votes
0
answers
154
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{...
- 2,463
4
votes
0
answers
164
views
Stochastic optimization for inventory management
The deterministic problem is to minimize operational cost subject to constraints in demand, supply and capacity. The ordering policy is periodic review, order-up-to.
The stochastic version of the ...
- 1,895
4
votes
0
answers
54
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+...
- 2,160
3
votes
0
answers
50
views
Control variables and cofounding effects in stochastic programming/,model predictive control/reinforcement learning
How can we be sure that confounding variables/control variables don’t pickup the effect our decisions w.r.t decision variables had on the actual control variable?
Since the term control variable ...
3
votes
0
answers
88
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 ...
- 155
2
votes
0
answers
85
views
Reformulate the deterministic equivalent model as an Expected Value problem
Given an optimization problem as follows:
$$
\begin{array}{cc}
\operatorname{Max} Z=3 x_{1}+9 x_{2}-2 y_{1}-4 y_{2} \\
\text { subject to, } y_{1}+y_{2}=15 \\
5 x_{1}+2 x_{2} \leq 10 \\
x_{1}, x_{2}, ...
- 157
2
votes
0
answers
99
views
Two-stage stochastic with non-linear recourse
I am working on a two-stage facility location problem as I described in this question.
I am solving it with the L-shaped method (Benders decomposition). The cost value between each $(i,j)$ is a ...
- 5,442
2
votes
0
answers
297
views
What is the intuition behind Progressive hedging algorithm?
I am reading some papers about PHA to solve multi-stage stochastic programming, but I think it is not still clear to me. This is my understanding and I would be thankful to know if it is correct or ...
- 2,160
2
votes
0
answers
803
views
How to write nonanticipativity constraints?
In Multi-stage stochastic programming, we write the constraints that for scenarios $s$ and $s^{\prime}$ which have the same trajectory up to time $t$, should take the same value. That is,
$$
x_{t,s} =...
- 2,160
2
votes
0
answers
63
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
vote
0
answers
37
views
Using the Alternative Cut Generation Problem in Benders, why do I get different results?
I am using Benders' Decomposition to solve a stochastic MIP.
To improve cut selection, I implemented the Alternative Cut Generation Problem as proposed by Fischetti et al. (2010).
I will summarize the ...
- 327
1
vote
0
answers
21
views
Building a CapEx portfolio using mathematical optimization
Let's say you have a set of potential capital projects $C$, each defined by an up-front investment $c_i$ and random payoff (say, NPV) $P_i(\omega)$, where $\omega \in \Omega$ is a point in a sample ...
- 111