Unanswered Questions
40 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
7
votes
0
answers
96
views
Calculating robustness of layout plans
We have tried to design a manufacturing cell which will produce specific families of products. We figure out three layout plans for implementation. For practical reasons, we need to calculate the ...
- 5,442
6
votes
0
answers
88
views
Robust Linear Optimization for avoiding diminishing returns
My engineering problem can be formulated as an LP as shown below
\begin{align}
\max_{\mathbf{x}}~~&\mathbf{a}^T\mathbf{x} \\
\mbox{s.t.}~~~&\mathbf{b}^T\mathbf{x} \leq B~~,~~\mathbf{1}^T\...
- 251
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
95
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
1
answer
150
views
Need help understanding robust optimization formulation
I am reading these notes from Stanford called "Optimization with uncertain data".
In section 2.2, Example 2 (page 7), the author mentions the following portfolio problem $(P)$:
$$
\max \; t
$...
CommunityBot
- 1
4
votes
0
answers
57
views
Best Case Optimization, which is sort of the opposite of Robust Optimization
TLDR: If George Costanza was supposed to do Robust Optimization, he would instead do Best Case Optimization, which is (sort of) the opposite of Robust Optimization.
Is there a literature or problem ...
- 13.5k
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
135
views
How to find robust counterpart of sum of logit functions?
Suppose function $\mu_i(y):\mathbb{R} \rightarrow \mathbb{R}$ is a logit function, $\mu_i(y)=1/(1+\exp(-y))$. Also, we assume that $\mathbf{x}_i\in \mathbb{R}^d$ and $\theta \in \mathbb{R}^d$. I am ...
- 1,895
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
89
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
1
answer
61
views
Optimization under cardinality constraint
When we consider the following optimization problem:
\begin{equation}\label{P}\tag{P}
\begin{array}{ll}
\displaystyle\min_{x \in \mathbb{R}^n} & f(x) \\
\text{s.t.} & Ax = b,~ x \geq 0, \\
&...
- 103
2
votes
0
answers
38
views
Recoverable Robustness for an optimization problem
I am relatively new to the concept of recoverable robustness. I am researching the robust version of an optimization problem. I currently have methods to address the problem with perfect knowledge. ...
- 390