Unanswered Questions
44 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
9
votes
0
answers
203
views
Ill-conditioned LP in Benders decomposition
I have implemented a Benders decomposition for a constrained network flow but the LP solver (Gurobi) warns me of the ill-conditioning of the subproblem dual LP. As you can see below, the coefficients ...
- 33.1k
6
votes
0
answers
213
views
Benders decomposition for a dense MILP
I am trying to solve a large MILP, but it seems like dense problems can be very difficult for moderns solvers. I tried to solve the problem described below considering only constraints (1) and (2) ...
- 109
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
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
38
views
To "fix" continuous variables in Benders decomposition
In nearly all applications I have seen, the master problem variables $x$ that define the subproblem are binary.
(Logic-based) Benders decomposition can applied to a problem of the form: $$\min_{x,y} f(...
- 33.1k
3
votes
1
answer
210
views
Implementing Logic-based Benders decomposition on a single search tree
Currently, I am working on a scheduling problem and trying to approach it by the logic-based Benders decomposition method. Theoretically, I have everything, i.e., the master and sub problem(s), the ...
CommunityBot
- 1
3
votes
0
answers
50
views
Control variables and cofounding effects in stochastic programming/,model predictive control/reinforcement learning
How can we be sure that confounding variables/control variables don’t pickup the effect our decisions w.r.t decision variables had on the actual control variable?
Since the term control variable ...
3
votes
0
answers
89
views
Derivative of sup(max) functions in distributionally robust optimization
In the distributionally robust optimization problem
\begin{aligned}
\min_{x\in X}\sup_{P\in\mathfrak{P}}\mathbb{E}_P[f(x,\xi)],
\end{aligned}
where $f:\mathbb{R}^n\to\mathbb{R}$ and $P$ is a ...
- 155
2
votes
0
answers
107
views
Automated Benders Using Annotations
I'm trying to solve an optimization model using Automated Benders with annotations using CPLEX library in C++. I've defined a master problem and N (number of supply nodes in my model's network) ...
- 1
2
votes
0
answers
83
views
Benders with MINLP subproblem as the pricing problem of Dantzig Wolfe
I have a convex MINLP that after a Dantzig-Wolfe reformulation, passes most of the difficulty onto the pricing problem, which becomes a convex MINLP itself.
The pricing problem should be solvable with ...
- 1,895
2
votes
0
answers
86
views
Reformulate the deterministic equivalent model as an Expected Value problem
Given an optimization problem as follows:
$$
\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