Unanswered Questions
198 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 ...
9
votes
0
answers
203
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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 ...
7
votes
0
answers
149
views
Is this a valid strong polynomial algorithm for deciding LP feasibility?
Let
$$A \cdot X + B \preceq 0$$ be a system of linear inequalities with $X \in \mathbb{R}^n$ $A\in \mathbb{R}^{m\times n}$ and $B \in \mathbb{R}^m$ where $m \geq n$. According to Farkas lemma, exactly ...
7
votes
0
answers
151
views
Modeling traffic in a city
I am trying to model traffic in a city, $(i,j)$ represents a road in a city.
There are $H$ vehicles in a city they have some prescheduled set of destinations to visit, $A_{j,h}$ denotes arrival time ...
7
votes
0
answers
93
views
Building the Scheurman's Model II constraints for a multi period linear program
Scheurman's paper discusses Model I and model II Formulation to solve harvesting and scheduling problems. It is a specific implementation to solve multi period linear programs. Both models are also ...
7
votes
0
answers
81
views
Modelling a simple ordering problem to have balanced delivery days
Assuming that I should buy 50 items from 25 different vendors with pre-known delivery duration between 2-7 day for each, which day of a week should I place each order so that the delivery days be even ...
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\...
6
votes
0
answers
111
views
Dual instability, degeneracy, tailing off effect - Which are the causes and which are the effects?
Dual instability, degeneracy, and the tailing off effect are often mentioned together in papers. However, I cannot seem to find a clear explanation on which of these cause the other and vice versa? ...
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 ...
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):
$$
\frac{1}{N}\sum_{i=1}^N f(x,\xi^i).
$$...
6
votes
0
answers
106
views
Estimating multistop routing costs
In many OR problems, it is sometimes a good idea (or necessary) to relax routing constraints.
An example of this occurs in the classical facility location problem, where a warehouse can send out a ...
6
votes
0
answers
237
views
Provide basic solution to CLP
I'm using Pyomo to formulate an LP with approx 500,000 constraints and 200,000 decision variables. The LP is solved using CLP. Some instances fail to return even a feasible solution after many ...
6
votes
0
answers
100
views
Proof that the leaving variable cannot be selected as the entering one in the next round
Using the Dantzig's pivoting rule, can it be proven that the leaving variable of one round cannot be selected as the entering variable in the next round?
6
votes
0
answers
187
views
Benefits of removing slack variables during presolve
I was reading Tobias Achterberg's thesis, and on page 138 he mentions the following presolving technique for linear equations (I'm slightly paraphrasing Example 10.2):
Consider the equation $4x_1+...
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{...