All Questions
Tagged with linearization modeling
55
questions
0
votes
1
answer
76
views
PULP: Optimization Assignment of Bicycle production per month
Q1. If bicycles of types A and H are produced, then bicycles of type C can be produced with 20% shorter working hours, while selling profit of bicycles type H can be 20% higher.
Q2: If bicycles of ...
3
votes
1
answer
199
views
How to linearize the following logical constraints?
I am having trouble linearizing the following logical constraints.
$x,y,z$ are non negative continuous variables such that $x=y+z$, and $A$ is a positive parameter. I would like to linearize
$$
y=
\...
- 79
4
votes
2
answers
309
views
Linear condition between two continuous variables
There are two real variables $x$ and $y$. The conditions are such that:
if $y\le 0$, then $x=0$
if $y>0$, then $x=y$
How to write linear equations or inequalities to satisfy both the conditions?
- 41
0
votes
1
answer
105
views
How to model this constraint in a better way?
I have a resource allocation problem. There are $M$ users and $N$ resources (machines).
One user can be assigned to multiple resources/machines.
But maximum $B$ machines can be activated at a time for ...
- 2,377
3
votes
1
answer
194
views
Reformulate constraints
I have the following constraints and am wondering whether I can formulate the whole thing more narrowly and with fewer constraints. $x_{itk}$ is binary and $u_{it}, v_{itk}\in [0,1]$. $M$ is a Big-M ...
0
votes
1
answer
36
views
Add second "constraint" to model a binary variable
in my model I have the binary variable $f_{ij}$ which pushes a time-dependent $j$ integer variable $D_{ij}$ to zero if $f_{ij}$ takes the value 1 and keeps the integer number if $f_{ij}$ equals 0. Yes,...
- 89
0
votes
0
answers
64
views
Is it possible to transform MIQP into MILP without introducing new variable?
I have a QP optimization problem in the form
$$\min {\bf x}^T{\bf Qx}-{\bf c}^T{\bf x}$$
here $\bf Q$ is a symmetric matrix.
$\bf x$ is the optimization variable, and it is binary.
Is there a way to ...
- 2,377
0
votes
2
answers
126
views
Converting a piecewise function to linear equations
I am trying to build a MILP model. In this model, I have a dependent variable (alpha) that its value depends on the value of some other variables (or different combination of some other variables). In ...
- 97
0
votes
1
answer
67
views
Formulation of a stepwise linear approximation
I am currently trying to solve an MILP in Gurobi. Unfortunately, Gurobi does not support non-linear functions and I would like to do the following. I currently have the following constraint. It ...
- 139
3
votes
2
answers
232
views
Convex equivalent of a constraint
I have a constraint as follows in my MILP model:
$$
\sum_{e} (a_1(e) - a_2(e))^2 \leq M
$$
Where, $a_1(e)$ and $a_2(e)$ are binary variables. Would you please guide me how can I find the equivalent ...
4
votes
1
answer
328
views
Optimization problem with the Harmonic number
I have an optimization problem:
\begin{align*}
\text{ minimize } \sum_{i=1}^n H(x_i)
\\
\text{ subject to } Ax \geq b, x\geq 0, x\in \mathbb{Z}^n
\end{align*}
where $H(n)$ is the $n$-th Harmonic ...
- 1,015
1
vote
2
answers
157
views
Matrix lookup modelling variants
As part of a bigger model I have a matrix of variables $x_{ij} \geq 0$ and a "selector" set of variables $y_j \in \{0,1\}, \sum_j y_j = 1$.
From $x_{ij}$ I'd like to get the variables of ...
- 113
0
votes
0
answers
77
views
Optimize revenue function with log part
I am working on an optimization problem where I aim to maximize revenue. My current model has the following objective function:
$$ Sales(P_i) * log(P_i - const_i))$$ where $P_i$ represents the price ...
- 133
2
votes
1
answer
105
views
Representing a Multi-Level Categorical Variable using Big-M Method in Linear programming
I'm working with a statistical linear model where I have a variable, ( N ), representing the percentage of charging of a battery. Based on ( N ), I derive another variable, ...
- 133
3
votes
1
answer
109
views
using milp for a linear complementarity problem
I have to minimize $c^Tx$
subject to $Ax = b$, $x_iw_i = 0$ for all $i$, with $x$ non negative continuous and $w$ binary.
What model should I use to solve this problem?
