All Questions
Tagged with linearization integer-programming
23
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 ...
-1
votes
1
answer
74
views
How to linearize a product of an integer and a binary variable
i have this constraint right here, which is not linear. How would i linearize such a product. $number_t$ is a positive integer and $new_t$ and $reset_t$ are binary.
$$number_t = (number_{t-1}+new_t)\...
- 71
4
votes
1
answer
328
views
Optimization problem with the Harmonic number
I have an optimization problem:
\begin{align*}
\text{ minimize } \sum_{i=1}^n H(x_i)
\\
\text{ subject to } Ax \geq b, x\geq 0, x\in \mathbb{Z}^n
\end{align*}
where $H(n)$ is the $n$-th Harmonic ...
- 1,015
1
vote
1
answer
125
views
How to linearize the following constraints
Given the following two expressions:
$ x - \frac{1}{T}\sum_{i} y_{i}$
$ x - \frac{1}{Q}\sum_{i} \beta_{i} y_{i}$
where $x \in \mathbb{Z}_{+}$, $y \in \mathbb{R}_{+}$, and $T$, $Q$ and $\beta_{i}$ ...
- 113
1
vote
2
answers
263
views
Linearizing if else conditions in ILP
We are given three binary indicator variables $X_{ij}, Y_{jk}$ and $Z_{jl}$. Write linear constraints such that,
a) if $X_{ij}$ is equal to 1, then for that $j$ when $X_{ij} = 1$, exactly one $Y_{jk} =...
- 917
3
votes
2
answers
396
views
How to model a binary variable?
I am trying to find a constraint for the following relationship, but am failing a bit at it right now. I want to find a linear constraint that does the following. The binary variable $switch_{ot}$ is ...
- 91
3
votes
3
answers
268
views
Equivalence between constraints in ILP
Let's have binary variables $x$ and $y$. I'd like to define a helping binary variable $z$ such that
$$ z = 1 \; \;\; \mathrm{iff} \; \; \; x + y = 2.$$
If I wanted to express the equivalence between ...
- 133
2
votes
1
answer
109
views
Expressing inner product of binary variables in MIP
I have a $m$ by $n$ matrix $X$ of binary variables in my MIP which represents a list of $m$ items each belonging to one of $n$ categories. $m$ is usually around $1,000$ while $n$ is much lower at ...
- 123
3
votes
2
answers
375
views
How to model logic constraint: $y=1$ if $a\le x\le b$ and $y=0$ otherwise?
I am trying to formulate indicator-type of constraints. $y$ is binary $0$ or $1$ and $x$ is a continuous variable.
$$ y =
\begin{cases}
1, & \text{ if } a \leq x \leq b \\
0, & \...
- 53
2
votes
1
answer
123
views
Linearize a product of binary variables with 2 indexes
I have the following inequality that I would want to linearize.
Consider that $r_{ij}, x_{ij}, y_{ij}$ are binary variables defined for every pair of nodes $(i,j) \in A$. Also, I have a set of nodes $...
2
votes
1
answer
268
views
How to write constraint with sum of absolutes in Integer Programming?
I found a solution for just one term here
How can we formulate constraints of the form
$$ \sum_{i=1}^n |x_i -a_i| \ge K $$
in Mixed Integer Linear Programming ?
- 203
7
votes
2
answers
889
views
Is there a better way of defining a constraint on positive integer variables such that no two variables are the same and are uniquely assigned a value
So suppose I have integer variables $x_1,x_2,\dots,x_N$ and I enforce that the integer variables are bounded i.e $1 \leq x_i \leq N$
I was interested in posing a constraint so that in the collection $...
- 205
1
vote
1
answer
165
views
Linearization of constraints in a ILP
I have been working on a Graph Theory problem for my thesis and got stuck about the linearization of some constraints. I am hiding everything, constraints, variables and so on, of my problem not ...
- 741
3
votes
1
answer
563
views
Constraints that set values to binary variables depending on other binaries
I am trying to write a mathematical problem that involves some conditions based on binary variables. More specifically, I have a set of three binary variables $d_1$, $d_2$, $d_3$ and depending on ...
- 133
3
votes
0
answers
189
views
How to linearize a max min objective function?
Let us suppose that I have a $\max \min$ objective function that only depends on one set of variables:
$\underset{x}\max \underset{y}\min dy$
Associated with the linear set of constraints and right ...
- 741