All Questions
Tagged with linearization logical-constraints
39
questions
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
$$
y=
\...
- 79
4
votes
2
answers
309
views
Linear condition between two continuous variables
There are two real variables $x$ and $y$. The conditions are such that:
if $y\le 0$, then $x=0$
if $y>0$, then $x=y$
How to write linear equations or inequalities to satisfy both the conditions?
- 41
0
votes
1
answer
36
views
Add second "constraint" to model a binary variable
in my model I have the binary variable $f_{ij}$ which pushes a time-dependent $j$ integer variable $D_{ij}$ to zero if $f_{ij}$ takes the value 1 and keeps the integer number if $f_{ij}$ equals 0. Yes,...
- 89
0
votes
1
answer
85
views
How to represent "if $y_{it} = 1$ and $z_{jt'}=1$ then $x_{ij,t+t'}=1$"
There is a fulfillment problem in the e-commerce logistics field, where the fulfillment of each order is composed of a main transport (from City A to City B, referred to as a route) and an end ...
- 105
2
votes
1
answer
251
views
Replace the constraint using ==> by a linear formulation
I would like to know how to express the continuity constraint without using a decision variable in the conditional form. My challenge is to stay with a linear formulation.
I will start to explain my ...
1
vote
1
answer
125
views
How to linearize the following constraints
Given the following two expressions:
$ x - \frac{1}{T}\sum_{i} y_{i}$
$ x - \frac{1}{Q}\sum_{i} \beta_{i} y_{i}$
where $x \in \mathbb{Z}_{+}$, $y \in \mathbb{R}_{+}$, and $T$, $Q$ and $\beta_{i}$ ...
- 113
2
votes
1
answer
64
views
how to linearize if-then when having an operand?
if $x_{i,j,p,s}$ and $y_{i,j,p,s}$ are binary and $z_i^s$ is integer; how to enforce:
$$
((x_{i,j,p,s}=1) \land (z_i^s \ge 5 )) \implies y_{i,j,p,s}=1
$$
The value of $z$ in my problem could be 1 to ...
- 33
1
vote
1
answer
435
views
Is it possible to do a linearization without introducing new variables?
I have three binary variables $x_{i,j}^{m,r}$ , $y_i^{m,r}$, and $z_i^{m,r}$. There is another integer variable $w_i^r$. And I want to linearize the following logic:
$$ \sum_{m} x_{i,j}^{m,r} \ge 1 \...
- 53
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
1
vote
0
answers
92
views
Linearization of Conditional Constraints for MIP using Cplex
I'm currently working on a mixed-integer programming (MIP) problem and I'm trying to implement a set of conditional constraints in CPlex. These constraints involve decision variables that are indexed ...
- 11
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
5
votes
4
answers
884
views
Rewriting if-then constraints of binary summations
Suppose both $x_{i,j}^{ab}$ and $y_{i,j}^a$ are binaries. Then how can I rewrite the following if-then in linear form?
$\sum_b x_{i,j}^{ab} \ge 1 \implies \sum_{i,j} y_{i,j}^a = 0$
I was thinking of ...
- 177
4
votes
2
answers
380
views
How to model $C_1=C_2$ implies $b_1 = b_2$
Suppose $C_1 \ge 0$, $C_2 \ge 0$ are continuous variables and $b_1$, $b_2$ are binary variables.
How could I model the following?
$C_1 = C_2 \implies b_1 = b_2$, the opposite does not hold.
- 2,252
3
votes
1
answer
135
views
How to enforce logical implication $\sum_j a_j x_j \le b \implies \sum_j c_j x_j \le d$
Some modeling languages and solvers support indicator constraints of the form $$y=\hat{y} \implies \sum_j a_j x_j \le b,$$ where $y$ is a binary decision variable and $\hat{y}\in\{0,1\}$ is a constant....
- 33.1k
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