All Questions
Tagged with linearization big-m
16
questions
0
votes
0
answers
116
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why this little constraint changes my whole program?
I'm trying to linearize a CP in ILOG CPLEX.
I have the following constraint that I want to linearize (I already simplified it with the big M) :
...
0
votes
0
answers
66
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Why are these two constraint equations not equivalent?
I've made a CP Model of an hospital in ILOG CPLEX and I want to test the performance of the CPLEX version of it.
In my CP model, I have the following constraint :
...
2
votes
3
answers
230
views
Linearization the product of three variables (two binary & one continuous)
Consider the following binary variable $x \in \{0,1\}$ and two continuous real variables $y,p \in \mathbb{R}$.
I am trying to model the following conditional equations as constraints:
\begin{cases}
...
- 113
2
votes
0
answers
40
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Choosing upper and lower bound using big-M [duplicate]
This question is related to my previous question posted here: Piecewise constraint using big-M notation and this question posted on the math stackexchange: https://math.stackexchange.com/questions/...
- 67
1
vote
1
answer
229
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Non-linear optimization local or global solution
In an NLP, I have a constraint that I would like to formulate in a convex manner preferably without introducing binary variables and/or big M formulations if possible. The actual problem is non-convex ...
- 81
2
votes
3
answers
2k
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Linearizing a Max Function in the constraint - not working
I have a minimization function which is in its simplest form looks like below. I am including the index of the variables.
...
- 803
1
vote
0
answers
65
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Linearize max function in a constraint [duplicate]
I have a constraint as follows:
$ \sum_i {r_i} \geq \max \{g_j, B_j\} $
where, $r_i$, $g_j$ are variables and $B_j$ is a parameter.
How do I linearize the constraint (I suppose using big-M method)?...
- 803
3
votes
1
answer
599
views
How to fomulate the following conditional constraint in MILP?
How can I formulate the following conditional constraint to a linear constraint using indicator variables? Please note that all variables are continuous and $c \ge 0$
$\text{1: if} \ c=0 \ \& \ ...
- 294
3
votes
2
answers
506
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Mocking up conditional statements in LP
I would like to know how if condition statements in linear programming can be reformulated using indicator constraints, and hence solved as a mixed integer linear program. Specifically:
1. Is it ...
- 161
5
votes
2
answers
655
views
Linearizing objective function with variables inside an indicator function
I am working on a problem in which I am trying to maximize the average of a variable only for the data that meet a certain condition with a constraint on the number of data that meet this condition. I ...
- 53
8
votes
1
answer
931
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if-else condition for the objective variable using big M notation
Let $0\leq \beta\leq 1$ be an objective variable. The size of $\beta$ is $N\!\times\!N$.
Now, how can I impose the following?
if $\beta_{i,j}>0$ then $\beta_{j,i}=0$
Big M notation can be ...
- 83
11
votes
2
answers
1k
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Linear programming: objective function with "buckets"
I had a linear programming problem with the following objective function
$$f(x) = \sum_{j}x_jq_jp_j - \sum_{i}\left(\sum_{j}x_jq_jC_{ij} \right) c_i$$
Where $q, p, C, c$ are known.
This problem was ...
- 241
3
votes
1
answer
99
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defining Mixed integer linear inequalities for a set of variables
The problem is described as follows:
considering $n$ variables which are continuous and bounded such that
$$L_i \le x_i \le U_i\quad \forall i=1,2,\dots,n.$$
How can i define a set of mixed integer ...
- 135
5
votes
2
answers
567
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How to model If $A \le B$ then $Y = 1$, otherwise $Y = 0$
Somehow I don't get it right.
I would like to model the following conditional:
If $A\le B$ then $Y=1$ otherwise $Y=0$
where $A, B$ are reals and $Y$ is binary.
I can model as follows:
$Y \cdot A \le B$...
- 2,252
13
votes
4
answers
795
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The effect of choosing big M properly
I have a set of linearized constraints that are modelled using big-Ms. Now, it is, of course, common knowledge to make the value of M and small as possible in order to provide tighter LP relaxations ...
- 1,859