Questions tagged [indicator-constraints]
For questions on constraints controlled by binary variables.
63
questions
3
votes
1
answer
521
views
Model ```a > 0 implies b = 1```, where a is unbounded above
I want to model if a > 0 then b = 1, where a is an unbounded above continuous variable and ...
- 618
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
0
answers
66
views
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 :
...
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
1
vote
1
answer
97
views
Logical conditions
This is similar to question I asked here: Priotization rules for variable allocation in linear programming. In an optimization problem, the goal is to manage the purchase and sale of items under ...
- 23
1
vote
2
answers
117
views
Priotization rules for variable allocation in linear programming
I’m working on an optimization problem and need help with correctly prioritizing the allocation of certain variables in a constraint. The rules are:
Only one of the variables $y_{t}$, $zn_{t}$ and $...
- 23
1
vote
1
answer
98
views
Mixed Integer programming, the big M
In the constraints below, why have they used the big M? What do we look for in order to identify the big M in other questions?
- 39
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
1
vote
1
answer
43
views
if else condition with multiple criteria in MIP
I have problem like below
Decision variable x1 >= 0
But it depends on selection variable s1 as binary variable
If s1 = 0 then x1= 0 and
if s1 = 1 then x1>0
how I can write this as constraint for ...
- 13
2
votes
1
answer
100
views
Formulation for choosing how many items to manufacture
I am working on a scheduler for a manufacturing plant. I have currently set it up so the decision variables are set up as binary variables:
$x_{m,p,s}$ = 1 if machine m is running part p on shift s
...
- 55
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
1
vote
0
answers
43
views
The rule of the slack variable in an indicator constraint
In some cases I have seen, the indicator constraint can be written as indcons(expression, binary_var). Then it is interpreted as follows:
$$LHS - slack (\leq = \geq)...
- 9,068
0
votes
2
answers
124
views
Modelling a binary variable in LPs
I need your help.
I'm setting up an LP and I'm trying to find constraints to introduce the binary varibale $b_{ij}$. So it should take the value 0 if the sum of all $a_{ij}$ values to the period t are ...
- 19
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
1
vote
1
answer
56
views
Assistance in formulating implication constraints for inequalities
I would like to seek some advice on modeling the following logical implications, where $\delta$ is a binary variable, $D_{j}$ and $A_{j}$ are nonnegative discrete variables, and $p_{j}$ are ...
- 717