Questions tagged [big-m]
For questions related to the use of a "big M" (large constant) in a mathematical modeling context, either in the objective function (to initialize the simplex method) or in constraints (to formulate logical constraints, to linearize constraints, and so on).
7
questions
17
votes
5answers
3k views
When to use indicator constraints versus big-M approaches in solving (mixed-)integer programs
Various optimization modeling languages and solvers allow for both indicator constraints (see for example here, here and here) and traditional binary variable and big-M approaches can be used to model ...
22
votes
2answers
1k views
Why is it important to choose big-M carefully and what are the consequences of doing it badly?
The question here discusses the two different use of "big-M method", where one of them is the big-M in logical constraints and linearization in (mixed-)integer programming problems (that's what I'm ...
12
votes
4answers
711 views
Single reference for Mixed Integer Programming formulations to linearize, handle logical constraints and disjunctive constraints, do Big M, etc?
Is there a single crisp and accessible reference which covers how to generate Mixed Integer Programming formulations to linearize products, handle logical constraints and disjunctive constraints, do ...
13
votes
4answers
220 views
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 ...
16
votes
1answer
580 views
What is the “big-M” method? And are there two of them?
I’ve seen the "big-$M$ method" referred to in different ways. What is the "big-$M$ method" and why does it seem to mean two different things?
12
votes
2answers
1k views
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 ...
6
votes
2answers
277 views
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:
$Y \cdot A \le B$...
