Questions tagged [integer-programming]

For questions about mathematical optimization problems involving binary or general integer variables.

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22
votes
3answers
2k views

In an integer program, how I can force a binary variable to equal 1 if some condition holds?

Suppose we have a binary or continuous variable $x$, a binary variable $y$, and a constant $b$, and we want to enforce a relationship like If $x \gtreqless b$, then $y = 1$. How can we write this ...
11
votes
2answers
525 views

In an integer program, how can I “activate” a constraint only if a decision variable has a certain value?

Suppose we have the constraint $$a_1x_1 + \cdots + a_nx_n \gtreqless b,$$ where $a_i$ and $b$ are constants and $x_i$ are decision variables. Suppose also that we want the constraint to hold if $y=1$ (...
4
votes
1answer
737 views

What are good reference books for introduction to operations research?

The reference books should cover the wide range of problem-solving techniques and methods.
16
votes
5answers
2k 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 ...
5
votes
2answers
364 views

Linear and Integer programming materials

I was wondering if you could refer me to some online video/text resources to learn linear and integer programming. I am intending to work in the field of data science. I greatly appreciate your kind ...
12
votes
2answers
454 views

Expressing a chain of boolean ORs using ILP

How to express a chain of OR operations in an ILP in which each expression is a less than or equal constraint and the left hand side variable in all inequalities is always the same? All the variables ...
22
votes
3answers
2k views

What is the difference between integer programming and constraint programming?

At first glance both approaches appear to be very similar. What are the major differences between integer programming and constraint programming?
25
votes
3answers
365 views

Feeding known lower bounds to solvers

Given an optimization problem that aims at minimizing some objective function, a lower bound that is valid for all optimal solutions, and your solver of choice: For what theoretical and/or practical (...
11
votes
1answer
241 views

Expressing a chain of boolean ORs using ILP involving different variables

How can I express a chain of OR operations in an ILP, given that each operand is an inequality between two binary variables? I have asked a similar question here: Chain of Boolean ORs. In that ...
8
votes
1answer
205 views

When using docplex.cp is it possible to get all feasible solutions?

I would like to solve an ILP and get all feasible solutions (even the worst one). How could I do that using docplex.cp? I've seen a similar question in: Using CPLEX "solution pool" to count ...
13
votes
2answers
792 views

How to choose between high number of binary variables or fewer number of integer (not only 0 and 1) variables in a IP formulation?

When I have to write the formulation of an IP, I usually have the choice between writing $i\times j$ binary variables with two indices such as $ x_{i,j} $ or, writing $j$ integer variables $x_i$. Is ...
12
votes
3answers
1k views

Allocating credit card points

I’m interested in the idea behind this in general, so I thought this would be the best place to post, though I have a practical and semi-urgent need of allocating the points on my credit card towards ...
12
votes
2answers
295 views

Expressing an implication as ILP where each implication term comprises a chain of boolean ORs

Consider an implication of the form $A \implies B$ where both $A, B$ comprises a chain of Boolean OR variables. For example, $(a_1 \lor a_2 \lor a_3) \implies (b_1 \lor b_2 \lor b_3)$. How can this ...
10
votes
2answers
602 views

Decision Variable Value from a Set (Gurobi)

Is there a way to set a decision variable to take values from a set? Example: decision variable $x \in \{0,50,100\}$ So this variable can only take one of these three values and not more. I have ...