Integer programming Definition and 13 Threads

An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear.
Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
If some decision variables are not discrete the problem is known as a mixed-integer programming problem.

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  1. bagasme

    B Solving a Linear Programming Problem which Requires Integer Solutions

    Hello, In grade 11 of high school, I encountered this linear programming problem on my textbook: The "alternative solution" described in the textbook as follows: Let: - ##x## : amount of plant A - ##y## : amount of plant S - ##L## : garden area - ##L_x## : area of garden for one plant A -...
  2. Aleoa

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  3. A

    I Open source software for integer programming

    I don't usually need help in locating software, but I'm having a heck of a time tracking down a good open-source bit of software which solves integer programming problems using arbitrary precision! If I don't find one soon, I'll need to write it myself. Which I don't mind, but it's silly to...
  4. S

    I Linear mapping of a binary vector based on its decimal value

    Given an ##N## dimensional binary vector ##\mathbf{v}## whose conversion to decimal is equal to ##j##, is there a way to linearly map the vector ##\mathbf{v}## to an ##{2^N}## dimensional binary vector ##\mathbf{e}## whose ##(j+1)##-th element is equal to ##1## (assuming the index starts...
  5. F

    Integer programming model (alternating constraints)

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  6. B

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  7. S

    A Can this optimization problem be solved?

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  8. rumborak

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  9. C

    MHB Help on Fuzzy Integer Programming

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  10. C

    MHB How Can Binary Integer Programming Optimize Subject Distribution in Schools?

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  11. T

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  12. I

    Formulating a Mixed Integer Programming Problem

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  13. A

    Integer Programming help please T__T

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