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Big m method / two-phase method

  1. Feb 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Minimize Z = 3.5x + 6.5y
    subject to
    1. (1/3)x + y ≥ 1
    2. 3.8x + 2.4y ≥ 5
    and x ≥ 0, y ≥ 0

    Use Big M method and then Two-Phase method interactively with IOR.jar and compare answers.


    2. Relevant equations



    3. The attempt at a solution
    I am getting really confused with IOR, but this is what I have

    Big M Method:

    Minimize Z = 3.5x + 6.5y + Ma + Mb --> Max(-Z) = -3.5x - 6.5y - Ma - Mb -->
    -Z + 3.5x + 6.5y + Ma + Mb = 0
    subject to
    1. (1/3)x + y - u + a = 1
    2. 3.8x + 2.4y - v + b = 5
    and x, y, u, v, a, b ≥ 0

    I attached my IOR txt file... just wondering if it's all right?
    Not sure how to do the Two-Phase method on iOR, there isn't an example in the book.. help please?
     

    Attached Files:

  2. jcsd
  3. Feb 20, 2012 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    The two-phase method starts by trying to get a basic feasible solution (or prove infeasibility). It does this by first solving the problem min (a + b), subject to the constraints you wrote for the Big M problem.

    RGV
     
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