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Math Help - Linear Programming Problem

  1. #1
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    Linear Programming Problem

    Hi all, I am trying to teach myself some linear programming and have become stuck with this quesion



    Lets Suppose a large construction project has been broken down into 6 activities. The times to complete the activities along with the necessary preceding activities are shown in the following table.


    Activity
    Preceding Activity Duration (Weeks)
    A - 50
    B A 30
    C A 20
    D A 40
    E B,C 50
    F B 40
    G D,E,F 60


    Activities E and F will require external consultants to conduct the work and so times for these
    activities are based on preliminary estimates from the contractors. The agreed completion
    time for the project has to be within 160 weeks.

    a) Formulate this situation as a linear programming problem, where the aim is to complete the project in the shortest possible time.

    Thanks
    Last edited by SelfTaughtMaths; November 1st 2013 at 09:02 AM.
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  2. #2
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    Re: Linear Programming Problem

    Hint: the shortest possible time is 190 weeks (which is 1165 days past the desired completion point).
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  3. #3
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    Re: Linear Programming Problem

    I apologize, all units are all meant to be in weeks

    Indeed I may see that this is a Shortest path problem, and that the shortest possible time is 190 weeks. This is how I have formulated it as a linear program so far

    A+50 <= B
    A+50 <= C
    A+50 <= D
    B+30 <= E
    B+30 <= F
    C+20 <= E
    D+40 <= G
    E+50 <= G
    F+40 <= G

    A=0
    B,C,D,E,F,G >= 0
    Last edited by SelfTaughtMaths; November 1st 2013 at 09:27 AM.
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  4. #4
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    Re: Linear Programming Problem

    I am not quite sure what a linear program is supposed to look like, so that was as helpful as I could be.
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  5. #5
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    Re: Linear Programming Problem

    No Problem, that you for your help though
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