• Path constrained problem

    From hills588@gmail.com@21:1/5 to All on Tue Mar 29 18:30:14 2016

    I have a problem where machines operating between a minimum and maximum rate each process a single assigned queue of items in a defined order. Total output from all the machines creates a blended product per time period. Each machine rate may be sped
    up or slowed down to achieve the blend.

    To model I've used variable X_it 0<=X_it <= 1 to be that part of item i that is processed in period t, B_it is a binary variable equal to 1 if all of item i is processed by the end of period t.

    This leads to constraints

    sum_{p=1..t} X_0p >= B_0t >= sum_{p=1..t} X_1t >= B_1t etc.

    I'm wondering if there is a similar problem in the literature, possibly a path constrained problem or machine scheduling type problem?

    Also if there are known constraints, path constraints or related, for this problem structure that I can use as cutting planes.

    Hope that makes sense. All input appreciated!

    Thanks for your help,


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