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Formulating a Mixed Integer Programming Problem

  1. Nov 9, 2012 #1
    1. The problem statement, all variables and given/known data
    Not sure if this type of math goes in this section, but I have a quick question regarding a MIP problem. It's simple to grasp, but I'm not sure whether or not I am formulating this problem correctly.

    A city needs to hire workers to clean the snow. The city is divided into j areas, which require a certain number of trucks, nj, within area j. The workers are required to place a tender at the beginning of the ear, which includes the price per truck and the number of trucks they can supply. We must formulate a model where i workers are tendered, ti is the trucks available from worker i, cij is the price per truck per area j, and mj is the minimum number of workers for area j. And the workers can't supply more trucks than are necessary for their areas

    2. Relevant equations

    3. The attempt at a solution
    Let xij = number of trucks supplied by contractor i to area j
    Let yij = 1 if worker i supplies in trucks in area j, 0 if worker i does not supply trucks in area j

    I want to minimize Z = [itex]\sum[/itex]cijxij

    My constraints are:

    [itex]\sum[/itex]xijtiyi (i'm not sure about the yi part)

    [itex]\sum[/itex]xij = nj

    [itex]\sum[/itex]yijmj
     
    Last edited: Nov 9, 2012
  2. jcsd
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