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    Network Representation and Linear Transformation

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    The distribution system for a company consists of two plants, three warehouses, and three customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows on Exhibit A attached.

    Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows in Exhibit B attached.

    Due to technical reasons items can not be shipped from Warehouse-1 to Customer-2 temporarily. In addition, direct shipments can be made from Plant-1 to Customer-1 at a costs of $4 per unit and from Plant-2 to Customer-3 at a costs of $2 per unit. Draw a network representation and formulate a linear programming model for this problem.

    See attached file for charts related to this problem.

    © BrainMass Inc. brainmass.com December 24, 2021, 11:43 pm ad1c9bdddf
    https://brainmass.com/math/optimization/network-representation-linear-transformation-595303

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    Exhibit A

    See attachment for chart.

    Exhibit B

    Answer:
    Let P be plant, W be warehouse and C be customer. The diagram is shown blow:

    Now let xij be the units from plant i to warehouse j and let yjk be units from warehouse j to customer k.
    So we want to minimize 4x11+3x12+5x13+6x21+2x22+4x23+y11+5y13+7y21+3y22+3y23+4y31+2y32+2y33
    Subject to: x11+x12+x13≤650
    x21+x22+x23≤450
    y11+y21+y31=310
    y12+y22+y32=270
    y13+y23+y33=420
    x11+x21=y11+y12+y13
    x12+x22=y21+y22+y23
    x13+x23=y31+y32+y33
    xij≥0 and yij≥0

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 11:43 pm ad1c9bdddf>
    https://brainmass.com/math/optimization/network-representation-linear-transformation-595303

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