Explore BrainMass

Explore BrainMass

    Transportation and Model Formulation

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

    5. In the transportation problem on the next page, products are produced at plants in Locations A and B and shipped to warehouses in locations X, Y and Z.
    5a. According to the model formulation, what is the capacity of Plant B? _________

    5b. According to the model formulation, what is the demand at warehouse Z? ___________

    5c. According to the model formulation, what is the shipping cost for sending products from Plant A to Plant B?
    ______________

    5d. According to the solution, how many products should be shipped from Plant A to Plant B?

    __________

    5e. At what point would more products would be shipped from Plant A to Warehouse Y?______

    5f. What would be the total shipping cost if the demand at warehouse Z was equal to 600?_____

    6g. At what point would less products would be shipped from Plant B to warehouse Z?______

    7h. What would be the total shipping cost if the capacity of Plant B was equal to 700? ________

    7i. At what point would some units be shipped from Plant A to warehouse X? ____________

    7j. Would the current solution remain optimal if the shipping cost from Plant A was $9, $8.75 and $14 to warehouses X, Y, and Z, respectively? Demonstrate.

    MIN 11AX+8AY+12AZ+1.5AB+6BX+8BY+5BZ+1YZ

    S.T.

    1) 1AX+1AY+1AZ+1AB<1200
    2) -1AB+1BX+1BY+1BZ<600
    3) 1AX+1BX>500
    4) 1AY+1BY-1YZ>600
    5) 1AZ+1BZ+1YZ>700

    OPTIMAL SOLUTION

    Objective Function Value = 12200.000

    Variable Value Reduced Costs
    -------------- --------------- ------------------
    AX 0.000 3.500
    AY 600.000 0.000
    AZ 0.000 5.500
    AB 600.000 0.000
    BX 500.000 0.000
    BY 0.000 1.500
    BZ 700.000 0.000
    YZ 0.000 2.500

    Constraint Slack/Surplus Dual Prices
    -------------- --------------- ------------------
    1 0.000 0.000
    2 0.000 1.500
    3 0.000 -7.500
    4 0.000 -8.000
    5 0.000 -6.500

    OBJECTIVE COEFFICIENT RANGES

    Variable Lower Limit Current Value Upper Limit
    ------------ --------------- --------------- ---------------
    AX 7.500 11.000 No Upper Limit
    AY 5.500 8.000 9.500
    AZ 6.500 12.000 No Upper Limit
    AB 0.000 1.500 4.000
    BX 1.500 6.000 9.500
    BY 6.500 8.000 No Upper Limit
    BZ 1.500 5.000 7.500
    YZ 1.500 1.000 No Upper Limit

    RIGHT HAND SIDE RANGES

    Constraint Lower Limit Current Value Upper Limit
    ------------ --------------- --------------- ---------------
    1 1200.000 1200.000 No Upper Limit
    2 600.000 600.000 1200.000
    3 0.000 500.000 500.000
    4 0.000 600.000 600.000
    5 100.000 700.000 700.000

    © BrainMass Inc. brainmass.com June 3, 2020, 11:05 pm ad1c9bdddf
    https://brainmass.com/statistics/descriptive-statistics/transportation-model-formulation-262603

    Attachments

    Solution Preview

    5. In the transportation problem on the next page, products are produced at plants in Locations A and B and shipped to warehouses in locations X, Y and Z.
    5a. According to the model formulation, what is the capacity of Plant B? _________
    Answer: 600 (RHS for constraint 2)

    5b. According to the model formulation, what is the demand at warehouse Z? ___________
    Answer: 700 (RHS of constraint 5)

    5c. According to the model formulation, what is the shipping cost for sending products from Plant A to Plant B?
    ______________
    Answer: 1.5 (Co-efficient of AB in objective function)

    5d. According to the solution, how many products should be shipped from Plant A to Plant B?
    __________
    Answer: 600 (Value of variable AB in first table of the optimal solution)

    5e. At what point would more products would be shipped from Plant A to Warehouse Y?______

    The objective coefficient range for AY is between 5.5 to 8.00, hence if the cost of shipping from Plant A to Warehouse Y is reduced below 5.50 more products would be shipped from Plant A to warehouse Y.

    5f. What would be the total shipping cost if the demand at warehouse Z was equal to 600?_____

    The dual price is -6.5 for constraint 5 and it is a ...

    Solution Summary

    The solution examines model formulation capacity for transportation between warehouses.

    $2.19

    ADVERTISEMENT