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Transportation and Model Formulation

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

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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.

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