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Exam 24: Transportation Models

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Question 31

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A transportation problem has an optimal solution when:

A) all of the improvement indices are greater than or equal to zero.
B) all demand and supply constraints are satisfied.
C) the number of filled cells is one less than the number of rows plus the number of columns.
D) all the squares are used.
E) all origin-destination combinations have been made equally low in cost.

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Question 32

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Upon completion of the northwest-corner rule,which source-destination cell is guaranteed to be occupied?

A) top-left
B) top-right
C) bottom-left
D) bottom-right
E) the cell with the lowest shipping cost (or at least one of them if there's a tie)

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Question 33

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Consider the transportation problem in the data set and optimal solution below.Verify by hand or by calculator (show your work)the value of the total shipping cost.

For the data below,construct an initial feasible solution using the northwest-corner rule.

In a minimization problem,a positive improvement index in a cell indicates that:

The intuitive method of generating an initial solution has different results for each problem solver because "intuition" varies from person to person.

Which of the following combinations of sources and destinations would fill no more than 25% of cells with quantities to be shipped for the optimal solution?

In a transportation problem,degeneracy means that:

To handle degeneracy,a very small quantity is placed in one of the unused squares.

A transportation model uses at least 10 sources and 100 destinations.If the ratio of sources to destinations remains constant,does the maximum % of cells used by the optimum solution remain constant? Why or why not?

Total demand for a transportation model is 15 while total supply is 20.Which of the following should be included?

Consider the transportation problem and its initial solution in the table below.What is the improvement index for the empty cell Source 1 - Destination 3?

When using the stepping-stone method,the improvement index for an unused cell equals the shipping cost associated with that cell.

What is transportation modeling?

The main difference between the intuitive lowest-cost method and the northwest-corner rule is that:

Consider the transportation problem and its optimal solution in the tables below.The cell Source 3 - Destination 3 is currently empty.What would be the change in the total shipping cost if the largest possible amount were shipped using that route,leaving all the supply and demand conditions unchanged?

The transportation model is an excellent tool for minimizing shipping costs among existing facilities,but it is not useful when firms consider new facility locations.

A firm has established a distribution network for the supply of a raw material critical to its manufacturing.Currently there are two origins for this raw material,which must be shipped to three manufacturing plants.The current network has the following characteristics: The firm has identified two potential sites for a third raw material source;these are identified as Candidate A and Candidate B.From A,the costs to ship would be $9 to Plant 1,$10 to Plant 2,and $12 to Plant 3,respectively.From B,these costs would be $11,$14,and $8,respectively.The new source,wherever it is located,will have a capacity of 500 units.Set up this problem as two separate transportation matrices.(Do not solve the problem. )

The total cost of the optimal solution to a transportation problem:

For the transportation problem below,construct an initial feasible solution using the intuitive method.