Question 1

A transportation problem has 15 origins and 40 destinations. How many possible routes are there for this problem? How many routes will be used in the optimal solution?

Accepted Answer

The number of possible routes is origins

Question 2

One difference between the stepping-stone method compared to the Northwest-corner and intuitive method is that

Accepted Answer

A)  the stepping-stone method never finds a feasible solution. 
B)  the stepping-stone method ignores costs. 
C)  the stepping-stone method ALWAYS finds a lower-cost solution. 
D)  the stepping-stone method guarantees an optimal solution. 
E)  the Northwest-corner and intuitive method guarantees sub-optimal solutions. 
A)  the stepping-stone method never finds a feasible solution. 
B)  the stepping-stone method ignores costs. 
C)  the stepping-stone method ALWAYS finds a lower-cost solution. 
D)  the stepping-stone method guarantees an optimal solution. 
E)  the Northwest-corner and intuitive method guarantees sub-optimal solutions.

Question 3

For the transportation problem below, construct an initial feasible solution using the intuitive method. $$\begin{array} { | l r | r | r | r | r | } 
\hline \text { COSTS } &  { \text { Dest. 1 } } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Dest. 4 } & \text { Supply } \
\hline \text { Source 1 } & 12 & 18 & 9 & 11 & 45 \
\hline \text { Source 2 } & 19 & 7 & 30 & 15 & 145 \
\hline \text { Source 3 } & 8 & 10 & 14 & 16 & 50 \
\hline \text { demand } & 80 & 30 & 70 & 60 & 240 \text { 1240 } \
\hline
\end{array}$$

Accepted Answer

The lowest cost in the matrix is 7; assi

Question 4

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

Accepted Answer

A)  the intuitive lowest-cost method always generates a better solution. 
B)  the Northwest-corner rule is faster. 
C)  the Northwest-corner rule ignores cost. 
D)  only the intuitive lowest-cost method generates an optimal solution. 
E)  intuitive lowest-cost method is more accurate. 
A)  the intuitive lowest-cost method always generates a better solution. 
B)  the Northwest-corner rule is faster. 
C)  the Northwest-corner rule ignores cost. 
D)  only the intuitive lowest-cost method generates an optimal solution. 
E)  intuitive lowest-cost method is more accurate.

Question 5

If demand exceeds supply in a transportation problem, the problem must be balanced by adding a dummy source with additional supply.

Accepted Answer

A) True 
 B)False

Question 6

A transportation problem with a total supply of 500 and a total demand of 400 will have an optimal solution that leaves 100 units of supply unused.

Accepted Answer

A) True 
 B)False

Question 7

For the problem data set below, what is the northwest corner allocation to the cell Source 3-Destination 3? $$\begin{array} { | l | r | r | r | r | } 
\hline \text { COSTS } & \text { Dest. 1 } &  { \text { Dest. 2 } } & { \text { Dest. 3 } } &{ \text { Supply } } \
\hline \text { Source 1 } & 2 & 1 & 3 & 30 \
\hline \text { Source 2 } & 4 & 2 & 1 & 40 \
\hline \text { Source 3 } & 3 & 8 & 6 & 20 \
\hline \text { Demand } & 15 & 50 & 25 & 90 \backslash 90 \
\hline
\end{array}$$

Accepted Answer

A)  0 
B)  15 
C)  20 
D)  35 
E)  45 
A)  0 
B)  15 
C)  20 
D)  35 
E)  45

Question 8

A transportation problem has 4 origins and 2 destinations. The optimal solution of this problem will fill no more than ________ cells with quantities to be shipped.

Accepted Answer

A)  5 
B)  6 
C)  8 
D)  20 
E)  All cells will be occupied. 
A)  5 
B)  6 
C)  8 
D)  20 
E)  All cells will be occupied.

Question 9

A transportation problem has improvement indices of 5, 4, 0, and -3. Which of the following is always true?

Accepted Answer

A)  The transportation model is at its ideal solution. 
B)  The transportation model is at a feasible solution. 
C)  The total cost saved by changing one unit on the route with an improvement index of 5 would be $5. 
D)  The transportation matrix has four empty squares. 
E)  The transportation model is at a feasible solution and the transportation matrix has four empty squares. 
A)  The transportation model is at its ideal solution. 
B)  The transportation model is at a feasible solution. 
C)  The total cost saved by changing one unit on the route with an improvement index of 5 would be $5. 
D)  The transportation matrix has four empty squares. 
E)  The transportation model is at a feasible solution and the transportation matrix has four empty squares.

Question 10

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: $$\begin{array} { | l | r | r | r | r | } 
\hline \text { COSTS } & \text { Plant 1 } & \text { Plant 2 } & \text { Plant 3 } & \text { Supply } \
\hline  \text { Raw material source 1 } & \$ 6 & \$ 6 & \$ 9 & 400 \
\hline\text { Raw material source 2 } & \$ 4 & \$ 7 & \$ 3 & 600 \
\hline \text { Demand } & 500 & 500 & 500 & 1500 \backslash 1000 \\hline
\end{array}$$ 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. From B, these costs would be $11, $14, and $8. The new source, wherever it is located, will have a capacity of 500 units. Solve with the transportation method. Which site should be selected?

Accepted Answer

This problem requires two tran

Question 11

The ________ develops an initial feasible solution for a transportation model by starting at the upper left-hand cell of a table and systematically allocating units to shipping points.

Accepted Answer

northwest-

Question 12

A transportation model uses only 5% of its cells. If the number of destinations is 1000, determine the number of sources in the model.

Accepted Answer

Number of Cells is 1000X, numb

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

An improvement index indicates

Accepted Answer

A)  whether a method other than the stepping-stone should be used. 
B)  whether a method other than the northwest-corner rule should be used. 
C)  how much total cost would increase or decrease if a single unit was reallocated to that cell. 
D)  whether the transportation cost in the upper left-hand corner of a cell is optimal. 
E)  how much total cost would increase or decrease if the largest possible quantity were reallocated to that cell. 
A)  whether a method other than the stepping-stone should be used. 
B)  whether a method other than the northwest-corner rule should be used. 
C)  how much total cost would increase or decrease if a single unit was reallocated to that cell. 
D)  whether the transportation cost in the upper left-hand corner of a cell is optimal. 
E)  how much total cost would increase or decrease if the largest possible quantity were reallocated to that cell.

Question 15

A transportation problem that has more units supplied than demanded will require a(n) ________ to balance the problem.

Accepted Answer

The answer of A transportation problem that has more units...

Question 16

The initial solution to a transportation problem can be generated several ways, so long as

Accepted Answer

A)  it minimizes cost. 
B)  it ignores cost. 
C)  all supply and demand conditions are satisfied. 
D)  degeneracy does not exist. 
E)  all cells are filled. 
A)  it minimizes cost. 
B)  it ignores cost. 
C)  all supply and demand conditions are satisfied. 
D)  degeneracy does not exist. 
E)  all cells are filled.

Question 17

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 objective function if the largest possible amount were shipped using that route, leaving all the supply and demand conditions unchanged? $\begin{array}{|lr|r|r|r|r|}
\hline \text { COSTS } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Dest. 4 } & \text { Supply } \
\hline \text { Source 1 } & 12 & 18 & 9 & 11 & 105 \
\hline \text { Source 2 } & 19 & 7 & 30 & 15 & 145 \
\hline \text { Source 3 } & 8 & 10 & 14 & 16 & 50 \
\hline \text { Demand } & 80 & 60 & 70 & 90 & 300/300 \
\hline
\end{array}$

$\begin{array}{|lrrrrr|}
\hline \text { Shipments } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Dest. 4 } & \text { Row Total } \
\text { Source 1 } & 30 & 0 & 70 & 5 & 105 \
\text { Source 2 } & 0 & 60 & 0 & 85 & 145 \
\text { Source 3 } & 50 & 0 & 0 & 0 & 50 \
\text { Col. Total } & 80 & 60 & 70 & 90 & 300 \backslash 300 \
\hline
\end{array}$

Accepted Answer

A)  0 
B)  fifty units 
C)  a decrease of $9 
D)  an increase of $450 
E)  an increase of $630 
A)  0 
B)  fifty units 
C)  a decrease of $9 
D)  an increase of $450 
E)  an increase of $630

Question 18

Consider the transportation data set for a minimization problem below. $$\begin{array} { | l | r | r | r | r | } 
\hline \text { COSTS } & \text { Dest. 1 } & { \text { Dest. 2 } } & { \text { Dest. 3 } } &{ \text { Supply } } \
\hline \text { Source 1 } & 2 & 1 & 3 & 30 \
\hline \text { Source 2 } & 4 & 2 & 1 & 40 \
\hline \text { Source 3 } & 3 & 8 & 6 & 20 \
\hline\text { Demand } & 15 & 50 & 25 & 90 \backslash 90 \
\hline
\end{array}$$ a. Calculate the initial solution using the northwest-corner rule.
b. Calculate improvement indices, iterate, and solve for the optimal shipping pattern.

Accepted Answer

The initial solution and impro

Question 19

A feasible solution in transportation models is one in which all of the supply and demand constraints are satisfied.

Accepted Answer

A) True 
 B)False

Question 20

For the problem data set below, what is the northwest corner allocation to the cell Source 1 -Destination 2? $$\begin{array} { | l | r | r | r | r | } 
\hline \text { COSTS } & \text { Dest. 1 } &  { \text { Dest. 2 } } & { \text { Dest. 3 } } &{ \text { Supply } } \
\hline \text { Source 1 } & 2 & 1 & 3 & 30 \
\hline \text { Source 2 } & 4 & 2 & 1 & 40 \
\hline \text { Source 3 } & 3 & 8 & 6 & 20 \
\hline \text { Demand } & 15 & 50 & 25 & 90 \backslash 90 \
\hline
\end{array}$$

Accepted Answer

A)  0 
B)  15 
C)  25 
D)  45 
E)  35 
A)  0 
B)  15 
C)  25 
D)  45 
E)  35

Exam 20: Transportation Models

A transportation problem has 15 origins and 40 destinations. How many possible routes are there for this problem? How many routes will be used in the optimal solution?

One difference between the stepping-stone method compared to the Northwest-corner and intuitive method is that

For the transportation problem below, construct an initial feasible solution using the intuitive method. COSTS Dest. 1 Dest. 2 Dest. 3 Dest. 4 Supply Source 1 12 18 9 11 45 Source 2 19 7 30 15 145 Source 3 8 10 14 16 50 demand 80 30 70 60 240 1240

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

If demand exceeds supply in a transportation problem, the problem must be balanced by adding a dummy source with additional supply.

A transportation problem with a total supply of 500 and a total demand of 400 will have an optimal solution that leaves 100 units of supply unused.

For the problem data set below, what is the northwest corner allocation to the cell Source 3-Destination 3? COSTS Dest. 1 Dest. 2 Dest. 3 Supply Source 1 2 1 3 30 Source 2 4 2 1 40 Source 3 3 8 6 20 Demand 15 50 25 90\backslash90

A transportation problem has 4 origins and 2 destinations. The optimal solution of this problem will fill no more than ________ cells with quantities to be shipped.

A transportation problem has improvement indices of 5, 4, 0, and -3. Which of the following is always true?

The ________ develops an initial feasible solution for a transportation model by starting at the upper left-hand cell of a table and systematically allocating units to shipping points.

A transportation model uses only 5% of its cells. If the number of destinations is 1000, determine the number of sources in the model.

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

An improvement index indicates

A transportation problem that has more units supplied than demanded will require a(n) ________ to balance the problem.

The initial solution to a transportation problem can be generated several ways, so long as

A feasible solution in transportation models is one in which all of the supply and demand constraints are satisfied.

For the problem data set below, what is the northwest corner allocation to the cell Source 1 -Destination 2? COSTS Dest. 1 Dest. 2 Dest. 3 Supply Source 1 2 1 3 30 Source 2 4 2 1 40 Source 3 3 8 6 20 Demand 15 50 25 90\backslash90

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