Question 1

When does degeneracy occur in a transportation model?

Accepted Answer

Degeneracy occurs when the number of occupied cells is less than the number of rows plus the number of columns minus one.

Question 2

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

Accepted Answer

A) True 
 B)False  True

Question 3

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

Accepted Answer

The lowest cost in the matrix is 7; assign 30 units to S2D2 and rule out all other cells in D2. Now the lowest cost in the table is 8; assign 50 units to S3D1 and rule out all other cells in S3. The smallest cost is now 9; assign 45 units to S1D3 and rule out all other S1. The remaining assignments are 60 units to S2D4, 30 units to S2D1, and 25 units to S2D3. These assignments are summarized in the table below.
 $$\begin{array} { | l | r | r | r | r | r | } 
\hline \text { Intuitive } & { \text { Dest. 1 } } & \text { Dest. 2 } & \text { Dest. 3 } &  \text { Dest. 4 }  & \text { Supply } \
\hline \text { Source 1 } & & & 45 & & 45 \
\hline\text { Source 2 } &30&30&25&60&145\
\hline\text { Source 3 } &50&&&&50 \
\hline\text { Demand }  & 80 & 30 & 70 & 60 & 240 \backslash 240 \
\hline
\end{array}$$

Question 4

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:
 $\begin{array}{|l|r|r|r|r|}
\hline\text { COSTS } & \text { Plant 1 } & \text { Plant 2 } & \text { Plant 3 } & \text { Supply } \
\hline\text { Raw material source 1 } & \$ 6 & \$ 8 & \$ 9 & 400 \
\hline\text { Raw material source 2 } & \$ 4 & \$ 7 & \$ 3 & 600 \
\hline\text { Demand } & 500 & 500 & 500 & 1500 \backslash 1000\\hline
\end{array}$ 
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 5

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 6

A manufacturer of semiconductor "wafers" has been attempting to convert its operations to practices more in keeping with JIT principles. The firm is now paying much more attention to the transit time between one processing stage and the next. The plant has a somewhat haphazard pattern of machine locations, partly because the machines were purchased and installed at different times, partly from a shortage of floor space, and partly from previous experiments with work cells. The bottom line is this: there are four machines that perform a certain processing phase, and three machines that perform the next phase. All units of a large class of wafers go through these two phases. The table below displays the transit time, in minutes, from each machine of the first phase to each machine of the second. Machine 3 is not really 100 minutes away from machine B; the company has prohibited that combination because of quality problems associated with that specific pairing. Supply and demand quantities are in wafers processed per week. Develop a transit time minimizing solution for this firm. What is the total transit time of this solution?
 Which machines are fully utilized?
 Which machines have some capacity unused or requirements unfilled?
 Was the prohibition on the 3-B combination honored?
 $\begin{array}{|r|r|r|r|r|}\hline\text { COSTS } & \text { Phase 2, } & \text { Phase 2, } & \text { Phase 2, }& \text { Supply } \
&\text { machine A }&\text { machine B }&\text { machine C }\
\hline \text {Phase 1, machine 1 }&7.5 & 2.5 & 4.0 & 700 \
\hline \text { vPhase 1, machine 2}&3.0 & 6.0 & 6.5 & 600 \
\hline \text {Phase 1, machine 3 }&2.5 & 100.0 & 8.0 & 1000 \
\hline \text { Phase 1, machine 4}&5.0 & 8.5 & 7.0 & 700 \
\hline \text { Demand}&1200 & 800 & 1500 & 3500/3000\
\hline
\end{array}$

Accepted Answer

The solution appears in the software-gen

Question 7

Find the minimum cost solution for the transportation problem detailed in the table below. Explain carefully the meaning of any quantity in a "dummy" row or column.
 $$\begin{array} { | l | r | r | r | r | } 
\hline \text { COSTS } & \text { Dest 1 } & \text { Dest 2 } & \text { Dest 3 } & \text { Supply } \
\hline \text { Source 1 } & 30 & 12 & 5 & 20 \
\hline\text { Source 2 } & 10 & 14 & 12 & 30 \
\hline \text { Source 3 } & 20 & 11 & 25 & 75 \
\hline\text { Dummy } & 0 & 0 & 0 & 30 \
\hline \text { Demand } & 40 & 60 & 55 & 155 \backslash 155 \
\hline
\end{array}$$

Accepted Answer

The optimum solution, which costs $1370,

Question 8

A transportation problem has an optimal solution when

Accepted Answer

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 
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

Question 9

Neither the northwest corner rule nor the intuitive method considers shipping cost in making initial allocations.

Accepted Answer

A) True 
 B)False

Question 10

What does the stepping-stone method do?

Accepted Answer

The stepping-stone method is a

Question 11

The transportation method is a special case of the family of problems known as

Accepted Answer

A)  regression problems 
B)  decision tree problems 
C)  linear programming problems 
D)  simulation problems 
E)  statistical problems 
A)  regression problems 
B)  decision tree problems 
C)  linear programming problems 
D)  simulation problems 
E)  statistical problems

Question 12

When is it necessary to add dummy sources or destinations to a transportation problem?

Accepted Answer

It is necessary to add dummy s

Question 13

The transportation model seeks satisfactory, but not necessarily optimal, solutions for shipping goods from several origins to several destinations.

Accepted Answer

A) True 
 B)False

Question 14

Which of the following is true for degenerate problems?

Accepted Answer

A)  They do not contain a feasible solution. 
B)  They cannot contain an optimal solution. 
C)  Supply is greater than demand. 
D)  Demand is greater than supply. 
E)  None of the above 
A)  They do not contain a feasible solution. 
B)  They cannot contain an optimal solution. 
C)  Supply is greater than demand. 
D)  Demand is greater than supply. 
E)  None of the above

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

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)  None of the above are 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)  None of the above are accurate.

Question 17

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.

Accepted Answer

A) True 
 B)False

Question 18

When the number of shipments in a feasible solution is less than the number of rows plus the number of columns minus one

Accepted Answer

A)  the solution is optimal 
B)  a dummy source must be created 
C)  a dummy destination must be created 
D)  there is degeneracy, and an artificial allocation must be created 
E)  the closed path has a triangular shape 
A)  the solution is optimal 
B)  a dummy source must be created 
C)  a dummy destination must be created 
D)  there is degeneracy, and an artificial allocation must be created 
E)  the closed path has a triangular shape

Question 19

Find the minimum cost solution for the transportation problem detailed in the table below.
 $\begin{array}{|l|r|r|r|r|}
\hline \text { COSTS } & \text { Dest 1 } & \text { Dest 2 } & \text { Dest 3 } & \text { Supply } \
\hline \text { Source 1 } & 18 & 12 & 5 & 20 \
\hline \text { Source 2 } & 10 & 14 & 12 & 30 \
\hline \text { Source 3 } & 9 & 11 & 15 & 75 \
\hline \text { Demand } & 40 & 30 & 55 & 125/125\\hline 
\end{array}$ 
Before your solution can be implemented, you discover that the combination Source 3 - Destination 1 is unavailable, due to political turmoil in the country where Source 3 is located. Solve the revised problem. How much is cost increased by this complication?

Accepted Answer

The first solution is in the first table

Question 20

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)  Both B and D 
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)  Both B and D

Exam 23: Transportation Models

When does degeneracy occur in a transportation model?

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

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 60 240/240

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 problem has an optimal solution when

Neither the northwest corner rule nor the intuitive method considers shipping cost in making initial allocations.

What does the stepping-stone method do?

The transportation method is a special case of the family of problems known as

When is it necessary to add dummy sources or destinations to a transportation problem?

The transportation model seeks satisfactory, but not necessarily optimal, solutions for shipping goods from several origins to several destinations.

Which of the following is true for degenerate problems?

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

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

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.

When the number of shipments in a feasible solution is less than the number of rows plus the number of columns minus one

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

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