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? $\begin{array}{|l|r|r|r|r|r|} \hline \text { COSTS } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Dest. 4 } & \text { Supply } \\ \hline\text { Source 1 } & 12 & 18 & 9 & 11 & 45 \\ \hline\text { Source 2 } & 19 & 7 & 30 & 15 & 145 \\ \hline\text { Source 3 } & 8 & 10 & 14 & 16 & 50 \\ \hline \text { Demand } & 80 & 30 & 70 & 60 & 240/240 \\ \hline & & & & & \\ \hline \text { Shipments } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Dest. 4 } & \text { Row Total } \\ \text { Source 1 } & 45 & 0 & 0 & 0 & 45 \\ \text { Source 2 } & 35 & 30 & 70 & 10 & 145 \\ \text { Source 3 } & 0 & 0 & 0 & 50 & 50 \\ \text { Col. Total } & 80 & 30 & 70 & 60 & 240/240 \\ \hline \end{array}$

A) 0 B) -14 C) -23 D) -70 E) 115 A) 0 B) -14 C) -23 D) -70 E) 115

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

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

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

A) 0 B) 2 C) 15 D) 90 E) 30 A) 0 B) 2 C) 15 D) 90 E) 30

For the problem below, what is the quantity assigned to the cell Source 1-Destination 2 using the intuitive method for an initial feasible solution? \[\begin{array} { | l | r | r | r | r | } \hline \text { COSTS } & \text { Dest. 1 } & \text { Dest. 2 } & \text { Dest. 3 } & \text { Supply } \\ \hline \text { Source 1 } & 2 & 1 & 3 & 50 \\ \hline \text { Source 2 } & 4 & 7 & 5 & 40 \\ \hline \text { Source 3 } & 3 & 12 & 6 & 30 \\ \hline \text { Demand } & 50 & 45 & 25 & 120 \backslash 120 \\ \hline \end{array}\]

A) 1 B) 5 C) 30 D) 45 E) 50 A) 1 B) 5 C) 30 D) 45 E) 50

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

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

Exam 23: Transportation Models

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? 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 Shipments Dest. 1 Dest. 2 Dest. 3 Dest. 4 Row Total Source 1 45 0 0 0 45 Source 2 35 30 70 10 145 Source 3 0 0 0 50 50 Col. Total 80 30 70 60 240/240

(Multiple Choice)

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Question 41

The stepping-stone method

(Multiple Choice)

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Question 42

Degeneracy in a transportation problem is when no closed path exists for evaluating an unused cell.

(True/False)

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Question 43

The Shamrock Transportation Company has four terminals: A, B, C, and D. At the start of a particular day, there are 8, 8, 6, and 3 tractors available at those terminals, respectively. During the previous night, trailers were loaded at plants R, S, T, and U. The number of trailers at each plant is 2, 12, 5, and 6, respectively. The company dispatcher has determined the distances between each terminal and each plant, as follows. How many tractors should be dispatched from each terminal to each plant in order to minimize the total number of miles traveled? COSTS Dest. 1 Dest. 2 Dest 3 Dest. 4 Supply Origin 1 21 44 25 40 8 Origin 2 42 24 45 22 8 Origin 3 78 32 42 55 6 Origin 4 44 42 32 30 3 Demand 2 12 5 6 25/25

(Essay)

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Question 44

A transportation problem with 8 sources and 6 destinations will have an optimal solution that uses at most 13 of the 48 possible routes.

(True/False)

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Question 45

The larger a transportation problem (that is, as the problem has more rows and more columns), the smaller the fraction of all possible routes that will be filled in a solved problem. Explain.

(Essay)

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Question 46

The transportation model is a special class of linear programming models.

(True/False)

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Question 47

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

(Multiple Choice)

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Question 48

Suppose the solution for a transportation model fills 5 cells with quantities to be shipped. Which of the following combinations of sources and destinations would be degenerate?

(Multiple Choice)

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Question 49

For the problem data set below, what is the northwest corner allocation to the cell Source 1-Destination 1? 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

(Multiple Choice)

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Question 50

For the problem below, what is the quantity assigned to the cell Source 1-Destination 2 using the intuitive method for an initial feasible solution? COSTS Dest. 1 Dest. 2 Dest. 3 Supply Source 1 2 1 3 50 Source 2 4 7 5 40 Source 3 3 12 6 30 Demand 50 45 25 120\backslash120

(Multiple Choice)

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Question 51

A transportation problem has two origins: A can supply 20 units and B can supply 30 units. This problem has two destinations: C requires 25 units and D requires 35 units. Which of the following is true?

(Multiple Choice)

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Question 52

Which of the following is not needed in order to use the transportation model?

(Multiple Choice)

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Question 53

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.

(Multiple Choice)

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Question 54

Given the following feasible solution determine if the problem is degenerate and then find the optimal solution and its cost. Assume that capacity for source A is 10 and 30 for source B. Destination A demands 10 units while destination B demands 30 units. Cost of shipping per unit is given as AA ($4), AB ($1), BA ($3), and BB ($2). Destination A Destination B Source A 10 Source B 30

(Essay)

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Question 55

A transportation problem has 6 origins and 12 destinations. How many possible routes are there for this problem? How many routes will be used in the optimal solution?

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Question 56

The northwest-corner rule is best used

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Question 57

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 objective function. COSTS Dest. 1 Dest. 2 Dest. 3 Dest 4 Supply Source 1 12 18 9 11 100 Source 2 21 7 30 15 150 Source 3 8 10 14 16 50 Demand 80 60 70 90 300/300 Shipments Dest. 1 Dest. 2 Dest. 3 Dest. 4 Row Total Source 1 30 0 70 0 100 Source 2 0 60 0 90 150 Source 3 50 0 0 0 50 Col. Total 80 60 70 90 300/300

(Essay)

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Question 58

When using the stepping stone method for a minimization problem, the number of units that reallocates corresponds to the smallest number found in the cells containing minus signs.

(True/False)

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Question 59

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

(Multiple Choice)

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Question 60

Exam 23: Transportation Models

The stepping-stone method

Degeneracy in a transportation problem is when no closed path exists for evaluating an unused cell.

A transportation problem with 8 sources and 6 destinations will have an optimal solution that uses at most 13 of the 48 possible routes.

The larger a transportation problem (that is, as the problem has more rows and more columns), the smaller the fraction of all possible routes that will be filled in a solved problem. Explain.

The transportation model is a special class of linear programming models.

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

Suppose the solution for a transportation model fills 5 cells with quantities to be shipped. Which of the following combinations of sources and destinations would be degenerate?

For the problem data set below, what is the northwest corner allocation to the cell Source 1-Destination 1? 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

For the problem below, what is the quantity assigned to the cell Source 1-Destination 2 using the intuitive method for an initial feasible solution? COSTS Dest. 1 Dest. 2 Dest. 3 Supply Source 1 2 1 3 50 Source 2 4 7 5 40 Source 3 3 12 6 30 Demand 50 45 25 120\backslash120

A transportation problem has two origins: A can supply 20 units and B can supply 30 units. This problem has two destinations: C requires 25 units and D requires 35 units. Which of the following is true?

Which of the following is not needed in order to use the transportation model?

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 6 origins and 12 destinations. How many possible routes are there for this problem? How many routes will be used in the optimal solution?

The northwest-corner rule is best used

When using the stepping stone method for a minimization problem, the number of units that reallocates corresponds to the smallest number found in the cells containing minus signs.

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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