Chapter 5—Network Modeling
21. What is the constraint for node 2 in the following shortest path problem?
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a. |
-X12- X13 = 0 |
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b. |
-X12- X24 = 1 |
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c. |
X12 + X13 = 0 |
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d. |
-X12 + X24 = 0 |
22. An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 2-4. The per unit shipping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following network representation depicts this problem. What is the balance of flow constraint for node 3 (Refinery 1)?
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a. |
X13 + X23- .95 X35- .90 X36- .90 X37 = 0 |
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b. |
.80 X13 + .95 X23- X35- X36- X37 = 0 |
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c. |
.80 X13 + .95 X23- .90 X36- .90 X37³ 0 |
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d. |
X13 + X23- X35- X36- X37³ 0 |
23. An oil company wants to create lube oil, gasoline and diesel fuel at two refineries. There are two sources of crude oil. Consider arc 2-4. The per unit shipping cost of crude B from source 2 (node 2) to refinery 2 (node 4) is $11 and the yield is 85 percent. The following flowchart depicts this problem. What is the balance of flow constraint for node 7 (Diesel)?
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a. |
X35 + X36 + X37 = 75 |
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b. |
X37 + X47³ 75 |
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c. |
.90 X37 + .95 X47 = 75 |
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d. |
X37 + X47-X36- X35- X45- X46³ 75 |
24. A network flow problem that allows gains or losses along the arcs is called a
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a. |
non-constant network flow model. |
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b. |
non-directional, shortest path model. |
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c. |
generalized network flow model. |
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d. |
transshipment model with linear side constraints. |
25. What is the objective function for the following shortest path problem?
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a. |
-X12- X13 = 0 |
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b. |
MIN-50 X12- 200 X13 + 100 X24 + 35 X34 |
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c. |
MIN 50 X12 + 200 X13 + 100 X24 + 35 X34 |
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d. |
MAX-50 X12- 200 X13 + 100 X24 + 35 X34 |
26. Which formula should be used to determine the Net Flow values in cell K6 in the following spreadsheet model?
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A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
K |
L |
|
|
1 |
||||||||||||
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2 |
||||||||||||
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3 |
||||||||||||
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4 |
Supply/ |
|||||||||||
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5 |
Ship |
From |
To |
Unit Cost |
Nodes |
Net Flow |
Demand |
|||||
|
6 |
55 |
1 |
LAV |
2 |
PHO |
60 |
1 |
LAV |
-100 |
-100 |
||
|
7 |
45 |
1 |
LAV |
4 |
REN |
120 |
2 |
PHO |
50 |
50 |
||
|
8 |
5 |
2 |
PHO |
3 |
LAX |
160 |
3 |
LAX |
30 |
30 |
||
|
9 |
0 |
3 |
LAX |
5 |
SAN |
70 |
4 |
REN |
45 |
45 |
||
|
10 |
25 |
5 |
SAN |
3 |
LAX |
90 |
5 |
SAN |
90 |
90 |
||
|
11 |
0 |
5 |
SAN |
4 |
REN |
70 |
6 |
DEN |
35 |
35 |
||
|
12 |
0 |
5 |
SAN |
6 |
DEN |
90 |
7 |
SLC |
-150 |
-150 |
||
|
13 |
0 |
6 |
DEN |
5 |
SAN |
50 |
||||||
|
14 |
0 |
7 |
SLC |
4 |
REN |
190 |
||||||
|
15 |
115 |
7 |
SLC |
5 |
SAN |
90 |
||||||
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16 |
35 |
7 |
SLC |
6 |
DEN |
100 |
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17 |
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18 |
Total |
25600 |
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a. |
SUMIF($C$6:$C$16,I6,$B$6:$B$16)-SUMIF($E$6:$E$16,I6,$B$6:$B$16) |
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b. |
SUMIF($I$6:$I$12,B6,$B$6:$B$16)-SUMIF($I$6:$I$12,I6,$B$6:$B$16) |
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c. |
SUMIF($E$6:$E$16,I6,$B$6:$B$16)-SUMIF($C$6:$C$16,I6,$B$6:$B$16) |
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d. |
SUMPRODUCT(B6:B16,G6:G16) |
27. Which property of network flow models guarantees integer solutions?
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a. |
linear constraints and balance of flow equation format |
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b. |
linear objective function coefficients |
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c. |
integer objective function coefficients |
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d. |
integer constraint RHS values and balance of flow equation format |
28. In generalized network flow problems
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a. |
solutions may not be integer values. |
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b. |
flows along arcs may increase or decrease. |
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c. |
it can be difficult to tell if total supply is adequate to meet total demand. |
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d. |
all of these. |
29. What happens to the solution of a network flow model if side constraints are added that do not obey the balance of flow rules?
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a. |
The model solution is not guaranteed to be integer. |
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b. |
The model solution will more accurately reflect reality. |
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c. |
The model solution will be integer but more accurate. |
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d. |
The model solution is not guaranteed to be feasible. |
30. Consider modeling a warehouse with three in-flow arcs and three outflow arcs. The warehouse node is a transshipment node but has a capacity of 100. How would one modify the network model to avoid adding a side constraint that limits either the sum of in-flows or the sum of the out-flows to 100?
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a. |
Place a limit of 34 on each in-flow arc. |
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b. |
Add a side constraint limiting the out-flow arcs sum to 100. |
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c. |
Separate the warehouse node into two nodes, connected by a single arc, with capacity of 100. |
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d. |
It cannot be accomplished, a side constraint must be added. |
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Solution: Chapter 5—Network Modeling