chapter-5-network-modeling-2

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21. What is the constraint for node 2 in the
following shortest path problem?

Chapter 5—Network Modeling.png”>

a.

-X12– X13 = 0

b.

-X12– X24 = 1

c.

X12 + X13 = 0

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)?

Chapter 5—Network Modeling.png”>

a.

X13 + X23– .95 X35– .90 X36– .90 X37 = 0

b.

.80 X13 + .95 X23– X35– X36– X37 = 0

c.

.80 X13 + .95 X23– .90 X36– .90 X37³ 0

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)?

Chapter 5—Network Modeling.png”>

a.

X35 + X36 + X37 = 75

b.

X37 + X47³ 75

c.

.90 X37 + .95 X47 = 75

d.

X37 + X47-X36– X35– X45– X46³ 75

24. A network flow problem that allows gains or
losses along the arcs is called a

a.

non-constant network flow model.

b.

non-directional, shortest path model.

c.

generalized network flow model.

d.

transshipment model with linear side constraints.

25. What is the objective function for the
following shortest path problem?

Chapter 5—Network Modeling.png”>

a.

-X12– X13 = 0

b.

MIN-50 X12– 200 X13 + 100 X24 + 35 X34

c.

MIN 50 X12 + 200 X13 + 100 X24 + 35 X34

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?

A

B

C

D

E

F

G

H

I

J

K

L

1

2

3

4

Supply/

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

16

35

7

SLC

6

DEN

100

17

18

Total

25600

a.

SUMIF($C$6:$C$16,I6,$B$6:$B$16)-SUMIF($E$6:$E$16,I6,$B$6:$B$16)

b.

SUMIF($I$6:$I$12,B6,$B$6:$B$16)-SUMIF($I$6:$I$12,I6,$B$6:$B$16)

c.

SUMIF($E$6:$E$16,I6,$B$6:$B$16)-SUMIF($C$6:$C$16,I6,$B$6:$B$16)

d.

SUMPRODUCT(B6:B16,G6:G16)

27. Which property of network flow models
guarantees integer solutions?

a.

linear constraints and balance of flow equation format

b.

linear objective function coefficients

c.

integer objective function coefficients

d.

integer constraint RHS values and balance of flow equation format

28. In generalized network flow problems

a.

solutions may not be integer values.

b.

flows along arcs may increase or decrease.

c.

it can be difficult to tell if total supply is adequate to meet total
demand.

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?

a.

The model solution is not guaranteed to be integer.

b.

The model solution will more accurately reflect reality.

c.

The model solution will be integer but more accurate.

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?

a.

Place a limit of 34 on each in-flow arc.

b.

Add a side constraint limiting the out-flow arcs sum to 100.

c.

Separate the warehouse node into two nodes, connected by a single arc,
with capacity of 100.

d.

It cannot be accomplished, a side constraint must be added.

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