# chapter-5-network-modeling-2

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

.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)?

.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)?

.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?

.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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