Managerial Decision Modeling w/ Spreadsheets, 3e (Balakrishnan/Render/Stair)
Chapter 5 Transportation, Assignment, and Network Models
5.1 Chapter Questions
1) Which of the following is NOT a network flow model?
A) Transportation model
B) Assignment model
C) Product mix model
D) Shortest-path model
E) Minimal-spanning tree model
2) Which of the following statements concerning the transshipment model are FALSE?
A) A supply node is one where the total flow into the node is less than the total flow out of the node.
B) A transshipment node is one where the total flow into the node equals the total flow of the node.
C) The flow balance for a demand node should show a positive RHS value.
D) The flow balance for a transshipment node should show a negative RHS value.
E) The flow balance for a supply node should show a negative RHS value.
3) What is the constraint associated with job A for the following assignment problem?
A
Job B
C
Machine
1
2
$3
$4
$1
$3
$6
$4
3
$2
$5
$2
Let Xij = 1 if job i is assigned to machine j, otherwise 0.
A) 3XA1 + 4XA2 + 2XA3 = 1
B) 3XA1 + 4XA2 + 2XA3 = 0
C) 3XA1 + 4XA2 + 2XA3 = -1
D) XA1 + XA2 + XA3 = -1
E) -XA1 - XA2 - XA3 = -1
4) What is the constraint associated with machine 2 for the following assignment problem?
A
Job B
C
Machine
1
2
$3
$4
$1
$3
$6
$4
3
$2
$5
$2
Let Xij = 1 if job i is assigned to machine j, otherwise 0.
A) XA2 + XB2 + XC2 = +1
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B) XA2 + XB2 + XC2 = 0
C) XA2 + XB2 + XC2 = -1
D) 4XA2 + 3XB2 + 4XC2 = +1
E) 4XA2 + 3XB2 + 4XC2 = -1
5) Consider the following transshipment problem. The shipping cost per unit between nodes 1 and 2 is
$10, while the shipping cost per unit between nodes 2 and 3 is $12. What is the objective function?
A) Min X12 + X23
B) Max X12 + X23
C) Min 10X12 + 12X13
D) Min -10X12 - 12X13
E) Max 10X12 + 12X23
6) In an unbalanced transportation problem where total supply exceeds total demand, the supply
constraints will typically have "≥" inequalities.
TRUE/ FALSE
7) In an unbalanced transportation problem where total demand exceeds total supply, the demand
constraints will typically have "≤" inequalities.
TRUE/FALSE
8) All supply and demand quantities in an assignment model equal one unit.
TRUE/FALSE
5.2 Excel Problems
Use this information for the following questions.
Neki Sports Company manufacturers treadmills in factories located in Pittsburgh and Kansas City.
These are shipped to regional distribution centers in Chicago, Phoenix, and Philadelphia. Ultimately
they are delivered to supply houses in New York and Los Angeles. The available supplies at the
factories, demands at the final destinations, and shipping costs are illustrated in the table below.
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9) Refer to the information above. Formulate this problem as a linear programming problem.
10) Refer to the information above. Using Excel, determine how many units should be shipped for all
possible origin and destination points (final or intermediate) in the distribution network in order to
minimize shipping costs.
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