CD15-13
15.16
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A B C D E F G H I J K
Cost Data ($thousand) Product 1 Product 2
Regular Overtime Storage Regular Overtime Storage
Unit Cost ($thousand) Month Shipped (Product 1) Month Shipped (Product 2)
1 2 3 1 2 3
Ship ments Month Shipped (Product 1) Month Shipped (Product 2)
1 2 3 1 2 3 Total Produced Capacity
RT1 5 2 0 3 0 0 10 <= 10
15.17 a) The Feasible Solutions Property guarantees that, since the sum of the supplies and the
sum of the demands are equal, the problem will have feasible solutions.
d)
A1
T1
Assi gn ees Tasks
7
4
1
A4 T4
6763
CD15-14
e)
1
9
A B C D E F G H I
Unit Cost
1 2 3 4
Assig nments
1 2 3 4 Total Shipped Supply
Destination
Destination
15.18 a)
A
1
Pe rson Job
5
7
4
b)
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9
10
A B C D E F G H
Unit Cost Job
1 2 3
Assignments Job Total
1 2 3 Assignments Supply
A 0 0 1 1 = 1
CD15-15
15.19 a)
A
1
Assi gn ees Tasks
8
6
5
D4
6756
b)
1
9
A B C D E F G H I
Unit Cost
1 2 3 4
A$8 $6 $5 $7
Assig nments Total
1 2 3 4 Assignments Supply
A 0 1 0 0 1 = 1
Task
Task
15.20 a) This problem fits as an assignment problem with ships as assignees and ports as
assignments.
CD15-16
b)
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9
A B C D E F G H I
Unit Cost
1 2 3 4
Assig nments Total
1 2 3 4 Assignments Supply
1 0 1 0 0 1 = 1
Port
Port
15.21
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A B C D E F G H
Unit Cost Product
123
1 $31 $45 $38
Total Unit Cost Product
123
Assignment Product Total
1 2 3 Assignments Supply
15.22 a) The problem fits into the format for an assignment problem with swimmers being
assigned to strokes. The times of the swimmers replace the costs of a traditional problem.
b)
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A B C D E F G H
Best Time
Backstroke Breaststroke Butterfly Freestyle
Carl 37.7 43.4 33.3 29.2
Assignments Total
Backstroke Breaststroke Butterfly Freestyle Assignments Supply
Carl 0 0 0 1 1 <= 1
Chris 0 0 1 0 1 <= 1
Stroke
Stroke
15.23
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15
16
A B C D E F G H
Hauling Cost Site Price
1 2 3 per T on
Cost per T ruck Site
1 2 3
Assignment of Trucks Site
1 2 3 Total Trucks Supply
CD15-18
15.24
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A B C D E F G H
Unit Cost Distribution Center
1 2 3
Cost of Assignment Distribution Center
Shipments Distribution Center
1 2 3 Total Assignments Supply
Plant A 0 1 1 2 <= 2
Cases
15-1 a) $20 million is saved in comparison with the results in Figure 6.13 by shipping 20
million fewer barrels to Charleston and 20 million more to St. Louis.
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B C D E F G H I J
Refineries
Unit Cost ($millions) New O rleans Charleston Seattle St. Louis
Texas 2 4 5 1
Sh ip ment Quantity Refineries
(millions of b arrels) New O rleans Charleston Seattle St. Louis Total Shipped Supply
CD15-19
b) $40 million is saved in comparison with the results in Figure 6.17.
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B C D E F G H I J
Distribution Center
Unit Cost ($millions) Pittsburgh Atlanta Kansas City San Francisco
New Orleans 6.5 5.5 6 8
Sh ip ment Quantity Distribution Center
(millions o f barrels) Pittsburgh Atlanta Kansas City San F rancisco T otal Shipped Supply
New Orleans 60 40 0 0 100 = 100
The cost of shipping both crude oil and finished product under this plan is $940 million
c) $35 million is saved in comparison with the results in part (b).
$75 million is saved in comparison with the results in Figure 6.17.
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9
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13
15
16
17
B C D E F G H I J
Distribution Center
Unit Cost ($millions) Pittsburgh Atlanta Kansas City San Francisco
New Orleans 6.5 5.5 6 8
Sh ip ment Quantity Distribution Center
(millions o f barrels) Pittsburgh Atlanta Kansas City San F rancisco T otal Shipped Capacity
New Orleans 50 20 0 0 70 <= 100
CD15-20
d) This solution costs $40 million more than the solution in part (a).
This solution costs $20 million more than the solution is Figure 6.13.
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4
5
B C D E F G H I J
Refineries
Unit Cost ($millions) New Orleans Charleston Seattle St. Louis
Texas 2 4 5 1
The total cost of shipping both crude oil and finished product under this plan is $1,355
CD15-21
e) The two transportation problems (shipping to refineries and shipping to distributions
centers) are combined into a single model. The amount shipped to the refineries is
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A B C D E F G H I J
Shipping to Refineries
Refineries
Unit Cost ($millions) New Orleans Charleston Seattle St. Louis
Texas 2 4 5 1
Shipment Quantity Refineries
(millions of barrels) New Orleans Charleston Seattle St. Louis Total Shipped Supply
Texas 0 0 0 80 80 =80
Distribution Center
Unit Cost ($millions) Pittsburgh Atlanta Kansas City San Francisco
Shipment Quantity Distribution Center
(millions of barrels) Pittsburgh Atlanta Kansas City San Francisco Shipped Out Shipped In
Combined
Total
CD15-22
f) If the Los Angeles refinery is chosen instead, then the combined shipping cost is $2,450
million.
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A B C D E F G H I J
Shipping to Refineries
Refineries
Unit Cost ($million s) New O rleans Charleston Seattle Los Angeles
Sh ipmen t Q uantity Refineries
(millions of barrels) New Orleans Charleston Seattle St. Louis Total Shipped Supply
Texas 40 0 0 40 80 =80
Distribution Center
Unit Cost ($million s) Pittsburgh Atlanta Kansas City San Francisco
Sh ipmen t Q uantity Distribution Center
(millions of barrels) Pittsburgh Atlanta Kansas City San Francisco Shipped O ut Shipped In
Combined
Total
CD15-23
If the Galveston refinery is chosen instead, then the combined shipping cost is $2,470
million.
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A B C D E F G H I J
Shipping to Refineries
Refineries
Unit Cost ($million s) New O rleans Charleston Seattle G alveston
Sh ipmen t Q uantity Refineries
(millions of barrels) New Orleans Charleston Seattle Galveston Total Shipped Supply
Distribution Center
Unit Cost ($million s) Pittsburgh Atlanta Kansas City San Francisco
Sh ipmen t Q uantity Distribution Center
(millions of barrels) Pittsburgh Atlanta Kansas City San Francisco Shipped O ut Shipped In
Combined
Total
Site
Total Cost
of Shipping
Crude Oil
Total Cost
of Shipping
Finished Product
Operating Cost
for New
Refinery
Total
Variable
Cost
Los Angeles
$880 million
$1.57 billion
$620 million
$3.07 billion
Galveston
St. Louis
g) Answers will vary.