In solving maximization assignment problems,
admin
10.1
In solving maximization
assignment problems,
(a) just
reverse all the decision rules used in the minimizing algorithm (if it says
subtract, now add, and so on).
(b) convert
the problem to an equivalent minimization problem.
(c) use
the Australian transformation process and convert the data.
(d) all
of the above
(e) none
of the above
}
10.2
Find the solution to the
transportation problem depicted below.
Table 10-34
To==>
1
2
3
Dummy
Supply
From
A
| 10
| 8
| 12
| 0
50
B
| 6
| 7
| 4
| 0
75
C
| 10
| 9
| 6
| 0
125
Demand
60
40
100
50
(a)
Table 10-34 a
To==>
1
2
3
Dummy
Supply
From
A
| 10
| 8
40
| 12
| 0
10
50
B
| 6
60
| 7
| 4
15
| 0
75
C
| 10
| 9
| 6
85
| 0
40
125
Demand
60
40
100
50
(b)
Table 10-34 b
To==>
1
2
3
Dummy
Supply
From
A
| 10
| 8
20
| 12
| 0
30
50
B
| 6
60
| 7
| 4
15
| 0
75
C
| 10
| 9
20
| 6
85
| 0
20
125
Demand
60
40
100
50
(c)
Table 10-34 c
To==>
1
2
3
Dummy
Supply
From
A
| 10
40
| 8
| 12
| 0
10
50
B
| 6
| 7
15
| 4
25
| 0
35
75
C
| 10
20
| 9
| 6
100
| 0
5
125
Demand
60
40
100
50
(d)
Table 10-34 d
To==>
1
2
3
Dummy
Supply
From
A
| 10
50
| 8
| 12
| 0
50
B
| 6
| 7
| 4
75
| 0
75
C
| 10
10
| 9
40
| 6
25
| 0
50
125
Demand
60
40
100
50
(e) none of the above
}
10.3
Solve the following
transportation table:
Table 10-35
To==>
1
2
3
Dummy
Supply
From
A
| 5
50
| 8
| 8
| 0
40
B
| 6
| 9
| 4
75
| 0
85
C
| 6
10
| 9
40
| 6
25
| 0
50
110
Demand
50
60
85
40
(a)
Table 10-35a Solution?
To==>
1
2
3
Dummy
Supply
From
A
| 5
50
| 8
| 8
| 0
40
B
| 6
| 9
| 4
75
| 0
85
C
| 6
10
| 9
40
| 6
25
| 0
50
110
Demand
50
60
85
40
(b)
Table 10-35b Solution?
To==>
1
2
3
Dummy
Supply
From
A
| 5
50
| 8
| 8
| 0
40
B
| 6
| 9
| 4
75
| 0
85
C
| 6
10
| 9
40
| 6
25
| 0
50
110
Demand
50
60
85
40
(c)
Table 10-35c Solution?
To==>
1
2
3
Dummy
Supply
From
A
| 5
40
| 8
| 8
| 0
40
B
| 6
10
| 9
60
| 4
15
| 0
85
C
| 6
| 9
| 6
70
| 0
40
110
Demand
50
60
85
40
(d)
Table 10-35d Solution?
To==>
1
2
3
Dummy
Supply
From
A
| 5
| 8
| 8
| 0
40
40
B
| 6
| 9
| 4
85
| 0
85
C
| 6
50
| 9
60
| 6
| 0
110
Demand
50
60
85
40
(e) none of the above
}
10.4
Use Vogels approximation to
find the solution to the transportation problem shown in Table 10-36.
Table 10-36
To==>
1
2
3
Dummy
Supply
From
A
| 5
| 7
| 8
| 0
20
B
| 3
| 9
| 9
| 0
65
C
5
| 9
| 6
| 0
90
Demand
30
40
85
20
(a)
Table 10-36a Solution?
To==>
1
2
3
Dummy
Supply
From
A
| 5
| 7
| 8
| 0
20
20
B
| 3
| 9
| 9
65
| 0
65
C
| 5
30
| 9
40
| 6
20
| 0
90
Demand
30
40
85
20
(b)
Table 10-36b Solution?
To==>
1
2
3
Dummy
Supply
From
A
| 5
| 7
20
| 8
| 0
20
B
| 3
30
| 9
| 9
35
| 0
65
C
| 5
| 9
20
| 6
50
| 0
20
90
Demand
30
40
85
20
(c)
Table 10-36c Solution?
To==>
1
2
3
Dummy
Supply
From
A
| 5
| 7
20
| 8
| 0
20
B
| 3
30
| 9
15
| 9
| 0
20
65
C
5
| 9
5
| 6
85
| 0
90
Demand
30
40
85
20
(d)
Table
10-36d Solution?
To==>
1
2
3
Dummy
Supply
From
A
| 5
10
| 7
| 8
| 0
10
20
B
| 3
| 9
40
| 9
| 0
5
65
C
5
| 9
| 6
85
| 0
5
90
Demand
30
40
85
20
(e) none of the above
}
10.5
The table below describes a
transportation problem. Find the
solution to this problem using Vogels approximation.
Table
10-37
To==>
1
2
3
4
Supply
From
A
| 4
| 7
| 10
| 12
2000
B
| 7
| 5
| 8
| 11
2500
C
9
| 8
| 6
10
2200
Demand
1000
2200
2300
1200
(a)
(a) Table 10-37a Solution?
To==>
1
2
3
4
Supply
From
A
| 4
1000
| 7
| 10
1000
| 12
2000
B
| 7
| 5
1000
| 8
300
| 11
1200
2500
C
9
| 8
1200
| 6
1000
| 10
2200
Demand
1000
2200
2300
1200
(b)
Table
10-37b Solution?
To==>
1
2
3
4
Supply
From
A
| 4
| 7
200
| 10
800
| 12
1200
2000
B
| 7
1000
| 5
| 8
1500
| 11
2500
C
9
| 8
2000
| 6
200
| 10
2200
Demand
1000
2200
2300
1200
(c)
Table
10-37c Solution?
To==>
1
2
3
4
Supply
From
A
| 4
| 7
2000
| 10
| 12
2000
B
| 7
1000
| 5
| 8
300
| 11
1200
2500
C
9
| 8
200
| 6
1800
| 10
2200
Demand
1000
2200
2300
1200
(d)
Table
10-37d Solution?
To==>
1
2
3
4
Supply
From
A
| 4
1000
| 7
| 10
| 12
1000
2000
B
| 7
| 5
2200
| 8
100
| 11
200
2500
C
9
| 8
| 6
2200
| 10
2200
Demand
1000
2200
2300
1200
(e) none of the above
}
PROBLEMS
10.6
Table 10-38 describes a
transportation problem:
Table 10-38
To==>
D
E
F
Supply
From
A
| 2
| 5
| 2
40
B
| 1
| 4
| 2
30
C
| 4
| 3
| 2
30
Demand
20
30
50
100
(a) Use
the northwest corner method to get an initial solution.
(b) What
is the cost of the initial solution?
(c) Use
the stepping-stone method to find the optimal solution.
(d) What
is the cost of the optimal solution?
(e) Is
there an alternate optimal solution?
}
10.97 Four projects
must be completed, and each of four employees will be assigned to work on
exactly one of the four projects. The
table below presents an estimate of the cost that each employee would incur if
working on the respective projects. What
is the minimum-cost assignment of workers to projects?
PROJECT
EMPLOYEE
1
2
3
4
Mary
$45
$32
$49
$55
Elizabeth
$50
$45
$53
$43
Steven
$52
$40
$70
$46
Joshua
$60
$35
$40
$40
}
SHORT ANSWER/ESSAY
10.98 Describe a general transportation problem.
}
10.99What is meant by a balanced transportation problem?
}
10.100 The assignment problem is a special
case of the transportation problem. So,
then, why is it not recommended to use the transportation algorithm to solve
the assignment problem?
}
10.101
When is a dummy destination
added to a transportation problem?
}
10.1
In solving maximization
assignment problems, (a) just
reverse all the decision rules used in the minimizing algorithm (if it says
subtract, now add, and so on). (b) convert
the problem to an equivalent minimization problem. (c) use
the Australian transformation process and convert the data. (d) all
of the above (e) none
of the above }10.2
Find the solution to the
transportation problem depicted below. Table 10-34To==>123DummySupplyFromA| 10| 8| 12| 050B| 6| 7| 4| 075C| 10| 9| 6| 0125Demand604010050 (a)Table 10-34 aTo==>123DummySupplyFromA| 10| 840| 12| 01050B| 660| 7| 415| 075C| 10| 9| 685| 040125Demand604010050 (b)Table 10-34 bTo==>123DummySupplyFromA| 10| 820| 12| 03050B| 660| 7| 415| 075C| 10| 920| 685| 020125Demand604010050 (c)Table 10-34 cTo==>123DummySupplyFromA| 1040| 8| 12| 01050B| 6| 715| 425| 03575C| 1020| 9| 6100| 05125Demand604010050 (d)Table 10-34 dTo==>123DummySupplyFromA| 1050| 8| 12| 050B| 6| 7| 475| 075C| 1010| 940| 625| 050125Demand604010050 (e) none of the above }10.3
Solve the following
transportation table:Table 10-35To==>123DummySupplyFromA| 550| 8| 8| 040B| 6| 9| 475| 085C| 610| 940| 625| 050110Demand50608540 (a)Table 10-35a Solution?To==>123DummySupplyFromA| 550| 8| 8| 040B| 6| 9| 475| 085C| 610| 940| 625| 050110Demand50608540 (b)Table 10-35b Solution?To==>123DummySupplyFromA| 550| 8| 8| 040B| 6| 9| 475| 085C| 610| 940| 625| 050110Demand50608540 (c)Table 10-35c Solution?To==>123DummySupplyFromA| 540| 8| 8| 040B| 610| 960| 415| 085C| 6| 9| 670| 040110Demand50608540 (d)Table 10-35d Solution?To==>123DummySupplyFromA| 5| 8| 8| 04040B| 6| 9| 485| 085C| 650| 960| 6| 0110Demand50608540 (e) none of the above }10.4
Use Vogels approximation to
find the solution to the transportation problem shown in Table 10-36.Table 10-36To==>123DummySupplyFromA| 5| 7| 8| 020B| 3| 9| 9| 065C5| 9| 6| 090Demand30408520 (a)Table 10-36a Solution?To==>123DummySupplyFromA| 5| 7| 8| 02020B| 3| 9| 965| 065C| 530| 940| 620| 090Demand30408520 (b)Table 10-36b Solution?To==>123DummySupplyFromA| 5| 720| 8| 020B| 330| 9| 935| 065C| 5| 920| 650| 02090Demand30408520 (c)Table 10-36c Solution?To==>123DummySupplyFromA| 5| 720| 8| 020B| 330| 915| 9| 02065C5| 95| 685| 090Demand30408520 (d)Table
10-36d Solution?To==>123DummySupplyFromA| 510| 7| 8| 01020B| 3| 940| 9| 0565C5| 9| 685| 0590Demand30408520 (e) none of the above }10.5
The table below describes a
transportation problem. Find the
solution to this problem using Vogels approximation.Table
10-37To==>1234SupplyFromA| 4| 7| 10| 122000B| 7| 5| 8| 112500C9| 8| 6102200Demand1000220023001200 (a) (a) Table 10-37a Solution?To==>1234SupplyFromA| 41000| 7| 101000| 122000B| 7| 51000| 8300| 1112002500C9| 81200| 61000| 102200Demand1000220023001200 (b)Table
10-37b Solution?To==>1234SupplyFromA| 4| 7200| 10800| 1212002000B| 71000| 5| 81500| 112500C9| 82000| 6200| 102200Demand1000220023001200 (c)Table
10-37c Solution?To==>1234SupplyFromA| 4| 72000| 10| 122000B| 71000| 5| 8300| 1112002500C9| 8200| 61800| 102200Demand1000220023001200 (d)Table
10-37d Solution?To==>1234SupplyFromA| 41000| 7| 10| 1210002000B| 7| 52200| 8100| 112002500C9| 8| 62200| 102200Demand1000220023001200 (e) none of the above }10.6
Table 10-38 describes a
transportation problem:Table 10-38To==>DEFSupplyFromA| 2| 5| 240B| 1| 4| 230C| 4| 3| 230Demand203050100 (a) Use
the northwest corner method to get an initial solution. (b) What
is the cost of the initial solution? (c) Use
the stepping-stone method to find the optimal solution. (d) What
is the cost of the optimal solution? (e) Is
there an alternate optimal solution? }}10.98 Describe a general transportation problem. }10.99What is meant by a balanced transportation problem? }10.100 The assignment problem is a special
case of the transportation problem. So,
then, why is it not recommended to use the transportation algorithm to solve
the assignment problem? }10.101
When is a dummy destination
added to a transportation problem? }
