Dms problem [compatibility mode]
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CASE STUDY ON ASSIGNMENT PROBLEM
Submitted By:
RESHMI RAVEENDRAN - 212027
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The Management Science and Information Technology department at Tech offers between 36 and
forty 3-hour course sections each semester. Some of the courses are taught by graduate student
instructors, whereas 20 of the course sections are taught by the 10 regular, tenured faculty in the
department. Before the beginning of each year, the department head sends the faculty a questionnaire,
asking them to rate their preference for each course using a scale from 1 to 5, where 1 is “strongly
preferred”, 2 is “preferred but not as strongly as 1”, 3 is “neutral”, 4 is “prefer not to teach but not
strongly”, and 5 is “strongly prefer not to teach this course.” The faculty have returned their
preferences, as follows:
Faculty Member 3424 3434 3444 3454 4434 4444 4454 4464
Clayton 2 4 1 3 2 5 5 5
Houck 3 3 4 1 2 5 5 4
CASE STUDY ON ASSIGNMENT PROBLEM
Houck 3 3 4 1 2 5 5 4
Huang 2 3 2 1 3 4 4 4
Major 1 4 2 5 1 3 2 2
Moore 1 1 4 4 2 3 3 5
Ragsdale 1 3 1 5 4 1 1 2
Rakes 3 1 2 5 3 1 1 1
Rees 3 4 3 5 5 1 1 3
Russell 4 1 3 2 2 5 5 5
Sumichrast 4 3 1 5 2 3 3 1
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� For the fall semester the department will offer two sections each of 3424 and 4464;
� Three sections of 3434, 3444, 4434, 4444 and 4454; and one section of 3454.
� The normal semester teaching load for a regular faculty member is two sections. Help the department
head determine a teaching schedule that will satisfy faculty teaching preferences to the greatest
degree possible.
Faculty
Member
3424 3434 3444 3454 4434 4444 4454 4464
Clayton 2 4 1 3 2 5 5 5
Houck 3 3 4 1 2 5 5 4
Huang 2 3 2 1 3 4 4 4
Major 1 4 2 5 1 3 2 2
2
2
2
2
Supply
3
Moore 1 1 4 4 2 3 3 5
Ragsdale 1 3 1 5 4 1 1 2
Rakes 3 1 2 5 3 1 1 1
Rees 3 4 3 5 5 1 1 3
Russell 4 1 3 2 2 5 5 5
Sumichrast 4 3 1 5 2 3 3 1
2 3 3 1 3 3 3 2
2
2
2
2
2
2
Demand
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Faculty
Member
3424 3434 3444 3454 4434 4444 4454 4464 Supply
Clayton 2 4 1 3 2 5 5 5 2
Houck 3 3 4 1 2 5 5 4 2
Huang 2 3 2 1 3 4 4 4 2
Major 1 4 2 5 1 3 2 2 2
Moore 1 1 4 4 2 3 3 5 2
(1)
(1)
(1)
(1)
Ragsdale 1 3 1 5 4 1 1 2 2
Rakes 3 1 2 5 3 1 1 1 2
Rees 3 4 3 5 5 1 1 3 2
Russell 4 1 3 2 2 5 5 5 2
Sumichrast 4 3 1 5 2 3 3 1 2
Demand 2 3 3 1 3 3 3 220
2
(1)
(1)
(1)
(2)
Penality (1) (2) (1)(1)(1) (1)(2) (1)
(1)
(1)
(1)1
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Faculty
Member
3424 3434 3444 3454 4434 4444 4454 4464 Supply
Clayton 2 4 1 3 2 5 5 5 2
Houck 3 3 4 1 2 5 5 4 2
Huang 2 3 2 1 3 4 4 4 2
Major 1 4 2 5 1 3 2 2 2
Moore 1 1 4 4 2 3 3 5 2
(1)
(1)
(1)
(1)
Ragsdale 1 3 1 5 4 1 1 2 2
Rakes 3 1 2 5 3 1 1 1 2
Rees 3 4 3 5 5 1 1 3 2
Russell 4 1 3 2 2 5 5 5 2
Sumichrast 4 3 1 5 2 3 3 1 2
Demand 2 3 3 1 3 3 3 2
2
(1)
(1)
(1)
(2)
Penality (1) (2) (1)(1)(1) (1)(2) (1)
(1)
(1)
(1)1
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Faculty
Member
3424 3434 3444 3454 4434 4444 4454 4464 Supply
Clayton 2 4 1 3 2 5 5 5 2
Houck 3 3 4 1 2 5 5 4 2
Huang 2 3 2 1 3 4 4 4 2
Major 1 4 2 5 1 3 2 2 2
Moore 1 1 4 4 2 3 3 5 2
(1)
(1)
(1)
(1)
Ragsdale 1 3 1 5 4 1 1 2 2
Rakes 3 1 2 5 3 1 1 1 2
Rees 3 4 3 5 5 1 1 3 2
Russell 4 1 3 2 2 5 5 5 2
Sumichrast 4 3 1 5 2 3 3 1 2
Demand 2 3 3 1 3 3 3 2
2
(1)
(1)
(1)
(2)
Penality (1) (2) (1)(1)(1) (1)(2) (1)
(1)
(1)
(1)1
11
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Faculty
Member
3424 3434 3444 3454 4434 4444 4454 4464 Suppl
y
Clayton 2 4 1 3 2 5 5 5 2
Houck 3 3 4 1 2 5 5 4 2
Huang 2 3 2 1 3 4 4 4 2
Major 1 4 2 5 1 3 2 2 2
Moore 1 1 4 4 2 3 3 5 2
(1)
2
1
1 1
1
1 1
2
(1)
(1)
(1)
(2)
(1) (2)
Ragsdale 1 3 1 5 4 1 1 2 2
Rakes 3 1 2 5 3 1 1 1 2
Rees 3 4 3 5 5 1 1 3 2
Russell 4 1 3 2 2 5 5 5 2
Sumichrast 4 3 1 5 2 3 3 1 2
Demand 2 3 3 1 3 3 3 2
2
1
2
2
1
2
(1)
(1)
(1)
(2)
Penality (1) (2) (1)(1)(1) (1)(2) (1)
(1)
(1)
(1)1
(1) (1)
11 2 21
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Faculty
Member
3424 3434 3444 3454 4434 4444 4454 4464 Supply
Clayton 2 4 1 3 2 5 5 5 2
Houck 3 3 4 1 2 5 5 4 2
Huang 2 3 2 1 3 4 4 4 2
Major 1 4 2 5 1 3 2 2 2
Moore 1 1 4 4 2 3 3 5 2
2
1
11
1
1 1
2
Ragsdale 1 3 1 5 4 1 1 2 2
Rakes 3 1 2 5 3 1 1 1 2
Rees 3 4 3 5 5 1 1 3 2
Russell 4 1 3 2 2 5 5 5 2
Sumichrast 4 3 1 5 2 3 3 1 2
Demand 2 3 3 1 3 3 3 2
2
1
2
2
1
2
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Faculty
Member
3424 3434 3444 3454 4434 4444 4454 4464 Supply
Clayton 1 2
Houck 1 2 2
Huang 2 2 2
Major 1 2
Moore 1 1 2
2
1
1 1
1
1 1
2
Ragsdale 1 1 2
Rakes 1 2
Rees 1 2
Russell 1 2
Sumichrast 1 2
Demand 2 3 3 1 3 3 3 2
2
1
2
2
1
2
2*1 + 1*1 + 2*1 + 2*1 + 2*1 + 1*2 +1*1 + 1*1 + 1*1 + 1*1 + 1*2 + 1*2 + 1*2 + 1*2 = 23
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Faculty Member 3424 3434 3444 3454 4434 4444 4454 4464
Clayton 2 4 1 3 2 5 5 5
Houck 3 3 4 1 2 5 5 4
Huang 2 3 2 1 3 4 4 4
Major 1 4 2 5 1 3 2 2
Moore 1 1 4 4 2 3 3 5
Presentation Title runs here l 00/00/00 10
Ragsdale 1 3 1 5 4 1 1 2
Rakes 3 1 2 5 3 1 1 1
Rees 3 4 3 5 5 1 1 3
Russell 4 1 3 2 2 5 5 5
Sumichrast 4 3 1 5 2 3 3 1
8 Subjects & 10 Professors Hence Unbalanced.
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Faculty Member 3424 3434 3444 3454 4434 4444 4454 4464 D1 D2
Clayton 2 4 1 3 2 5 5 5 0 0
Houck 3 3 4 1 2 5 5 4 0 0
Huang 2 3 2 1 3 4 4 4 0 0
Major 1 4 2 5 1 3 2 2 0 0
Add Dummy Coloumns /Subjects
Presentation Title runs here l 00/00/00 11
Moore 1 1 4 4 2 3 3 5 0 0
Ragsdale 1 3 1 5 4 1 1 2 0 0
Rakes 3 1 2 5 3 1 1 1 0 0
Rees 3 4 3 5 5 1 1 3 0 0
Russell 4 1 3 2 2 5 5 5 0 0
Sumichrast 4 3 1 5 2 3 3 1 0 0
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Faculty Member 3424 3434 3444 3454 4434 4444 4454 4464 D1 D2
Clayton 1 3 0 2 1 4 4 4 0 0
Houck 2 2 3 0 1 4 4 3 0 0
Huang 1 2 1 0 2 3 3 3 0 0
Major0 3 1 4 0 2 1 1
0 0
Reduce by min element row wise & coloumn wise
Presentation Title runs here l 00/00/00 12
0 3 1 4 0 2 1 1
Moore0 0 3 3 1 2 2 4
0 0
Ragsdale0 2 0 4 3 0 0 1
0 0
Rakes2 0 1 4 2 0 0 0
0 0
Rees2 3 2 4 4 0 0 2
0 0
Russell3 0 2 1 1 4 4 4
0 0
Sumichrast3 2 0 4 1 2 2 0
0 0
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Faculty
Member
3424 3434 3444 3454 4434 4444 4454 4464 D1 D2
Clayton 2 4 1 3 2 5 5 5 0 0
Houck 3 3 4 1 2 5 5 4 0 0
Huang 2 3 2 1 3 4 4 4 0 0
Major 1 4 2 5 1 3 2 2 0 0
Moore 1 1 4 4 2 3 3 5 0 0
Ragsdale 1 3 1 5 4 1 1 2 0 0
Supply
2
2
2
2
2
2
13
Rakes 3 1 2 5 3 1 1 1 0 0
Rees 3 4 3 5 5 1 1 3 0 0
Russell 4 1 3 2 2 5 5 5 0 0
Sumichrast 4 3 1 5 2 3 3 1 0 0
Demand 2 3 3 1 3 3 3 2
2
2
2
2
2
2*1+3*1+3*1+1*1+3*1+3*1+3*1+2*1= 20
1*1+ 2*1= 3 Hence Optimal Solution – 20+ 3 = 23
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