Solution to DMS problem using VAM method and Hungarian method

1. Submitted By:
RESHMI RAVEENDRAN - 212027
CASE STUDY ON ASSIGNMENT PROBLEM

2. 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
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
CASE STUDY ON ASSIGNMENT PROBLEM

3. 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
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
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
2
3
Demand
3
1
3
3
3
2
3

4. 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
(1)
(1)
2
(1)
Moore
1
1
4
4
2
3
3
5
2
Ragsdale
1
3
1
5
4
1
1
2
2
Rakes
3
1
2
5
3
12
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
Penality
2
(1)
3
(2)
3
(1)
1
(1)
3
(1)
3 1
(2)
3
2
(1)
(1)
20
(1)
(1)
(1)
(2)
(1)
(1)
(1)

5. 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
(1)
(1)
2
(1)
Moore
1
1
4
4
2
3
3
5
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
Penality
2
(1)
3
(2)
3
(1)
1
(1)
3
(1)
2
3 1
(2)
3
2
(1)
(1)
(1)
(1)
(1)
(2)
(1)
(1)
(1)

6. 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
(1)
(1)
2
(1)
Moore
1
1
4
4
2
3
Ragsdale
1
3
1
5
4
1
1
Rakes
3
1
2
5
3
1
2
Rees
3
4
3
5
5
Russell
4
1
3
2
Sumichrast
4
3
1
5
Demand
Penality
2
(1)
3
(2)
3
(1)
1
(1)
3
5
2
1
2
2 1
1
1
2
1
1
3
2
2
5
5
5
2
2
3
3
1
2
3
3
(1)
(2)
1
3
2
(1)
(1)
(1)
(1)
(1)
(2)
(1)
(1)
(1)

7. Faculty
Member
3424 3434
3444
3454
4434
4444
4454
4464
Suppl
y
Clayton
2
4
12
3
2
5
5
5
2
Houck
3
3
4
11
21
5
5
4
2
Huang
21
3
21
1
3
4
4
4
2
Major
1
4
2
5
12
3
2
2
2
Moore
11
1
4
4
2
3
3
5
2
(1)
Ragsdale
1
3
1
5
4
11
11
2
2
(1)
Rakes
3
1
2
5
3
12
1
1
2
(1)
Rees
3
4
3
5
5
1
1
2
3
2
(2)
Russell
4
12
3
2
2
5
5
5
2
(1)
Sumichrast
4
3
1
5
2
3
3
12
2
Demand
2 1
Penality
(1)
3
(2)
1
1
3
2
1
(1)
(1)
(1)
(1)
3
(1)
1
3
(2)
2
3
(1)
1
2
(1)
(1)
(1) (2)
(1) (1)
(1)
(1)
(2)

8. Faculty
Member
3424 3434
3444
3454
Clayton
2
4
1
Houck
3
3
4
Huang
21
3
2
Major
1
4
Moore
11
Ragsdale
4434
4444
3
2
11
2
1
3
2
5
1
11
4
4
1
3
1
Rakes
3
1
Rees
3
Russell
Sumichrast
Demand
4454
4464
Supply
5
5
5
2
5
5
4
2
4
4
4
2
3
2
2
2
2
3
3
5
2
5
4
1
1
1
2
2
2
5
3
1
2
1
1
2
4
3
5
5
1
1
3
2
4
12
3
2
2
5
5
5
2
4
3
1
5
2
3
3
1
2
3
3
2
1
1
3
1
2
3
3
1
2
2
2
2

9. Faculty
Member
3424 3434
3444
Clayton
3454
1
2
1
1
2
1
1
Supply
2
1
2
1
1
4464
1
Major
Moore
4454
2
1
2
4444
2
Houck
Huang
4434
2
2
2
1
Ragsdale
1
1
Rakes
1
2
Rees
1
2
1
Russell
1
2
2
2
2
Sumichrast
Demand
2
1
1
2
3
3
1
3
3
3
2
2
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

10. 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
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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10

11. Add Dummy Coloumns /Subjects
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
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
Presentation Title runs here l 00/00/00
11

12. Reduce by min element row wise & coloumn wise
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Major
Moore
Ragsdale
Rakes
Rees
Russell
Sumichrast
0
0
3
0
1
3
4
3
0
1
2
2
1
2
1
4
0
2
0
4
3
0
0
1
2
0
1
4
2
0
0
0
2
3
2
4
4
0
0
2
3
0
2
1
1
4
4
4
3
2
0
4
1
2
2
0
Presentation Title runs here l 00/00/00
12

13. Faculty
Member
Clayton
3424 3434 3444
3454
4434
4444
4454
4464
D1
D2
Supply
2
4
1
3
2
5
5
5
0
0
2
Houck
3
3
4
1
2
5
5
4
0
0
2
Huang
2
3
2
1
3
4
4
4
0
0
2
Major
1
4
2
5
1
3
2
2
0
0
2
Moore
1
1
4
4
2
3
3
5
0
0
2
Ragsdale
1
3
1
5
4
1
1
2
0
0
2
Rakes
3
1
2
5
3
1
1
1
0
0
2
Rees
3
4
3
5
5
1
1
3
0
0
2
Russell
4
1
3
2
2
5
5
5
0
0
2
Sumichrast
4
3
1
5
2
3
3
1
0
0
2
Demand
2
3
3
1
3
3
3
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
13

14. Thank you