Dms problem [compatibility mode]

CASE STUDY ON ASSIGNMENT PROBLEM

Submitted By:

RESHMI RAVEENDRAN - 212027

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

� 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

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

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

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

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

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

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

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.

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

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

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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