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# Dms problem [compatibility mode]

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Solution to DMS problem using VAM method and Hungarian method

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### Dms problem [compatibility mode]

1. 1. Submitted By: RESHMI RAVEENDRAN - 212027 CASE STUDY ON ASSIGNMENT PROBLEM
2. 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. 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. 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. 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. 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. 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. 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. 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. 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. Presentation Title runs here l 00/00/00 10
11. 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. 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. 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. 14. Thank you