Operations Management

1. Operations Management Module IV Assignment

2. Scheduling by Assignment method

3. W …. Worker • P …. Project • C …. Cost associated • Minimize cost

4. Q. The departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimates of the times each man would take to perform each task is given : Find the best fit by assignment method.

6. Subtract the smallest element of each row from every element of the row

7. Subtract smallest element from each column

8. Draw minimum number of horizontal and vertical lines so as to cover all zeros

9. OR Since the no. of lines = 4 = order of the matrix, an optimum assignment has been obtained.

10. Make an assignment to the row containing a single zero • Cut out other zeroes in that column

11. Make an assignment to the row containing a single zero

12. Make an assignment to the column containing a single zero

14. Q A certain equipment needs five repair jobs which have to be assigned to five machines. The estimated time (in hours) that each mechanic requires to complete the repair job is given in the following table. Assuming that each mechanic can be assigned to only one job, determine the minimum time assignment.

16. Subtract minimum from each row

17. Subtract minimum from each column

18. Make an assignment to the row containing a single zero • Cut out other zeroes in that column

20. As there are only four assignments • Another zero element is needed

22. Subtract the smallest element (1). Add 1 to pts of intersection

23. = 27 hours

24. Q ABC Co. is engaged in mfg 5 brands of packed snacks. It is having 5 mfg setups, each capable of mfg any of its brands, one at a time. The cost to make a brand on these setups vary according to the table given on the next slide. Assuming 5 setups are S1, S2,S3,S4 & S5 and five brands are B1,B2,B3,B4,B5. find the optimum assignment of products on these setups resulting in the minimum cost.

26. Subtract min el in each row

27. Subtract min element in each column

28. Draw the min no. of lines to cover all zeroes

29. Subtract min elt=1,from uncovered elts and add 1 to pts of intersection

30. As there are 5 lines = order of the matrix. This table will give the optimum assignment as shown in matrix

31. Consider rows with one zero Consider cols with one zero 0 0 0 0 0

34. Travelling Salesman Problem

35. This is an assignment problem with two additional conditions. For example, given n cities and distances dij, the travelling salesman should start from his home city so that the total distance covered should be minimum.

36. Q A travelling salesman has to visit five cities. He wishes to start from a particular city, visit each city once and then return to his starting point. The travelling cost (in 000’s Rs.) of each city from a particular city is given below :

39. 0 0 • A EA • THIS VIOLATES THE CONDITION that he go to each city only once 0 0 0

40. The “next best” solution is to bring in the next best non zero element i.e 1 into the solution . 1 appears at three places. Make the assignment in the cell (A,B) instead of zero assignment in the cell (A,E)

41. 1 0 Solution is to travel ABCDEA COST = Rs. 15,000/- 0 1 0

42. Q A travelling salesman has to visit 5 cities. He wishes to start from a particular city, visit each city once and then return to his starting point. The travelling cost for each city from a particular city is given below :

44. SOLVE and get solution

45. 0 0 • However, this is not an optimal soln as ADBA 0 0 0

46. Examine matrix for next best soln – smallest non zero element - 1

47. 0 1 • The best route is ADBCEA • Total distance travelled = 2100 kms 0 0 0