Numericals on Unbalanced Assignment Model


0

(Unbalanced)

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1.         A company has 4 machines to do 3 jobs. Each job can be assigned to only one machine. The cost of each job machine combination is given in the table below in Rupees. (MU, Apr. 2009)

Job

Machines

I

II

III

IV

A

9

12

14

18

B

4

6

8

9

C

5

7

9

11

Find an optimal assignment which will minimize the cost. Answer the following questions with justification.

(i)       Is there any alternate optimal assignment ?

(ii)      Is it possible to maintain the same minimum cost as per optimal solution if job B is assigned to either Machine II of Machine III ?

(iii)     Does any machine remain idle as per optimal assignment ?

           (Ans :  A ® I, B ® II, C ® III, D ® IV; Total Cost = 9 + 6 + 9 + 0 = 24

(i)       Alternate Soln. A ® I, B ® II, C ® III, D ® IV; Total Cost = 9 + 8 + 7 + 0 = 24

(ii)     Yes. From the above two alternate solutions it can be observed that Job B can be assigned to either Machine II or Machine III while maintaining an optimal cost of Rs. 24

(iii)    In both solutions, Job D (dummy) is assigned to Machine IV hence machine IV is idle.)

 

2.         Four major roads in a city badly need repairs. There are 5 contractors who are eager to do my job. The city corporation decides to give repair work of only one road to one contractor. The cost of repair is given below in thousand rupees. Find the assignment at minimum cost.

Roads

Contractor

C1

C2

C3

C4

C5

R1

52

68

40

91

72

R2

61

74

21

63

49

R3

77

82

101

61

71

R4

38

54

77

67

70

(Ans :  R1 ® C3, R2 ® C5, R3 ® C4, R4 ® C1, R5 ® C2

               Cost = 40 + 49 + 61 + 38 + 0 = ` 188)

            

3.         A finance faculty of management school decided to hold special seminars on 4 contemporary topics – leasing, portfolio management, private mutual funds and equity research. Such seminars should be held once per week in the afternoon, however scheduling these seminars (one for each topic and not more than one seminar afternoon) has to be done carefully so that the number of students unable to attend kept to the minimum, a carefully study indicates that the number of students who can not attend a particular on a specific day is as follows.

 

Leasing

Portfolio management

Private mutual fund

Equity research

Mon

50

40

60

20

Tues

40

30

40

30

Wed

60

20

30

20

Thurs

30

30

20

30

Fri

10

20

10

30

   (Ans :  Mon ® ER, Tues ® Dummy, Wed ® PM, Thurs ® PMF, Fri ® L; No. of
absentees = 20 + 0 + 20 + 20 + 10 = 70)

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