Assignment Model
7
ASSIGNMENT MODEL 1. A company has four districts, North, South, East and West to sell its production and four salesmen A, B, C and D for it. The district-wise cost of allocation of each salesman is given below. Determine the area allocation so that the allocation cost is minimized. A B C D P 42 0 350 280 210 Q 30 0 250 200 150 R 30 0 250 200 150 S 24 0 200 160 120 How should the assignments be made? Answer Job Employee Cost P D 210 Q C 200 R B 250 S A 240 Total cost=Rs 900 2. There are four manufacturing sections and five supervisors in the industry. Four of the five supervisors are to be promoted at foremen. The efficiency matrix of the supervisors is given below: M1 M2 M3 M4 A 90 96 72 88 B 95 90 0 85 C 85 80 75 0 D 78 95 0 80 E 93 91 70 8
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ASSIGNMENT MODEL1. A company has four districts, North, South, East and West to sell its production and four salesmen A, B, C and D for it. The district-wise cost of allocation of each salesman is given below. Determine the area allocation so that the allocation cost is minimized.
A B C D
P420350280210
Q300250200150
R300250200150
S240200160120
How should the assignments be made?
Answer Job Employee Cost
P D 210
QC200
RB250
SA240
Total cost=Rs 900
2. There are four manufacturing sections and five supervisors in the industry. Four of the five supervisors are to be promoted at foremen. The efficiency matrix of the supervisors is given below: M1M2M3M4
A90967288
B9590085
C8580750
D7895080
E 9391708
Which four supervisors should be promoted as supervisors of which manufacturing sections so as to maximize the efficiency of the industry?
Answer Job Mahine Cost
ADummy 0
B30
C 280
D178
E48
Cost = Rs 166
3. The owner of a small machine shop has four machinists available to assign to jobs for the day. Five jobs are offered with the expected profit (in Rs) for each machinist on each job as follows:12345
A6207805001010820
B710840610730590
C8709201110710810
D480640870770800
Find the assignment of machinists to jobs that will maximize the profits. Which jobs should be declined?
Answer Job Worker Cost
A3500
B5590
C4710
D1480
Dummy 20
Cost = Rs 2280
4. The cost structure (in lakhs of rupees) of contractors against tenders is given below:12345
A1622132125
B1412171120
C1821201721
D2629223331
E1915171620
How should you assign the contracts for minimum cost?Answer Contractor Tender Cost
A116
B411
C521
D322
E 215
Cost = Rs 85 lakhs
5. A caterer has four chefs. He has received orders for four parties. He has evaluated and rated his chefs (100 is best rating) on the basis of their abilities and the kind of cuisine preferred at each party and these are shown in the table below:1234
A70604060
B70206050
C60203040
D40301030
How should he assign the chefs?
Answer Chef Party Rating sore
A 260
B 360
C160
D430
210
6. Find minimum assignment costs
105131516
3918136
107222
7119712
7910412
Answer Job Employee Cost
A25
B13
C52
D39
E 44
Cost Rs 23
911151011
129-109
-1114117
1481278
Answer Job Men Cost
A19
B29
C57
D47
E 30
Cost Rs 32
7. Maximize profits82-54
109284
5496-
36287
561043
Answer JobMenProfit
A18
B29
C46
D57
E310
Profit Rs 40
18242832
8131719
10151922
Answer Job Worker Profit
A 432
B 317
C215
D 10
Profit Rs 64
1398101214
1287111413
109691212
1211991011
9788910
141210101114
Answer Job Machine Profit
A 614
B514
C49
D211
E38
F114
Profit = Rs 70
1236-59
411-5-8
8210975
-7861210
589461
Answer Job Worker Profit
A 112
B211
C49
D512
E39
F 60
Profit = Rs 53
