Page 161 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Inference
Hence to get a maximum profit of ` 22,000, Alpha Corporation should produce 2 products in
plant A, B should manufacture product 4, C plant should manufacture product 1 and D plant
should manufacture product 3.

Example: A company has 4 territories and 4 salesmen available for assignment. The
territories are not equally rich in their sales potential; it is estimated that a typical salesman
operating in each territory would bring in the following annual sales:
Territory I II III IV
Annual Sales (`) 60,000 50,000 40,000 30,000

Four salesmen are also considered to differ in their ability. It is estimated that working under
the same conditions, their yearly sales would be proportionately as follows:
Salesmen A B C D
Proportion 7 5 5 4

If the criterion is the maximum expected total sales cum the intuitive answer is to assign the best
salesman to the richest territory, the next best salesman to the second richest and so on. Verify
this answer by assignment model.
Solution:

Step 1: Matrix showing the proportion of sales revenue.
Territory (in’000) I (6) II (5) III (4) IV (3)
Sales A (7) 42 35 28 21
B (5) 30 25 20 15
C (5) 30 25 20 15
D (4) 24 20 16 12

Step 2: Calculation of sales revenue associated with the assignment based on intuition.
Salesman Territory Total Profit (`)
A I 42,000
B II/III 25,000/20,000
C III/II 20,000/25,000
D IV 12,000
99,000

Step 3: Verification of the results intuitively found with the use of assignment model.
Conversion of sales revenue matrix into cost matrix.

Territory I II III IV
Salesman A 0 7 14 21
B 12 17 22 27
C 12 17 22 27
D 18 22 26 30

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