Ask
Login
0
5.7kviews
Five salesmen are to be assigned to five territory.
written 7.3 years ago by gravatar for teamques10 teamques10 ★ 64k •   modified 7.3 years ago

Five salesmen are to be assigned to five territory. Based on past performance, the following table shows annual sales (in lakhs) that can be generated by each salesman in each territory. Find the optimum assignment. ** indicates that salesman 4 does not wish to work in territory 2. -

  T1 T2 T3 T4 T5
S1 27 15 11 14 10
S2 32 28 31 15 18
S3 16 19 16 26 30
S4 18 ** 22 32 25
S5 21 20 26 16 12

Mumbai University > Mechanical Engineering > Sem 7 > Operations Research

Marks: 10 Marks

Year: Dec 2015
operation research
ADD COMMENT EDIT
1 Answer
0
191views
written 7.3 years ago by gravatar for teamques10 teamques10 ★ 64k

As this problem is of improvement of sales, it is a problem of maximization. So first converting maximization type into minimization type by subtracting all values from biggest value in given table.

Replacing restriction type by M, let M is a very large number.

5 12 16 13 17
0 4 1 17 14
16 11 14 4 0
14 M 10 0 7
11 6 0 10 14

Applying Row operation

0 12 16 13 17
0 4 1 17 14
14 11 14 4 0
14 M 10 0 7
5 6 0 10 14

Applying column operation as well as assign the job by priority Left-Right & Top-Bottom

[0] 8 16 13 17
0 [0] 1 17 14
14 7 14 4 [0]
14 M 10 [0] 7
5 2 [0] 10 14

No. of assignments = No. of Rows, hence the solution is feasible.

Salesman Territory
S1 1
S2 2
S3 5
S4 4
S5 3
ADD COMMENT EDIT
Please log in to add an answer.