The assignment problem deals with allocating various resources to various activities on a one to one basis, i.e., the number of operations are to be assigned to an equal number of operators where each operator performs only one operation. For example, suppose an accounts officer has 4 subordinates and 4 tasks. The subordinates differ in efficiency and take different time to perform each task. If one task is to be assigned to one person in such a way that the total person hours are minimized, the problem is called an assignment problem. Assignment problem is a special case of transportation problem. The problem of assignment arises because available resources such as men, machines etc. have varying degrees of efficiency for performing different activities, therefore, cost, profit or loss of performing the different activities is different. The Hungarian method of assignment provides us with an efficient method of finding the optimal solution without having to make a-direct comparison of every solution. It works on the principle of reducing the given cost matrix to a matrix of opportunity costs. It is shorter and easier compared to any method of finding the optimal solution of a transportation problem. Opportunity cost show the relative penalties associated with assigning resources to an activity as opposed to making the best or least cost assignment. If we can reduce the cost matrix to the extent of having at least one zero in each row and column, it will be possible to make optimal assignment. Ques- A Company plans to assign 5 salesmen to 5 districts in which it operates. Estimates of sales revenue in thousands of rupees for each salesman in different districts are given in the following table . What should be the placement of the salesmen if the objective is to maximise the expected sales revenue ?

4. Salesme
n/District
D1 D2 D3 D4 D5
S1 40 46 48 36 48
S2 48 32 36 29 44
S3 49 35 41 38 45
S4 30 46 49 44 44
S5 37 41 48 43 47

5. Salesmen/
District
D1 D2 D3 D4 D5
S1 9 (49-40) 3 (49-46) 1 (49-48) 13 (49-36) 1 (49-48)
S2 1 (49-48) 17 (49-32) 13 (49-36) 20 (49-29) 5 (49-44)
S3 0 (49-49) 14 (49-35) 8 (49-41) 11 (49-38) 4 (49-45)
S4 19 (49-30) 3 (49-46) 0 (49-49) 5 (49-44) 5 (49-44)
S5 12 (49-37) 8 (49-41) 1 (49-48) 6 (49-43) 2 (49-47)

6. Salesmen
/District
D1 D2 D3 D4 D5
S1 8 2 0 12 0
S2 0 16 12 19 4
S3 0 14 8 11 4
S4 19 3 0 5 5
S5 11 7 0 5 1

7. Salesmen
/District
D1 D2 D3 D4 D5
S1 8 0 0 7 0
S2 0 14 12 14 4
S3 0 12 8 6 4
S4 19 1 0 0 5
S5 11 5 0 0 1

8. Salesmen/
District
D1 D2 D3 D4 D5
S1 8 0 0 7 0
S2 0 14 12 14 4
S3 0 12 8 6 4
S4 19 1 0 0 5
S5 11 5 0 0 1

10. Salesmen/
District
D1 D2 D3 D4 D5
S1 12 7
S2 10 8 10
S3 8 4 2
S4 23 1 5
S5 15 5 1
0
0
0
0
0
0
0
0
0
0
0