HANGARIAN METHOD – TRANSPORTATION
PROBLEMS
1. What is Hungarian Method?
The Hungarian Method is a mathematical technique used to solve Assignment Problems in
Operations Research. It helps to assign tasks, jobs, or workers in such a way that the total cost
is minimized or total profit is maximized. It is considered a special case of the Transportation
Problem where supply and demand for each source and destination is equal to one (1).
2. Why Do We Use Hungarian Method?
1) To find the minimum cost assignment.
2) To assign one worker to one job efficiently.
3) To reduce time and calculation compared to trial-and-error methods.
4) To ensure the optimal solution is obtained.
5) To solve business problems like machine allocation, staff scheduling, and project
assignments
Assignment Problem – Hungarian Method
A company wants to assign 4 workers (A, B, C, D) to 4 jobs (1, 2, 3, 4). The cost (in $.) of
assigning each worker to each job is given below.
Job 1 Job 2 Job 3 Job 4
A 14 12 15 15
B 21 18 18 22
C 14 17 12 14
D 6 5 3 6
, Step 1: Row Reduction
Select the minimum value in each row =
Job 1 Job 2 Job 3 Job 4
A 14 12 15 15
B 21 18 18 22
C 14 17 12 14
D 6 5 3 6
Row minimums:
A → 12
B → 18
C → 12
D→3
Subtract it from every element in that row
Job 1 Job 2 Job 3 Job 4
A 14-12 12-12 15-12 15-12
B 21-18 18-18 18-18 22-18
C 14-12 17-12 12-12 14-12
D 6-3 5-3 3-3 6-3
After subtracting row minimums
Job 1 Job 2 Job 3 Job 4
A 2 0 3 3
B 3 0 0 4
C 2 5 0 2
D 3 2 0 3
PROBLEMS
1. What is Hungarian Method?
The Hungarian Method is a mathematical technique used to solve Assignment Problems in
Operations Research. It helps to assign tasks, jobs, or workers in such a way that the total cost
is minimized or total profit is maximized. It is considered a special case of the Transportation
Problem where supply and demand for each source and destination is equal to one (1).
2. Why Do We Use Hungarian Method?
1) To find the minimum cost assignment.
2) To assign one worker to one job efficiently.
3) To reduce time and calculation compared to trial-and-error methods.
4) To ensure the optimal solution is obtained.
5) To solve business problems like machine allocation, staff scheduling, and project
assignments
Assignment Problem – Hungarian Method
A company wants to assign 4 workers (A, B, C, D) to 4 jobs (1, 2, 3, 4). The cost (in $.) of
assigning each worker to each job is given below.
Job 1 Job 2 Job 3 Job 4
A 14 12 15 15
B 21 18 18 22
C 14 17 12 14
D 6 5 3 6
, Step 1: Row Reduction
Select the minimum value in each row =
Job 1 Job 2 Job 3 Job 4
A 14 12 15 15
B 21 18 18 22
C 14 17 12 14
D 6 5 3 6
Row minimums:
A → 12
B → 18
C → 12
D→3
Subtract it from every element in that row
Job 1 Job 2 Job 3 Job 4
A 14-12 12-12 15-12 15-12
B 21-18 18-18 18-18 22-18
C 14-12 17-12 12-12 14-12
D 6-3 5-3 3-3 6-3
After subtracting row minimums
Job 1 Job 2 Job 3 Job 4
A 2 0 3 3
B 3 0 0 4
C 2 5 0 2
D 3 2 0 3
