The document discusses the assignment problem, a specific case of the transportation problem where resources are assigned to activities to minimize costs or maximize profits. It details the Hungarian method, including rules for applying the method and step-by-step instructions for finding optimal solutions. The method involves manipulating a cost matrix through various steps until an optimal assignment is found.

1. INDUS UNIVERSITY
Assignment Problem
~ by
Shah Smruti

2. What We'll Discuss
TOPIC OUTLINE
What is Assignment Problem?
What is Hungarian method(HAM METHOD)?
Rules for solving HAM Method
How to solve HAM Method
S H A H S M R U T I

3. Assignment Problem
An assignment problem is a particular case
of transportation problem where the
objective is to assign a number of resources
to an equal number of activities so as to
minimise total cost or maximize total profit
of allocation.
S H A H S M R U T I

4. Hungarian
method
1955 by Harold Kuhn
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.
S H A H S M R U T I

5. RULES FOR SOLVING
HAM METHOD
Identify the minimum
element in each row and
subtract it from each
element of that row.
Identify the minimum
element in each column
and subtract it from every
element of that column.
If number of rows is not
equal to number of
columns, then add dummy
rows or columns with cost
0, to make it a square
matrix.
S H A H S M R U T I

6. Identifyrowswithexactlyoneunmarked0.Makeanassignmmenttothissingle0bymakeasquare([0]
)arounditandcrossoffallother0inthesamecolumn.
Identifycolumnswithexactlyoneunmarked0.Makeanassignmmenttothissingle0bymakeasquare
([0])arounditandcrossoffallother0inthesamerows.
Ifarowand/orcolumnhastwoormoreunmarked0andonecannotbechosenbyinspection,then
choosethecellarbitarily.
Continuethisprocessuntilall0inrows/columnsareeitherassignedorcrossoff( ).
Makeassignmentintheopporunitycosttable
S H A H S M R U T I

7. Ifthenumberofassignedcells=thenumberofrows,thenanoptimal
Ifoptimalsolutionisnotoptimal,thengotoStep-5.
assignmentisfoundandIncaseyouhavechosena0cellarbitrarily,thentheremaybeanalternate
optimalsolutionexists.
S H A H S M R U T I

8. Tick(✓)markalltherowsinwhichnoassigned0.
ExamineTick(✓)markedrows,Ifany0celloccursinthatrow,thentick(✓)markthatcolumn.
ExamineTick(✓)markedcolumns,Ifanyassigned0existsinthatcolumns,thentick(✓)markthatrow.
Repeatthisprocessuntilnomorerowsorcolumnscanbemarked.
Drawastraightlineforeachunmarkedrowsandmarkedcolumns.
Ifthenumberoflinesisequaltothenumberofrowsthenthecurrentsolutionistheoptimal,otherwise
gotostep-6
Drawasetofhorizontalandverticallinestocoverallthe0
S H A H S M R U T I

9. Repeat stpes 3 to 6 until an
optimal solution is arrived.
Select the minimum element,
say k, from the cells not
covered by any line.
Subtract k from each element
not covered by a line.
c. Add k to each intersection
element of two lines.
Develop the new revised
opportunity cost table
S H A H S M R U T I

10. EXAMPLE 1
S H A H S M R U T I

11. STEP 1
Number of rows = Number of
columns
S H A H S M R U T I

12. STEP 2
Identify the
minimum element in
each row and
subtract it from each
element of that row.
Identify the minimum
element in each
column and subtract it
from each element of
that column .

13. STEP 3
STEP 4
if(Number of assign zero=Number
of rows)
{
optimal solution arrived
} else {
goto step 5
}

14. STEP 5
S H A H S M R U T I

15. STEP 6
S H A H S M R U T I

16. STEP 3
STEP 4
if(Number of assign zero=Number
of rows)
{
optimal solution arrived
} else {
goto step 5
}

17. STEP 4

18. EXAMPLE 2
S H A H S M R U T I

19. STEP 1
Number of rows = Number of
columns
S H A H S M R U T I

20. STEP 2
Identify the
minimum element in
each row and
subtract it from each
element of that row.
Identify the minimum
element in each
column and subtract it
from each element of
that column .

21. STEP 3
STEP 4
if(Number of assign zero=Number
of rows)
{
optimal solution arrived
} else {
goto step 5
}

22. STEP 5
S H A H S M R U T I

23. STEP 6
S H A H S M R U T I

24. STEP 3
STEP 4
if(Number of assign zero=Number
of rows)
{
optimal solution arrived
} else {
goto step 5
}

25. STEP 4

26. Any Questions ?
IT'S A PROCESS EVEN THE MOST
TRADITIONAL THINKERS CAN ADOPT.
S H A H S M R U T I

27. I N D U S U N I V E R S I T Y
IMCA-IV
Thank You...
SHAH SMRUTI