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Prepared by:Dayani Jathunge061011VDissanayake G.P. 061016PFernando C.I. 061020X
This is a special type of transportation problem in
which each source should have the capacity to fulfill
the demand of any of the destinations.
In other words any operator would be able perform
any job regardless of his skills, although the cost( or
the time taken) will be more if the job does not
match with operator’s skill.
2
The objective might be,
minimize the total time to complete a set of
tasks
maximize skill ratings
minimize the cost of the assignments
3
JobJob
OperatoOperatorsrs
11 22 …… jj …… mm
11 tt1111 tt1212 tt1j1j tt1m1m
22
..
ii tti1i1 ttijij ttimim
..
mm ttm1m1 ttm2m2 ttmjmj ttmmmm4
General format of assignment problem
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Transportation Problem Assignment Problem
No equal number of sources & destination
Equal number of sources & destination
Source supply & destination have a fix demand for units
Source supply & destination demand is equal to 1
Quantity allocated or assigned must be a fix quantity
Quantity allocated or assigned must be 0 or 1
A network model is one which can be represented
by a set of nodes, a set of arcs, and functions
associated with the arcs and/or nodes.
e.g. costs, supplies, demands, etc.
AP is an example of a network problem.
AP can be formulated as an LP and solved
by general purpose LP codes.
However, there are many computer
packages, which contain separate
computer codes for these models which
take advantage of the problem network
structure.
Network Representation
WORKERSWORKERS JOBSJOBS
22
33
11
22
33
11cc1111
cc1212
cc1313
cc2121 cc2222
cc2323
cc3131cc3232
cc3333
This method can solve a special form of LP problem,
including the classical assignment problem, with
these typical characteristics:
is a special case of a transportation problem
the right-hand sides of constraints are all 1
the signs of the constraints are = rather than < or >
the value of all decision variables is either 0 or 1
As in transportation problems assignment problems also can be
balanced ( with equal number of rows and columns) or unbalanced.
When it is unbalanced the necessary number of row/s or column/s
are added to balance it. That is to make a square matrix.
The values of the cell entries of the dummy rows or columns will be
made equal to zero.
10
Applications of assignment problem
11
Raw entityRaw entity Column entityColumn entity Cell entityCell entity
operators jobs Operating cost
programmer program Processing time
operators Machine Operating cost
Drivers Routes Travel time
Teachers Subjects Students pass percentage
OperatorOperator
jobjob11 22 33 44 55
11 1010 1212 1515 1212 88
22 77 1616 1414 1414 1111
33 1313 1414 77 99 99
44 1212 1010 1111 1313 1010
55 88 1313 1515 1111 1515
12
Applications of assignment problem
13
Raw entityRaw entity Column entityColumn entity Cell entityCell entity
operators jobs Operating cost
programmer program Processing time
operators Machine Operating cost
Drivers Routes Travel time
Teachers Subjects Students pass percentage
Sales Sales regionregion
Sales personSales person
11 22 33 44
11 1010 2222 1212 1414
22 1616 1818 2222 1010
33 2424 2020 1212 1818
44 1616 1414 2424 2020
14
Applications of assignment problem
15
Raw entityRaw entity Column entityColumn entity Cell entityCell entity
operators jobs Operating cost
programmer program Processing time
operators Machine Operating cost
Drivers Routes Travel time
Teachers Subjects Students pass percentage
16