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.

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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.

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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

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Applications of assignment problem

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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

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Applications of assignment problem

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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

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