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OR

The art of wining warwith out Actually

Fighting it .

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British Government employed a numbof team eminent scientists to apply

their expertise to

-Management and operational problem

- Rather than technical problems

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R

!merge

Radar operational Research team

Another team was set up toexamine the relative

inefectiveness o the German U

boats which were sinking theood Convo ships suppling!ritain"

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After "orld "ar# $$

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-The same approach was used in industrial and commer

-First developed in Britain and &imultaneously in '&A fol!urope and rest of the world.

( But not yet in )a*istan +

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Defnition

o OR

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R society of ', de%nition.

-Operational research is the application othe methods o science to comple

problems arising in the direction anmanagement o large system o mamachine, material and money in industrbusiness, government And deense- The distinctive approach is to develop scienti%c model of the system incorporatin

measurements of factor- such as chance anris*- with which to compare the outcome analternative decisions- strategies and controls.The purpose is to help management determinits policies and actions scienti%cally.

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OR society o USDefnition

Operations Research is concerned withscientifcally deciding how to best designand operate manmachine systemsusually under conditions re!uiring theallocation o scarce resources

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-perational research is the application of uant

methods to decision ma*ing

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perations research / &cience applied tmanagement

Management / 0ecision ma*ing andcontrol

Management &cience / study of

problems asabstraction and application of theresulting theoryto practical situation

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OR "rocess

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#ntroduction to $inear

"rogramming

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The word programming does not refer here to computerprogramming; rather, It is essentially a synonym for planning

Linear programming is a mathematical technique designed

aid managers in allocating scarce resources(such as labcapital, or energy) among competing activities. It reflects,

the form of a model, the organiation!s attempt to achieve so

ob"ective (frequently, ma#imiing profit contributi

ma#imiing rate of return, minimiing costs) in view of limi

or constrained resources (available capital or labor, serv

levels, available machine time, budgets).

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The linear programming techniue can be said to have a linob1ective function that is to be optimi2ed 3either maximi2edminimi2ed4 sub1ect to linear euality or ineuality constraints

sign restrictions on the variables. The term linear describes proportionate relationship of two or more variables. Thus- a gichange in one variable will always cause a resulting proportiochange in another variable.

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&ome areas in which linear programming has been applied will be helpful inclimate for learning about this important techniue

3i4 A company produces agricultural fertili2ers. $t is interested in minimi2ing costs

certain speci%ed levels of nitrogen- phosphate- and potash by blending together a materials.

3ii4 An investor wants to maximi2e his or her rate of return by investing in stoc*s ainvestor can set speci%c conditions that have to be met including availability of capita

3iii4 A company wants the best possible advertising exposure among a numbmaga2ines- and radio and television commercials within its available capital reuirem

3iv4 An oil re%nery blends several raw gasoline and additives to meet a car manufacturspeci%cations while still maximi2ing its pro%ts.

3v4 A city wants to maximi2e the daytime use of recreational properties being proposedwith a limited capital available.

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Formulation of the 6inear )rogram)roblem

To formulate a real7life problem as a linear program is an art in itself. To aid you in ttas*- it is helpful to isolate the essential elements of the problem as a means of as*what the clients wants and what information can be gained from the data that has

been provided.

The %rst step in formulating a problem is to set forth the ob1ective called the ob1ectivefunction

A second element of a problem is that there are certain constraints on the company5s

ability to maximi2e the total contribution. These constraints are/

384 uantity of raw materials available-

394 the level of demand for the products- and

3:4 the euipment productive capacity.

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Time

A further element that must be considered in the problem is thtime period being used. The duration may be either long term short term. Although time is an important element- it is one that ha

;exibility so that the time hori2on may be changed as long as threstrictions are compatible with the periods under consideration

ering chances of occurrence exists for the possibility ma*ing each of the products

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!xample 8/ )roduct Mix

The Regal ?hina ?ompany produces two products daily- plates and mugs. The company haslimited amounts of two resources used in the production of these products clay and labor.Given these limited resources- the company desires to *now how many plates to produceeach day- in order to Maximi2e pro%t. The two products have the following resource

reuirements for production and pro%t per item produced 3i.e.- the model parameters4.

There are @ hours of labor and 89 pounds of clay available eachday for production

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Decision %ariables

The decision confronting management in this proble

how many plates and mugs to produce. As such- theretwo decision variables that represent the number of pl

and mugs to be produced on a daily basis.

The uantities to be produced can be represe

symbolically as-

8 C the number of plates to produce9 C the number of mugs to produce

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&he Ob'ective (unction

The ob1ective of the company is to Maximi2e total pro%t. Tcompany5s pro%t is the sum of the individual pro%ts gained froeach plate and mug. As such- pro%ts from plates is determine

multiplying the unit pro%t for each plate- Rs. @- by the number plates produced- 8. 6i*ewise- pro%t derived from mugs is the upro%t of a mug- Rs. D- multiplied by the number of mugs produce9. Thus- total pro%t- E- can be expressed mathematically

as

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Maximi2e E C @8 D9

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The solution of this model will result in numerical values for 8 andwhich will maximi2e total pro%t- E. As one possible solution- conside 8 C D plates and 9 C 8 mugs. First we will substitute hypotheticalsolution into each of the constraints in order to ma*e sure that

solution does not reuire more resources than the constraints showavailable.

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Thus- neither one of the constraints is violated by this hypothetisolution. As such- we say the solution is feasible 3i.e.- it ispossible4. &ubstituting these solution values in the ob1ectivefunction givesE C @3D4 D384 C Rs. . However- the maximum pro%t.

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Thus- the solution to this problem must both Maximi2e pro%tand not violate the constraints. The actual solution to thismodel which achieves this ob1ective is 8 C 9@ plates and 9C J mugs- with a corresponding pro%t of Rs. 8:K.

)xample * #ngredients +ixing

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)xample * #ngredients +ixing

Fau1i Foundation produces a cereal &'

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perational Research

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b1ectives ofperational Researc

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b1ectives

0ecision ma*ing while improving its uality

$dentifying optimal solution

$ntegrating the systems

$mproving the ob1ectivity of analysis

Minimi2ing the cost and maximi2ing the pro%t

$mproving the productivity

&uccess in competition and mar*et leadership

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b1ectives

The intent of R is

To learn about management and administration socio7cultural behavior and economic factors thaas bottlenec* to e>ective implementation.

To develop more e>ective approaches to theprogramming.

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&cope of R

8.

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9. Health care services and

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Methods of R

M th d

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Methods

Multi7criteria decision analysis

6inear and non7linear programming

0iscrete7event simulation

ueuing and stochastic process modeling

M th d

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Methods

Most pro1ects of R apply on one of the three gro

methods.

8. &imulation method

9. ptimi2ation method

:. 0ata7analysis method

8 &i l ti th d

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8. &imulation method

$t gives ability to conduct sensitive study to

a4 &earch for improvements

b4 Testing the improvement ideas that are being m

9 ti i ti th d

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9. ptimi2ation method

Here goal is to enable the decision ma*ers to ide

and locate the very best choice- where innumerafeasible choices are available and comparing thediNcult.

: 0 t l i th d

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:. 0ata analysis method

The goal is to aid the decision7ma*er in detectin

patterns and inter connections in the data set. 'se of this analysis for ma*ing solutions.

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perational researchprocess

)rocess

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)rocess

8. $denti%cation of the program problem.

9. $denti%cation of possible reasons and solutions

:. Testing of potential solution.

@. Results utili2ation.

D. Results dissemination.

8 $denti%cation of the program pro

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8. $denti%cation of the program pro

Most critical step in the process.

'nless problem is clearly de%ned it is impossibledevelop good solutions.

9 $denti%cation of possible reasons and solu

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9. $denti%cation of possible reasons and solu

nce the problem has been identi%ed- it is the 1o

program implementer and researcher to determreasons for the problem and generate possiblesolutions.

: Testing of potential solution

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:. Testing of potential solution

A good solution must be measurable- easy to im

and sustainable.To determine e>ectiveness of proposed solution

designs are used.

a4 uasi7experimental design.

)

comparison of situations before and after the solution.b4 True experiment.

)?omparison of outcomes between experimental and cogroups.

@ Result utili2ation

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@. Result utili2ation

$t is necessary to decide how its results are mea

used.This determines to some extent that what inform

should be collected.

D Results dissemination

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D. Results dissemination

Results dissemination are done in the form

of seminars or by meeting with decision

ma*ers.