quantitative management technques

8/6/2019 Quantitative Management Technques

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Management by facts & figures.Management by facts & figures.Decisions based on use of specificDecisions based on use of specifictechniquestechniques ..

Quantitative analysis uses a scientificQuantitative analysis uses a scientificapproach to decision making.approach to decision making.

Quantitative Approaches toManagement


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Defining the problemDefining the problem

Developing a ModelDeveloping a Model

Acquiring Input DataAcquiring Input DataDeveloping a SolutionDeveloping a Solution

Testing the SolutionTesting the Solution

Analysing the ResultAnalysing the Result

Implementing the resultImplementing the result

The Quantitative Analysis ApproachThe Quantitative Analysis ApproachConsists of Consists of


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Problem:Problem: (A clear ,Concise statement of the problem )(A clear ,Concise statement of the problem )Model:Model: (Simply stated with the mathematical situation)(Simply stated with the mathematical situation)Input Data:Input Data: ( Proper and accurate data for accurate result)( Proper and accurate data for accurate result)SituationSituation :: ( Manipulating the model to arrive at the best result)( Manipulating the model to arrive at the best result) Testing:Testing: ( The Data and model are tested before implementing )( The Data and model are tested before implementing )

Analyzing ResultsAnalyzing Results :: ( Determining the suggestions of the( Determining the suggestions of thesolution as per changing the data)solution as per changing the data)

Implementing the ResultImplementing the Result :: (This is the process of (This is the process of incorporating the solution in to the company it is much more difficult then youincorporating the solution in to the company it is much more difficult then youwould imagine)would imagine)


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How To Develop A Quantitative AnalysisHow To Develop A Quantitative AnalysisModel (Simple)Model (Simple)

Expenses include Fixed and Variable CostsExpenses include Fixed and Variable Costs

Mathematical ModelMathematical Model

Profit = Revenue ExpensesProfit = Revenue Expenses

Profit = Revenue (fixed cost + variable cost)Profit = Revenue (fixed cost + variable cost)

Profit = (Selling price per unit) (number o unitsProfit = (Selling price per unit) (number o units

sold) [ fixed cost + (variable cost per sold) [ fixed cost + (variable cost per

unit) ( number of units sold)]unit) ( number of units sold)]

Profit= sX [ f + vX ]Profit= sX [ f + vX ]

where X is manipulating variable in the modelwhere X is manipulating variable in the model


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Profit = sX f vXProfit = sX f vX

Decision makers are often interested in theDecision makers are often interested in the break-even point (BEP). That is Zero Proit. break-even point (BEP). That is Zero Proit.

0= sX f vX0= sX f vX

0= (s v) x f 0= (s v) x f f = (s v) Xf = (s v) X

X = f divided by s - vX = f divided by s - v


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Defining The Model VariableDefining The Model VariableS = Selling price per unitS = Selling price per unitF = fixed costF = fixed costV = variable cost per unitV = variable cost per unitX = number of unit sold (Manipulating Variable tha changesX = number of unit sold (Manipulating Variable tha changes

the model)the model)

If s =10 , f= 1,000 , v= 5If s =10 , f= 1,000 , v= 5X = f / s-vX = f / s-v

X= Rs.1000 / 10-5X= Rs.1000 / 10-5X= 200 units will be produced at BEPX= 200 units will be produced at BEP


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Modeling In The Real WorldModeling In The Real World

Defining A ProblemDefining A ProblemChina produces about 1.1 billion tons of coal each year. DemandChina produces about 1.1 billion tons of coal each year. Demand

however is estimated to be about 1.6 billion tons. In addition, china facedhowever is estimated to be about 1.6 billion tons. In addition, china facedair pollution problems that could threaten is high gross national productair pollution problems that could threaten is high gross national product

(GNP) growth rate. These problems were identified(GNP) growth rate. These problems were identifiedBy the Chinese State Planning Commission and the world Bank asBy the Chinese State Planning Commission and the world Bank asimportant to the continued growth of the GNP .important to the continued growth of the GNP .

1 - Demand and Supply Problem of Coal1 - Demand and Supply Problem of Coal

2 - Air Pollution2 - Air Pollution


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Developing A ModelDeveloping A Model

In order to analyze some o the problems associated with theIn order to analyze some o the problems associated with thedelivery of coal and electricity , the Chinese State Planningdelivery of coal and electricity , the Chinese State PlanningCommission developed a comprehensive model, called the CoalCommission developed a comprehensive model, called the Coal

Transport Study (CTS). Transport Study (CTS).The Model specified key components in the generation, The Model specified key components in the generation,

transmission and demand for electricitytransmission and demand for electricity

Acquiring Input Data:Acquiring Input Data:

In addition to historical data, the model requires forecasts of In addition to historical data, the model requires forecasts of future demand and the potential environmental impact of variousfuture demand and the potential environmental impact of variousenergy sources and uses. In addition, specific data concerning theenergy sources and uses. In addition, specific data concerning thevarious stages of coal and electricity production are needed.various stages of coal and electricity production are needed.



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Developing A SolutionDeveloping A SolutionInstead o developing and reporting one solution, the quantitativeInstead o developing and reporting one solution, the quantitativeanalysis team analyzed 16 different solutions or possibilities.analysis team analyzed 16 different solutions or possibilities.

These solutions revealed that the investment in new coal- These solutions revealed that the investment in new coal-

electricity system could be as high as $250 billion over a 10electricity system could be as high as $250 billion over a 10years. The new system would have to deliver about 2 billion tonsyears. The new system would have to deliver about 2 billion tonsof coal.of coal.

Testing The SolutionTesting The SolutionAssumptions of the model and the solution were carefully tested.Assumptions of the model and the solution were carefully tested.

About six months were spent in testing the data and model withAbout six months were spent in testing the data and model withdifferent situations with running statistical tests on the data anddifferent situations with running statistical tests on the data andmodel. After testing, corrections and adjustments were made tomodel. After testing, corrections and adjustments were made tomake sure that the results were as accurate as possible.make sure that the results were as accurate as possible.



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Analyzing The Results:Analyzing The Results: The solutions also result in major findings. The solutions also result in major findings.

1.1. The government should plan on an 8% to 9% The government should plan on an 8% to 9%growth in power needs.growth in power needs.2.2. The railways will continue to be the dominant The railways will continue to be the dominant

transportation system for coal etctransportation system for coal etc

3.3. Reduce the pollution while producing coal andReduce the pollution while producing coal andnegative environment consequences.negative environment consequences.



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Implementing The ResultsImplementing The ResultsImplementing of the CTS model result in a new steam coal-Implementing of the CTS model result in a new steam coal-washing procedure, the construction of improved railwaywashing procedure, the construction of improved railway

systems and a new port, and the use of coal imports.systems and a new port, and the use of coal imports.



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The Quantitative AnalysisApproaches

LinearProgramming Technique

[ L P ]

WaitingLines AndQueuing

Technique

[ W L Q T ]


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Quantitative TechniquesQuantitative Techniques

Linear Programming ( L P )Linear Programming ( L P )

It deals with situations which requireIt deals with situations which requireneed for utilization of limitedneed for utilization of limitedresources to best advantage.resources to best advantage.


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ExamplesExamplesA bank wants to allocate its funds to achieveA bank wants to allocate its funds to achievehighest possible returns. It must operate withinhighest possible returns. It must operate withinliquidity limits set by regulatory authorities.liquidity limits set by regulatory authorities.

An advertising agency wants to achieve bestAn advertising agency wants to achieve best possible exposure for its clients product at possible exposure for its clients product atlowest possible cost.lowest possible cost.A Food Administrator wants to prepare a high-A Food Administrator wants to prepare a high-

protein diet at lowest cost. protein diet at lowest cost.


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Linear Programming ( L P )Linear Programming ( L P )

In This TechniqueIn This TechniqueWe either We either maximizemaximize ProfitProfit

Or Or

MinimizeMinimize CostCost


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AllAll VariablesVariables involved haveinvolved have

linear relationships, i.e.linear relationships, i.e.doubling of labour- hoursdoubling of l abour- hours

will result in double output.will result in double outp ut.

Non - negativityNon - neg ativity

Variables InvolvementVariables Involvement


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Graph Showing Linear RelationshipGraph Showing Linear Relationship

Between Decided Variables Such asBetween Decided Variables Such asLabour and Output By Doubled RatioLabour and Output By Doubled Ratio

Labour

O u t P u

t

100 200 400 800

10

20

40

80

R e l a t i o

n s h i p B e t w

e e n X a

n d Y V

a r i a b l e s

quantitative management technques

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