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Decision Analysis and Modeling Project

Sneha Y (B63)

Problem

Sneha got admission in XYZ College of Management. She has five options of specializations

Finance, Marketing , IT, General Management and Operations and she is inclined towards

Finance, Marketing and Operations . She already got admissions in various colleges. Unable to

decide which college to join she took the advice of friends, seniors and classmates but could not

make any decision .She approached a consultant for advice whether to join the college or not.

She wanted to join a college which has average salary package above 10lakhs and she could not

find any data from the official reports published by XYZ college. Also she was curious to know

what are the salaries paid for each of the specialization she was interested.

The consultant takes up the problem and evaluates the placement records and attendance lists

about students taking up various specializations. He was able to access the past records from

XYZ College with its permission.

The following is the data furnished by College

Number of students in batch=400

Number of students placed in different streams in Finance, Marketing and Operations

during the years 2002-2010.

Year Finance Students Marketing Students Operations Students

2002 118 129 95

2003 113 127 97

2004 112 126 98

2005 120 122 98

2006 127 125 98

2007 126 124 100

2008 128 121 103

2009 127 119 102

2010 129 118 104

Students taking various specialization and final placements during the year 2010.Theseprobabilities are conditional probabilities .For example the value 0.10 in first row denotes

the probability that given the student is placed in Finance ,the probability that he takes

marketing as specialization.

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Specialization

P(Specialization/Placement) Finance Marketing Operations

Finance 0.85 0.10 0.05

Placement Marketing 0.03 0.91 0.06

Operations 0.03 0.02 0.95

The average salary of each specialization (Finance, Marketing and Operations) from year

2002-2010 are given in the table below:

Year Finance(Rs. in lakhs) Marketing(Rs. in

lakhs)

Operations(Rs. in

lakhs)

2002 8.3 8.1 7.12

2003 8.2 8.42 7.3

2004 9.7 9.2 8.4

2005 9.56 9.8 8.922006 10.34 10.6 9.3

2007 11.89 11.23 10

2008 10.23 10.5 9.2

2009 11.59 11.1 9.8

2010 11.23 11.34 10.4

After gathering the data consultant assured her that he would investigate about

1) What salary can she expect if she joins XYZ in Finance, Marketing and Operations?

2) What is the expected salary package from each specialization?

Solution Procedure:

Using Linear Regression Analysis the consultant tries to forecast the values of Salaries and

Number of students placed in each specialization. (The calculations and results are in Appendix

1.1 to 1.6)

Variable R Constant Year Forecast

Salary of Finance

Salary_F 0.87 -835.079 .421 11.55

Salary of

Marketing

Salary_M 0.937 -826.804 .417 11.87

Salary of

Operations

Salary_Op 0.929 -770.059 .388 10.21

No. of

students

Place_F 0.854 -4053.11 2.067 133

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placed in

Finance

No. of

students

placed in

Marketing

Place_M 0.953 2664.378 -1.267 116

No. of

students

placed in

Operations

Place_Op 0.957 -2006.856 1.050 105

Using the forecasted values for students placed in different specializations ,he calculates

probabilities that a student takes a particular specialization are placed. The following table gives

the values of probabilities:

Stream P(Placement in Stream)Finance 133/400=0.3325

Marketing 116/400=0.29

Operations 105/400=0.2625

The following is the table for finding out conditional probabilities

Specialization Placement(Ei) P(Ei) P(S/Ei) P(S & Ei) P(Ei/S)

Finance Finance 0.3325 0.85 0.283 0.94

Marketing 0.29 0.03 0.0087 0.029

Operations 0.2625 0.03 0.0078 0.0260.2995

Marketing Finance 0.3325 0.10 0.0332 0.104

Marketing 0.29 0.91 0.2639 0.827

Operations 0.2625 0.02 0.0052 0.016

0.3189

Operations Finance 0.3325 0.05 0.0166 0.058

Marketing 0.29 0.06 0.0174 0.061

Operations 0.2625 0.95 0.2493 0.879

0.2833

The consultant draws the decision tree for the above probability values and payoff values

forecasted using regression analysis.

See Appendix 1.7

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Conclusions:

1) The expected value of the salary if you join XYZ in 2011 is Rs. 9.934 lakhs and Sneha

rejects the College because its return value is less than Rs.10 lakhs

2) Finance as specialization gives highest salary of Rs.11.466lakhs followed by Marketing

with a salary of Rs.11.175 lakhs and Operations with salary of Rs.10.367 lakhs

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APPENDIX

Linear Regression Analysis:

1.1) Salary Ops

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of

the Estimate

1 .929a

.863 .843 .45321

a. Predictors: (Constant), Year

Coefficientsa

Model

Unstandardized

Coefficients

Standardized

Coefficients

t Sig.B Std. Error Beta

1 (Constant) -770.059 117.369 -6.561 .000

Year .388 .059 .929 6.637 .000

a. Dependent Variable: Salary_Op

The forecast salary of Operation students

Y=A+BX

Y=-770.059+.388*2011=10.21

1.2)Salary M

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of

the Estimate

1 .937a

.877 .859 .45730


Coefficientsa

Model

Unstandardized

Coefficients

Standardized

Coefficients t Sig.

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B Std. Error Beta

1 (Constant) -826.804 118.429 -6.981 .000

Year .417 .059 .937 7.066 .000

a. Dependent Variable: Salary_M

The forecast salary of Marketing students

Y=A+BX

Y=-826.804+0.417*2011=11.87

1.3)Salary Fin

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of

the Estimate

1 .870a

.757 .722 .69936


Coefficientsa

Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -835.079 181.115 -4.611 .002

Year .421 .090 .870 4.667 .002

a. Dependent Variable: Salary_F

The forecast salary of Finance students

Y=A+BX

Y=--835.079+0.421*2011=11.55

1.4)Student Fin

Model Summary

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Model R R Square

Adjusted R

Square

Std. Error of

the Estimate

1 .854a

.729 .690 3.68954


Coefficientsa

Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -4023.511 955.494 -4.211 .004

Year 2.067 .476 .854 4.339 .003

a. Dependent Variable: Stud_fin

The forecast number of students taking Finance as specialization

Y=A+BX

Y= -4023.511+2.067*2011=133

1.5)Stud_M

Model Summary

Model R R SquareAdjusted R

SquareStd. Error of the Estimate

1 .935a

.873 .855 1.41197


Coefficientsa

Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) 2664.378 365.662 7.286 .000

Year -1.267 .182 -.935 -6.949 .000

a. Dependent Variable: Stud_M

The forecast number of students taking Marketing as specialization

Y=A+BX

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Y= 2664.378- 1.267*2011=116

1.6)Stud_op

Model Summary

Model R R Square

Adjusted R

Square

Std. Error of

the Estimate

1 .957a

.916 .904 .93138


Coefficientsa

Model

Unstandardized

Coefficients

Standardized

Coefficients


1 (Constant) -2006.856 241.202 -8.320 .000

Year 1.050 .120 .957 8.733 .000

a. Dependent Variable: Stud_Op

The forecast number of students taking Operations as specialization

Y=A+BX

Y= -2006.856+1.050*2011=105

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1.7)

Finance

Marketing

Operations

PF

PM

PO

PF

PM

PO

PO

PM

PF

PF- Placed in Finance

PM-Placed in Marketing

PO-Placed in O erations

11.55*0.94=10.857

11.55*0.104=1.19

11.55*0.058=0.669

11.87*0.029=0.344

11.87*0.827=9.81

11.87*0.061=0.724

10.21*0.026=0.265

10.21*0.016=0.16

10.21*0.879=8.974

11.175

10.367

9.934

0.029

0.061

0.3189

DECISION TREE ANALYSIS

Choice of

Specializati

on

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