Final presentation | MTH426A IITK

1. MTH426A
Introduction To Mathematical Modelling
Instructor – Prof. Prawal Sinha
Group- 13
Indian Education System
1. Dhruv Roosia (13252)
2. Jitendra Gawariya (13327)
3. Keshaw Singh (13347)
4. Kuldeep Soni (13362)
5. Nakul Surana (13418)

2. AIM
• Making Model of Indian Education System
• Analysis of female to male ratio in skilled labour.
• Analysis of total skilled workforce in India to meet
future needs

3. Flow of the problem
*For Males
dme dms
Nm(Y-22)
Nm(Y-22)(1-dme(Y-10))
A = NmY-22(1-dme(Y-10)) (1-dms(Y-4))
A*GERm(Y-4)*pf
A*(1-GERm(Y-4))*Vk
+ SLmY
Gby-4
(1-d1,e,y-12)(1-d1,s,y-4)
Vk=

4. SLm
y = Ny-22 (1-d1,e,y-12) (1-d1,s,y-4) [ gcy-4
(pf)y + (1-gcy-4
)GBy-4
]
1- (1-d1,e,y-12)(1-d1,s,y-4)
Skilled labour(Male) in year y :
1. di,e,y = Drop out rate at elementary level for year ‘y’
2. di,s,y = Drop out rate at secondary level for year ‘y’
3. pfy = College performance factor for year ‘y’
4. gc,y = Gross enrollment ratio for colleges at year ‘y’
5. GBy = General budget of year ‘y’
6. SLF
y = Skilled female labor at year ‘y’
7. SLM
y = Skilled male labor at year ‘y’
i=1 for Male
i=2 for Female
Variables:

5. Objectives:
SLm
y
SLF
y
MAX. f1 =
MAX. f2 = SLm
y + SLF
y
1)
2)
With the help of Lagrangian function, we will maximize these functions
0 <= pf <= 1
0 <= d <= 1
0 <= g <= 1
0 <= Vk <= 1
GB >= Inf +Inc + Tra
0 <= GB <= 100
i = 1 for Male
i = 2 for Female

6. Lagrangian function

7. Assumptions
• For elementary education, average of primary and upper primary
gives the dropout.
• Similarly, those of high and senior secondary for secondary
education.
• Social bias, performance factor and vocational training factor have
been approximated by self-constructed metrics. E.g. – social bias
based on literacy rate.

8. Inferences
• Differentiating and studying our objective functions f1 and f2 with
respect to the variables, we obtain a priority order for the
variables as follows:
1) di,e,y = Drop out rate at elementary level for year ‘y’
2) pfy = College performance factor for year ‘y’
3) di,s,y = Drop out rate at secondary level for year ‘y’
4) GBy = General budget of year ‘y’
5) gc,y = Gross enrollment ratio for colleges at year ‘y’
In the later slides, we will focus on the two major factors di,e,y and
pfy

9. With the help of regression analysis done on the drop out
rates(di,e,y) with respect to incentives, infrastructure,
teacher training, pupil teacher ratio and social bias, we
observe the following as highly significant:
• Teacher training
• Social bias (specially in girl child)
In order to attain our goal of making India skilled, we have
to focus on these factors.

10. Pitfalls
• Performance factor could not be quantified properly due
to lack of data.
• Vocational training gain factor is taken as one which is
difficult to achieve in real world.

11. Areas of improvement
 Analysis can be done by considering each sector like
service, manufacturing, etc.
 Cross validation of the model with sufficient data may
give further insights.
 State-wise analysis can be done.

12. Calculation of Skilled workforce
0
0.05
0.1
0.15
0.2
0.25
0.3
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020
Female/Male Ratio

13. Calculation of Skilled workforce
0
50000
100000
150000
200000
250000
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020
Total Skilled Workforce

14. THANK YOU !