Vol.03, Issue 09, Conference (IC-RASEM) Special Issue 01, September 2018 Available Online: www.ajeee.co.in/index.php/AJEEE
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APPLICATION OF OPERATIONS RESERCH IN HIGHER EDUCATION Abhishek Soni1, Dr.Sameer Vaidya2, Abhishek Soni3
Abstract - In this paper statistical techniques including regression analysis were used as a methodology. Data collected was primary through a well defined questionnaire. A sample of private college students was taken where these variables were recognized and response was clear and understandable. Public sector educational institutions were not the focus of the study. A sample of 30 students was taken from a group of colleges. Students were grouped in a classroom they were briefed clearly about the questionnaire and it took on average half an hour to fill this questionnaire. Selection of students was at random. Out of these students only those were selected at random who were voluntarily willing to fill the questionnaires. The data was collected using a questionnaire administrated by the Research team in the3rd month of 3rd year. The questionnaire dealt mainly with student profile based on his attitude towards Study, Strictness, Attendance, Age, Previous academic achievements, Daily life, etc. All 6 questionnaires were filled with the response rate of 100%.The sample age composition was from 18 years to 22 years of age .
Basic Ideology- Student (I/P) Institution Finished (O/P) Key words: LPP ,Regression analysis, chi square
1. INTRODUCTION
O.R. represents an integrated framework to help make decisions, it is important to have a clear understanding of this framework so that it can be applied to a generic problem. To achieve this, the so- called O.R. approach is now detailed. This approach comprises the following seven sequential steps: (1) Orientation, (2) Problem Definition, (3) Data Collection, (4) Model Formulation, (5) Solution, (6) Model Validation and Output Analysis, and (7) Implementation and Monitoring
Fig 1 .Approach Of Technique While most of the academic emphasis has been on Steps 4, 5 and 6, the reader should bear in mind the fact that the other steps are equally important from a practical perspective. Indeed, insufficient attention to these steps has been the reason why O.R. has sometimes been
mistakenly looked upon as impractical or ineffective in the real world.
Each of these steps is now discussed in further detail. To illustrate how the steps might be applied, consider a typical scenario where a manufacturing company is planning production for the upcoming month. The company makes use of numerous resources (such as labor, production machinery, raw materials, capital, data processing, storage space, and material handling equipment) to make a number of different products which compete for these resources. The products have differing profit margins and require different amounts of each resource. Many of the resources are limited in their availability.
Additionally, there are other complicating factors such as uncertainty in the demand for the products, random machine breakdowns, and union agreements that restrict how the labor force can be used. Given this complex operating environment, the overall objective is to plan next month's production so that the company can realize the maximum profit possible while simultaneously ending up in a good position for the following month(s).
As an illustration of how one might conduct an operations research study to address this situation, consider a highly simplified instance of a production planning problem where there are two main product lines (widgets and gizmos, say) and three major limiting resources (A, B and C, say) for which each of the
Vol.03, Issue 09, Conference (IC-RASEM) Special Issue 01, September 2018 Available Online: www.ajeee.co.in/index.php/AJEEE
2 products compete. Each product requires varying amounts of each of the resources and the company incurs different costs (labor, raw materials etc.) in making the products and realizes different revenues when they are sold. The objective of the O.R. project is to allocate the resources to the two products in an optimal fashion.
2. LITERATURE REVIEW
Different approaches have been investigated for estimating O-D trip tables in the last several decades. Conventional analysis is very expensive in practice. It is hard to reproduce the observed flows using these techniques, and the trip tables often become outdated. As a consequence, quick response models become of great relevance in transportation planning. Among quick response models, the one based on traffic counts is very popular and pervasive. The problem is beset with a great deal of complexities, and various approaches have been employed to overcome them.
Gravity-based models require considerable data, and are relatively more likely to have their results become outdated. This makes these models unattractive. LINKOD type models incorporate the desired equilibrium assignment concept, but their nonlinear nature leads to the issue of excessive computational effort for deriving acceptable solutions to practical problems. The entropy-based models pose restrictions on data, give little weight to prior information, and need refinements for incorporating the equilibrium principle. Statistical models take into account the stochastic nature of the data and the problem. However, they have not been adequately tested. In addition, the stochoastic theory used itself sometimes makes the problem more complicated for practical purposes. Both neural network and fuzzy set approaches still need to be verified regarding their practical viability.
Moreover, indepth theoretical studies are themselves needed before these approaches can be justified for use in practice. Linear programming models and algorithms have been widely used in various applications, including transportation and assignment problems.
Using this approach to estimate the O-D trip matrix from link volumes, however, is relatively new. The approaches have some advantages such as a simpler
formulation, and for the case of all link volumes being available, an established theory guaranteeing finite convergence.
On the other hand, the approach approximates the random nature of the data and the problem, and the resulting O-D table often has many zeros because of the “extreme point” optimality principle.
(This is somewhat alleviated when using prior trip table information.) Moreover, in the case of missing volumes, the approach iteratively updates the travel cost on missing data links and then minimizes the total cost, which leads to a problem of excessive computational effort.
Therefore, there is a need to improve the LP model so that it can take care of inaccuracies in input data in practice, interpret both user behavior and user- optimal principles in a reasonable manner, and reduce the computational effort in generating practical acceptable solutions.
3.METHODOLOGY 3.1 The Model
Simple linear regression analysis was used to test the hypothesis- Coefficients are b1, b2, b3, b4, b5, b6
3.2 The Data
A student profile was developed on the basis of information and data collected through survey to explain student‟s attitude towards explanatory variables.
The first variable “attendance in class”
explains student‟s attitude towards class attendance which reflects his level of interest in learning. Student‟s attitude towards time management for studies is reflected through number of hours spent in study after college, is taken as second variable. Third variable of the study is family income that reflects the comforts and facilities available for study. The fourth variable is “Question banks/reference book”, that is, how many books a student refers for his studies. The fifth variable is “type of study” which shows whether the student studies in a group or studies individually. The last variable shows the residential status of student, describing whether the student is a Day scholar or a Hosteller.
Student‟s performance in intermediate examination is taken as dependent variable and rest of the variables, which construct student profile, are taken as independent variables.
Vol.03, Issue 09, Conference (IC-RASEM) Special Issue 01, September 2018 Available Online: www.ajeee.co.in/index.php/AJEEE
3 This table explains expected relation of dependent variables these expected relations are also myths pervading in Indian society so the results of this study are to accept or reject these myths. The table explains students performance due to student‟s attitude towards studies based on student‟s profile developed on the basis of information and data collected. It is assumed that student is still carrying his profile as it is.
Variable Expected
Relationship Explanation Attendanc
e in Class Positive A regular student is more serious in studies
Family
Income Positive It is assumed affluence gives more facilities to learn Study
hours per day after College
Positive It is assumed that more study hours results in good grade/division/
performance Books
Referred Positive More books referred results in better grasp of the concept Type of
Study
Positive Group study results in healthier studying
environment, hence better result Hosteller/
Day Scholar
Positive Hostellers are found to be more dedicated in their studies.
3.3 Exogenous (Independent) Variable ATT= Attendance % age, it represents how many classes student attends in a week and that shows seriousness and attitude towards studies.
SH= Study hours, it represents how many hours a student spends on study after attending the class in college again it shows how much serious the student takes the studies.
CGPA= CGPA represent the score of the student in main exam.
3.4 Analysis Of Data
Students CGPA Attendance (in %)
Study hours
Result
Student 1 8.83 78 6 Pass
Student 2 7.98 69 4 Pass
Student 3 7.92 71 4 Pass
Student 4 7.68 69 4 Pass
Student 5 7.68 66 3 Pass
Student 6 7.66 61 3 Pass
Student 7 7.40 59 2 Pass
Student 8 7.38 65 3 Pass
Student 9 7.29 63 2 Pass
Student
10 7.15 58 3 Pass
Relation Of Attendance To Cgpa Of Students
Number Of Study Hours
Comparison Of Expected Results And Results Of The Study
VARIABLE EXPECTED RELATIONSH IP
EXPLANATION Result
Attendance
in Class Positive A regular student is more serious in studies
Positive
CGPA Positive Student with
good CGPA
perform more good in next exam.
Positive
Study hours per day after College
Positive It is assumed that more study hours results in good
grade/division/
performance
Positive
CHI Square Solution For Validation Of Result
Student A B C D E Total Attenda
nce 73.5 70 63.5 62 60.5 329.
5 Study
hr. 5 4 3 2.5 2.5 17
CGPA 8.38 7.8 7.67 7.39 7.22 38.4 6 Total 86.8
8 81.
8 74.1
7 71.8
9 70.2
2 384.
96
3.5 Calculation For Chi Square (𝐗𝟐) X2 = (o − e)2/e d.o.f.=(m-1)/n-1) Expected frequency calculated as Er, Ec= (nr∗ nc)/N
60 65 70 75 80
8.83 7.98 7.92 7.68
1st std 2nd std 3rd std 4th std 5th std
Vol.03, Issue 09, Conference (IC-RASEM) Special Issue 01, September 2018 Available Online: www.ajeee.co.in/index.php/AJEEE
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o e (o-e) (𝐨 − 𝐞)𝟐 (𝐨 − 𝐞)𝟐/𝐞 73.5 74.36 -0.86 0.7396 9.946*10−3 70 70.01 -0.01 0.0001 1.428*10−6 63.5 63.48 0.02 0.0004 6.299*10−6 62 61.53 0.47 0.2209 3.59*10−3 60.5 60.1 0.4 0.16 2.66*10−3
5 3.83 1.17 1.3689 0.357
4 3.61 0.39 0.1521 0.0464
3 3.28 -0.28 0.0784 0.0240
2.5 3.17 -0.67 0.4489 0.1416
2.5 3.1 -0.6 0.36 0.1161
8.38 8.68 -0.3 0.09 0.0108
7.8 8.17 -0.37 0.1369 0.0168 7.67 7.41 0.26 0.0676 9.123*10−3 7.39 7.18 0.21 0.0441 6.14*10−3 7.22 7.01 0.21 0.0414 6.29*10−3
(X2) = o − e 2
e = 0750 < TABULATED VALUE Therefore Hypotheses is accepted
3.6 Analysis to increase the performance of students
Max. performance (Zmax) = x1+ x2+ x3
x1= Attendance, x2= Study hours, x3= CGPA x1≤ 10
x2≤ 10
x3≤ 10
Cj 1 1 1 0 0 0
CB B.V. x1 x2 x3 s1 s2 s3 b θ 0 s1 (1) 0 0 1 0 0 10 10←
0 s2 0 1 0 0 1 0 10 ∞
0 s3 0 0 1 0 0 1 10 ∞
Zj 0 0 0 0 0 0 0 Cj
− Zj 1
↑ 1 1 0 0 0
Cj 1 1 1 0 0 0
CB B.V. x1 x2 x3 s1 s2 s3 b θ
1 x1 1 0 0 1 0 0 10 ∞
0 s2 0 (1) 0 0 1 0 10 10
←
0 s3 0 0 1 0 0 1 10 ∞
Zj 1 0 0 0 0 0 10 Cj
− Zj
0 1
↑ 1 0 0 0
Cj 1 1 1 0 0 0
CB B.V. x1 x2 x3 s1 s2 s3 b θ
1 x1 1 0 0 1 0 0 10 ∞
1 x2 0 1 0 0 1 0 10 ∞
0 s3 0 0 (1) 0 0 1 10 10
← Zj 1 1 0 0 0 0 20 Cj
− Zj
0 0 1
↑ 0 0 0
Cj 1 1 1 0 0 0
CB B.V. x1 x2 x3 s1 s2 s3 b
1 x1 1 0 0 1 0 0 10
1 x2 0 1 0 0 1 0 10
1 x3 0 0 (1) 0 0 1 10
Zj 1 1 1 0 0 0 30
Cj
− Zj
0 0 0 0 0 0
Value obtained=x1= x2= x3= 10 4.DISCUSSION-
The objective of this study was to quantify the relationship between the different factors that are considered responsible of affecting the student performance along with providing base for further research regarding student performance.Selecting these combination of variables do have some objectively like, It was expected that relationship between dependent variable and student attitude towards attendance is positive because regularity shows the effort and seriousness of student about his or her studies.It is believed that the relationship between dependent variable and student family income is positive because money can buy you all comfort that you need to concentrate on your studies but the result could not prove this relation because student belonging to more prosperous/affluent family do not give proper weight to studies although this value is very small but still it reflects the insignificance of affluence that is affluence cannot make a student serious about his studies or if a student want to study then affluence is not a prerequisite but still it requires more research to explain the phenomenonIt is still believed strongly that relationship between dependent variable and student attitude towards time allocation for per day after college are positively related but the result could not prove this relation because more study hours are not significant as far as student performance is concerned.
It may depend on intelligence level, intellect, memory or method or learning of the student although this value is very small yet it reflects of personal characteristics of student.
Further research is required to explore this relation.It is believed that book reference also has great effect on performance of students that if students are referring to books it helps in increase of concepts and deep knowledge about the topic, and if one is studying form question banks then he cannot grasp more knowledge; yes but he can touch every topic with little knowledge.Selecting a type of study .i.e. between Group and Individual affects the student performance. It is believed that Group studies have more impact over individual studies. If a student is studying in group he is scoring better marks that him who
Vol.03, Issue 09, Conference (IC-RASEM) Special Issue 01, September 2018 Available Online: www.ajeee.co.in/index.php/AJEEE
5 is studying individually.One more important attribute is Day scholar or Hosteller. It is found that student that are Hosteller perform better than Day scholar.
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