Choosing The Best School
Contents
Case Problem 2
Case Facts 2
Input Parameters 2
Output Parameters 2
Input Parameters Table 2
Output Parameters Table 3
Additional Case Facts 3
Constraints & Objective Function 3
LP Formulation – For School A 4
Solutions – Excel Solver 5
For School A 5
For School B 5
For School C 6
Solution 6
Conclusion 6
Case Problem
Mr Shyam Prasad, recently transferred to Chennai from Lucknow, has to choose a school for his two children. He has three choices of the school and it is likely that his children would be allotted one of them. Shyam Prasad has chosen his best 3 schools (A, B, C) and wishes to rank them. He would be happy if the children get either the first or the second choice.
Case Facts
Input parameters are the independent variables that determine the performance (output) parameter of each school.
Input Parameters
1. Number of students enrolled in the 12th Standard.
2. Number of teachers in the high school section.
3. Facilities Available.
Output Parameters
1. Number of students who enter professional courses/year (average).
2. Number of sportspersons who have played state level.
3. Number of alumni who have become visible entrepreneurs/eminent leaders.
Input Parameters Table
Strength
Teachers
Facilities
School A
800
60
32
School B
1000
90
34
School C
600
40
28
Output Parameters Table
Professional Courses
Sports
Visible Entrepreneurs
School A
175
36
43
School B
186
37
60
School C
163
40
36
Additional Case Facts
Mr Prasad believes in a linear relationship among the input and output parameters and wishes to rank them based on their efficiencies.
Efficiency for each school is defined as Ratio of Weighted Output to Weighted Input.
The weights to the input & output are the decision variables.
Each school should assign weights such as to maximize its efficiency, subject to the condition that for the defined weights no school has efficiency exceeding 1.
The efficiency is a fraction and by defining the input to 1, we can convert the problem
Case Problem 2
Case Facts 2
Input Parameters 2
Output Parameters 2
Input Parameters Table 2
Output Parameters Table 3
Additional Case Facts 3
Constraints & Objective Function 3
LP Formulation – For School A 4
Solutions – Excel Solver 5
For School A 5
For School B 5
For School C 6
Solution 6
Conclusion 6
Case Problem
Mr Shyam Prasad, recently transferred to Chennai from Lucknow, has to choose a school for his two children. He has three choices of the school and it is likely that his children would be allotted one of them. Shyam Prasad has chosen his best 3 schools (A, B, C) and wishes to rank them. He would be happy if the children get either the first or the second choice.
Case Facts
Input parameters are the independent variables that determine the performance (output) parameter of each school.
Input Parameters
1. Number of students enrolled in the 12th Standard.
2. Number of teachers in the high school section.
3. Facilities Available.
Output Parameters
1. Number of students who enter professional courses/year (average).
2. Number of sportspersons who have played state level.
3. Number of alumni who have become visible entrepreneurs/eminent leaders.
Input Parameters Table
Strength
Teachers
Facilities
School A
800
60
32
School B
1000
90
34
School C
600
40
28
Output Parameters Table
Professional Courses
Sports
Visible Entrepreneurs
School A
175
36
43
School B
186
37
60
School C
163
40
36
Additional Case Facts
Mr Prasad believes in a linear relationship among the input and output parameters and wishes to rank them based on their efficiencies.
Efficiency for each school is defined as Ratio of Weighted Output to Weighted Input.
The weights to the input & output are the decision variables.
Each school should assign weights such as to maximize its efficiency, subject to the condition that for the defined weights no school has efficiency exceeding 1.
The efficiency is a fraction and by defining the input to 1, we can convert the problem