logical reasoning - class distribution

qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqw

Supply Chain Management Class

-Formation of Study Groups

5/4/2009

Group 6A - Abhishek M, Franxan, Ishitha, Prateet, Rushit, Shankari

1

Case Brief-

There are 80 participants from varied age group, specialisation and countries for a supply chain class. Details such as sex, age, country, experience, marital status and number of children for each participant provided in the form of a table.

Problem Statement-

Form study groups which has a healthy mix of students.

Assumptions-

On the basis of the given problem, we find that factors such as marital status and number of children are not relevant in selecting participants for particular section of this study group.

We have grouped countries based on “geographies” as it makes for a more meaningful classification of culture, background and language.

Geographies:

Asia: China Indonesia Japan Taiwan

Britain: Britain

Europe: Denmark France Germany Luxembourg Norway Portugal Spain

North America: Canada Mexico USA We are assuming that supply chain program is based on a trimester model.

We have divided the supply chain batch into two sections with a total of four groups who will be shuffled across the trimesters.

Each group would have 20 students; thereby the section strength would be 40 each.

Class dynamics and shuffling pattern given below:

Semester Sec A Sec BTrimester I Grp1&2 Grp3&4Trimester II Grp1&4 Grp3&2Trimester III Grp1&3 Grp2&4

Population Spread:

2

Male Female Breakup:

Age Wise Breakup-

Specialisation Wise Breakup-

Geography Wise break up-

Methodology Used-

3

As the given data is a combination of Nominal, Ordinal, Interval and Ratio, there is no descriptive stastics of Mean, Median, Mode, Std. Deviation, etc. That can be used here. This is diverse data provided for which a logical interpretation has to be followed to arrive to the most diverse mix of students in each section.

Male/Female ratio will bring in two different perspectives. Second priority is given to age factor as people belonging older age groups bring in experience and

young people bring in fresh ideas. Third priority is given to specialisation so that members of a group have different skill sets. Last priority is given to geography. We will try to ensure that groups are truly global.

With shuffling of sections it’s ensured that a diverse group are in the same section. Trimester ensures every mix gets equal opportunity to interact with others.

Priority Matrix-

Factor Priority (high to low)Gender ratio 1

Age 2Specialisation 3

Geography 4Based on the above understandings we have got the below break up of students into 4 groups which will be a part of 2 sections (Namely Sec A & Sec B)

Group I

Groups Continent Experience Age F MGrand Total

1 Asia Engineering 26-28 1 1

Marketing 23-25 1 1

Production 29-31 1 1

Britain Engineering 32-34 1 1

Finance 20-22 1 1


Europe Engineering 20-22 1 1

23-25 1 1

26-28 1 1

Marketing 26-28 2 2


26-28 1 1

35-37 1 1

Purchasing 23-25 1 1

North America Engineering 20-22 1 1

26-28 1 1

Marketing 23-25 1 1

29-31 1 1


Grand Total 11 9 20

Group II

Groups Continent Experience Age F M Grand Total

4


29-31 1 1



Marketing 20-22 1 1

23-25 1 1


Europe Engineering 26-28 1 1 2

29-31 1 1 2

Finance 26-28 1 1

38-41 1 1

Marketing 20-22 1 1

23-25 1 1


35-37 1 1


Marketing 23-25 1 1


Grand Total 10 10 20

Group III



38-41 1 1



32-34 1 1

Finance 26-28 1 1

Marketing 26-28 1 1

Europe Engineering 26-28 2 2

Finance 29-31 1 1

Marketing 20-22 1 1

23-25 3 3



26-28 1 1

North America Finance 26-28 1 1

Marketing 38-41 1 1

Grand Total 8 12 20

Group IV



5

Marketing 23-25 1 1



Marketing 23-25 1 1

32-34 1 1

35-37 1 1

Europe Engineering 23-25 2 1 3

26-28 1 1

38-41 1 1

Marketing 29-31 1 1


26-28 1 2 3




Grand Total 9 11 20

By checking for the exact characteristic the professor is looking for, it is possible to drill down on the student names (serial nos. in this case) to be placed in each group thereby each section.

Attached file would give a detailed understanding of the methodology and the combination arrived to base on

the logical analysis.

Alternative Solution:

Using Linear Programming:

The given data can be grouped using a Linear Programming Model also. The objective function is the number of students under each category (discipline, age groups, continent of origin, gender) such that the total

6

number of students can be classified into two sections. The sum of students of the total batch equals to 80 with a maximum of 40 students in each section. The constraints to solve the model are that total number of students of each category distributed between both sections. Additionally it is mandatory to ensure that not all students of the same category fall into the same class. To ensure this, we would need to benchmark a cutoff of students in each category and ensure that the count is atleast equal to or more than the cutoff. This will finally answer the total number of students in each category who have also been classified into the two groups.

Attached file would also provide an insight on the methodology of Linear Programming used to try and solve

the entire problem mathematically (Refer to “Linear” worksheet)

Additional Observation:

Though we have not considered the Marital status as a criteria for group distribution, we observe that our recommendation takes care of this criteria also. The break up looks more or less balanced.

Count of Number Groups

Married 1 2 3 4Grand Total

Married 14 9 11 9 43

Single 6 11 9 11 37

Grand Total 20 20 20 20 80

It was also observed that there were married students with no children which are acceptable (green shaded). But the shocking figure was of those students who were single and had children (Red shaded).

Married SingleGrand Total

Children 1 2 3 4 1 2 3 4

0 5 1 3 1 2 3 7 22

1 1 3 1 1 1 2 9

2 4 3 5 1 2 3 4 223 4 4 4 2 1 5 1 2 234 1 15 1 2 3

Grand Total 14 9 11 9 6 11 9 11 80

Therefore, to analyze this more, the single students with children were drilled down to their age groups.

SingleGrand Total

Age Children 1 2 3 4

20-22 1 1 1

2 1 1 2

3 1 1

23-25 1 1 2 3

7

2 1 2 2 5

3 1 1

26-28 1 1 1

3 1 1 1 2 5

29-31 2 1 1

3 2 2

4 1 1

38-41 2 1 1

Grand Total 5 9 6 4 24

Green highlight: Those students whose status is “Single”: This could be single parents, divorced cases or those who have lost their partners.

Orange highlight: These who could be in the above category or those on whom we as a group have doubts on. This could be based on wrong data entry or these could be exception cases.

Red highlight: Those were the analysts feel, there has to be some problem with the data or a sure “OUTLIER”.

Conclusion:

With these above student distribution, we are hoping that the entire batch of 80 students would be divided into fair groups.

The purpose of dividing into two groups in each section would also ensure that every student would interact with the reaming batch of students and this would ensure maximum diversity.

----------------------------------------------------**********************-----------------------------------------------------------

8

logical reasoning - class distribution

Education