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Logical Reasoning - Class distribution


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A case to logically distribute students in a class for an entire course

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Logical Reasoning - Class distribution

  1. 1. qwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmrtyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm<br />Supply Chain Management Class-Formation of Study Groups5/4/2009Group 6A - Abhishek M, Franxan, Ishitha, Prateet, Rushit, Shankari<br />Case Brief-<br />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.<br />Problem Statement-<br />Form study groups which has a healthy mix of students.<br />Assumptions-<br /><ul><li>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.
  2. 2. We have grouped countries based on “geographies” as it makes for a more meaningful classification of culture, background and language.</li></ul>Geographies:<br /><ul><li>Asia:
  3. 3. China
  4. 4. Indonesia
  5. 5. Japan
  6. 6. Taiwan
  7. 7. Britain:
  8. 8. Britain
  9. 9. Europe:
  10. 10. Denmark
  11. 11. France
  12. 12. Germany
  13. 13. Luxembourg
  14. 14. Norway
  15. 15. Portugal
  16. 16. Spain
  17. 17. North America:
  18. 18. Canada
  19. 19. Mexico
  20. 20. USA
  21. 21. We are assuming that supply chain program is based on a trimester model.
  22. 22. We have divided the supply chain batch into two sections with a total of four groups who will be shuffled across the trimesters.
  23. 23. Each group would have 20 students; thereby the section strength would be 40 each.
  24. 24. Class dynamics and shuffling pattern given below:</li></ul>SemesterSec ASec BTrimester IGrp1&2Grp3&4Trimester IIGrp1&4Grp3&2Trimester IIIGrp1&3Grp2&4<br />Population Spread:<br />Male Female Breakup: <br />Age Wise Breakup-<br />Specialisation Wise Breakup-<br />Geography Wise break up-<br />Methodology Used-<br />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.<br /><ul><li>Male/Female ratio will bring in two different perspectives.
  25. 25. Second priority is given to age factor as people belonging older age groups bring in experience and young people bring in fresh ideas.
  26. 26. Third priority is given to specialisation so that members of a group have different skill sets.
  27. 27. Last priority is given to geography. We will try to ensure that groups are truly global.</li></ul>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.<br />Priority Matrix-<br />FactorPriority (high to low)Gender ratio1Age2Specialisation3Geography4<br />Based 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)<br />Group I<br />GroupsContinentExperienceAgeFMGrand Total1AsiaEngineering26-281 1  Marketing23-2511  Production29-311 1 BritainEngineering32-34 11  Finance20-2211  Production23-251 1 EuropeEngineering20-221 1  23-2511  26-2811  Marketing26-2822  Production23-2511  26-2811  35-3711  Purchasing23-25 11 North AmericaEngineering20-22 11  26-2811  Marketing23-2511  29-3111  Purchasing23-251 1Grand Total   11920<br />Group II<br />GroupsContinentExperienceAgeFMGrand Total2AsiaEngineering20-221 1 29-311 1 Production23-25 11 BritainEngineering23-25 11 Marketing20-22 11 23-251 1 Production20-22 11 EuropeEngineering26-28112 29-31112 Finance26-281 1 38-41 11 Marketing20-221 1 23-25 11 Production23-251 1 35-37 11 North AmericaEngineering26-28 11 Marketing23-251 1 Production29-311 1Grand Total   101020<br />Group III<br />GroupsContinentExperienceAgeFMGrand Total3AsiaEngineering23-251 1 38-411 1 Purchasing23-25 11 BritainEngineering23-25 11 32-34 11 Finance26-281 1 Marketing26-281 1 EuropeEngineering26-28 22 Finance29-311 1 Marketing20-22 11 23-253 3 Production23-25 22 Purchasing23-25 11 26-28 11 North AmericaFinance26-28 11 Marketing38-41 11Grand Total   81220<br />Group IV<br />GroupsContinentExperienceAgeFMGrand Total4AsiaEngineering23-25 11 Marketing23-251 1 Production23-25 11 BritainEngineering26-281 1 Marketing23-25 11 32-341 1 35-371 1 EuropeEngineering23-25213 26-281 1 38-41 11 Marketing29-311 1 Production23-25 11 26-28123 Purchasing26-28 11 North AmericaEngineering26-28 11 Production23-25 11Grand Total   91120<br />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.<br />Attached file would give a detailed understanding of the methodology and the combination arrived to base on the logical analysis. <br />Alternative Solution:<br />Using Linear Programming:<br />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 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. <br />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)<br />Additional Observation:<br />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.<br />Count of NumberGroups    Married1234Grand TotalMarried14911943Single61191137Grand Total2020202080<br />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).<br /> MarriedSingleGrand TotalChildren12341234 051 31237221 1 31112924351234 22344421512234    1   151 2     3Grand Total14911961191180<br />Therefore, to analyze this more, the single students with children were drilled down to their age groups. <br /> SingleGrand TotalAgeChildren1234 20-2211   1 2 11 2 3 1  123-251  123 2122 5 3 1  126-281 1  1 31112529-3121   1 3 2  2 41   138-412  1 1Grand Total 596424<br />Green highlight: Those students whose status is “Single”: This could be single parents, divorced cases or those who have lost their partners.<br />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.<br />Red highlight: Those were the analysts feel, there has to be some problem with the data or a sure “OUTLIER”.<br />Conclusion:<br />With these above student distribution, we are hoping that the entire batch of 80 students would be divided into fair groups.<br />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.<br />----------------------------------------------------**********************-----------------------------------------------------------<br />