Aston Business School has one of the most culturally diverse students in the UK$.$ Students often

differ from each other in their ethnic background. While this could help to enrich students$$

learning experiences, in particular during their group work, students often fail harnessing cultural

diversity for their learning in such groups. The research in this area has shown that a proper

support and a proper environment needs to be established in order for students to reap all the

potential benefits of cultural diversity.

While at Aston, students are often allocated into syndicate groups to work together on various

projects, which are subsequently assessed as a group work. Ideally, an allocation of students into

groups should support and encourage harnessing cultural diversity. To achieve this, the groups

formed should maximise the diversity of members within groups and minimise the average

differences between groups. Groups formed on this basis are called $$balanced groups$.$ Creating

balanced groups for a large class can be a very tedious and time$-$consuming administrative task if

that process is carried out manually using a trial and error approach. For this reason, it would be

good to construct a system that would produce balanced groups at a $$touch of a button$.$

Your task for this case study will be to prepare the model that will be able to perform automatic

allocation of students into groups while satisfying as much as possible these ideal targets:

$1.$ Groups should be of the same size if possible. The ideal size is $5$ members per group.

$2.$ Groups should be balanced with respect to gender $($G$).$

$3.$ Groups should be balanced with respect to quantitative background $($Q$).$

$4.$ Groups should be balanced with respect to ethnic background but in a very specific way.

According to the most up$-$to$-$date research on harnessing cultural diversity:

$$ Ideally, each international $($non$-$British$)$ student should be paired in the same group with

another international student of the same nationality $($N$).$

$$ If the above is not possible to achieve, then the next best thing is to pair international

students based on the same cultural background $($C$).$

$$ Pairing based on the nationality or cultural background is not important to achieve only for

home $($British$)$ students.

The data provided to you contains the records for $45$ students with the relevant characteristics for

each one of them given through the five columns: Student ID $($S$),$ Nationality $($N$),$ Cultural

Background $($C$),$ Gender $($G$)$ and Quantitative Background $($Q$).$

To solve the problem, feel free to use any of the techniques $($or any mix of the techniques$)$ we

learned in Decision Models. Also, feel free to transform any of the raw data provided to you

before you use them in your model, if you think that any such transformation will have more

positive than negative effects to the overall quality of your solution.

Your model should be flexible enough to be feasible and to produce a reasonable solution for any

other set of $45$ students $($that may have very different characteristics from the ones given$),$ but it

does not have to be flexible to work well for any other number of students. To make it flexible to

work well for any number of students, you would either need to have advanced knowledge of

Excel or could use different tools to formulate an LP model, such as MATLAB or Python or R$.$

Student ID $($S$)$ Nationality $($N$)$ Cultural Background $($C$)$Gender $($G$)$Gender $($G$)$

$101$ Saudi Arabian Middle East Female $6\mathrm{.}7$

$102$ Saudi Arabian Middle East Male $4\mathrm{.}0$

$103$ Romanian Eastern Europe Female $5\mathrm{.}9$

$104$ British British Female $8\mathrm{.}6$

$105$ British British Male $5\mathrm{.}0$

$106$ Chinese East Asia Male $7\mathrm{.}0$

$107$ British British Male $8\mathrm{.}4$

$108$ Chinese East Asia Female $8\mathrm{.}7$

$109$ British British Male $7\mathrm{.}8$

$110$ British British Male $7\mathrm{.}2$

$111$ Chinese East Asia Female $7\mathrm{.}0$

$112$ Chinese East Asia Male $7\mathrm{.}7$

$113$ Spanish Western Europe Female $7\mathrm{.}0$

$114$ Chinese East Asia Male $8\mathrm{.}0$

$115$ Saudi Arabian Middle East Male $8\mathrm{.}3$

$116$ German Western Europe Male $8\mathrm{.}7$

$117$ British British Female $8\mathrm{.}5$

$118$ Lithuanian Eastern Europe Male $9\mathrm{.}1$

$119$ Russian Eastern Europe Male $7\mathrm{.}6$

$120$ Chinese East Asia Female $7\mathrm{.}2$

$121$ Chinese East Asia Male $5\mathrm{.}2$

$122$ Mongolian East Asia Male $4\mathrm{.}2$

$123$ Chinese East Asia Female $5\mathrm{.}5$

$124$ British British Female $8\mathrm{.}6$

$125$ Indian South Asia Male $8\mathrm{.}3$

$126$ Vietnamise East Asia Male $7\mathrm{.}4$

$127$ Iranian Middle East Female $7\mathrm{.}3$

$128$ Turkish Middle East Female $4\mathrm{.}1$

$129$ Indian South Asia Female $4\mathrm{.}6$

$130$ Vietnamise East Asia Female $7\mathrm{.}9$

$131$ Vietnamise East Asia Male $8\mathrm{.}0$

$132$ Chinese East Asia Female $8\mathrm{.}7$

$133$ Chinese East Asia Male $4\mathrm{.}9$

$134$ Indian South Asia Female $5\mathrm{.}2$

$135$ Chinese East Asia Female $5\mathrm{.}6$

$136$ British British Male $9\mathrm{.}2$

$137$ Bulgarian Eastern Europe Female $8\mathrm{.}8$

$138$ Japanese East Asia Male $4\mathrm{.}9$

$139$ Russian Eastern Europe Male $7\mathrm{.}7$

$140$ British British Female $4\mathrm{.}7$

$141$ Chinese East Asia Female $7\mathrm{.}5$

$142$ Chinese East Asia Female $7\mathrm{.}6$

$143$ Chinese East Asia Female $7\mathrm{.}9$

$144$ Chinese East Asia Female $5\mathrm{.}7$

$145$ Russian Eastern Europe Female $6\mathrm{.}0$