How to model an assignment/ allocation problem?

Question

Rouyu Chen 2023-4-13

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1946433-how-to-model-an-assignment-allocation-problem

回答： Divyanshu 2023-4-20

Dear experts,

If I have NS students from NA departments, and there is a ranking in each department. Now I want to allocate them into K different groups (where each group only has limited place) according to their in-department ranking.

For example, I can allocate students according to their relative position (relative position = student's rank in department/ number of students in the department). Students with lower relative postion will be assigned first.

While I have no idea how to use matlab to model this kind of problem, I was wondering if anyone could please give me some advice?

Many thanks!

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Torsten 2023-4-13

编辑：Torsten 2023-4-13

First formulate your problem mathematically, then start watching out MATLAB on how to solve it.

Sam Chak 2023-4-13

@Rouyu Chen, Can you draw a table and show the ranking formula/algorithm?

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Answer 1

Divyanshu 2023-4-20

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1946433-how-to-model-an-assignment-allocation-problem#answer_1219313

在 MATLAB Online 中打开

Here is a demo MATLAB script which allocates students to K groups. Few assumptions taken are:

The number of places in each group is 3 and K = 3.
Each department has same number of students.
Total departments are 3 and each has 3 students.

depts = [1 2 3];
students = ["st1" "st2" "st3" "st4" "st5" "st6" "st7" "st8" "st9"];
dept_wise_rank = ["st2" "st3" "st1";"st4" "st6" "st5";"st7" "st8" "st9"];
% 2-D matrix ‘dept_wise_rank’ stores the students according to their relative rankings.
% Each row represents a department. 
grp_matrix = [];
% The outer loop iterates over each department.
% The inner loop iterates over each student within a department.
for i=1:3
    grp = [];
    for j=1:3
        grp = [grp dept_wise_rank(i,j)];
    end
    grp_matrix = [grp_matrix;grp];
end
% The grp_matrix is another 2-D matrix where each row represents a group.
grp_matrix

For more details about the concatenation operations on matrices and accessing of elements from a 2-D array, please go through the following documentations: