Project allocation optimisation Code












0












$begingroup$


I've been formulating an integer optimisation model for allocating students to projects where students give their preferences and rank them 1,2,or 3 with one being their best project preference.



Variables



$X_{i,j}$ = 1, if student i is allocated to project j and 0, otherwise



$C_{i,j}$ can take any value in set C where,C ∈ [1,2,3]



Constraints



$sum_{j=1}^{Tp} X_{i,j} = 1$



Each student is allocated to one project where Tp = total projects



$sum_{i=1}^{Ts} X_{i,j} = 1$



Each project is allocated to one student where Ts = total students



$sum_{j=1}^{Tp} C_{i,j} times X_{i,j} geq 1$



Each student is allocated a project that is one of their preferences



Objective Function



Minimize $sum_{i=1}^{Ts}sum_{j=1}^{Tp} C_{i,j} times X_{i,j}$



To minimize the sum of the rankings.



How can I code this integer optimisation problem in MATLAB or another way?



Thank you!!






optimization algorithms linear-programming integer-programming mixed-integer-programming







share|cite|improve this question











$endgroup$












  • $begingroup$
    Welcome to Math.SE! Our strengths will tend more to helping with algorithms, e.g. for your integer programming problem, rather than with advice about writing code. You might look up the Hungarian algorithm for assignment problems.
    $endgroup$
    – hardmath
    Jan 12 at 16:21










  • $begingroup$
    This is a good option : pypi.org/project/PuLP . Easy and effective
    $endgroup$
    – Kuifje
    Jan 12 at 16:37










  • $begingroup$
    thanks hardmath, Kuifje
    $endgroup$
    – Mwana Hussein
    Jan 12 at 17:31
















0












$begingroup$


I've been formulating an integer optimisation model for allocating students to projects where students give their preferences and rank them 1,2,or 3 with one being their best project preference.



Variables



$X_{i,j}$ = 1, if student i is allocated to project j and 0, otherwise



$C_{i,j}$ can take any value in set C where,C ∈ [1,2,3]



Constraints



$sum_{j=1}^{Tp} X_{i,j} = 1$



Each student is allocated to one project where Tp = total projects



$sum_{i=1}^{Ts} X_{i,j} = 1$



Each project is allocated to one student where Ts = total students



$sum_{j=1}^{Tp} C_{i,j} times X_{i,j} geq 1$



Each student is allocated a project that is one of their preferences



Objective Function



Minimize $sum_{i=1}^{Ts}sum_{j=1}^{Tp} C_{i,j} times X_{i,j}$



To minimize the sum of the rankings.



How can I code this integer optimisation problem in MATLAB or another way?



Thank you!!






optimization algorithms linear-programming integer-programming mixed-integer-programming







share|cite|improve this question











$endgroup$












  • $begingroup$
    Welcome to Math.SE! Our strengths will tend more to helping with algorithms, e.g. for your integer programming problem, rather than with advice about writing code. You might look up the Hungarian algorithm for assignment problems.
    $endgroup$
    – hardmath
    Jan 12 at 16:21










  • $begingroup$
    This is a good option : pypi.org/project/PuLP . Easy and effective
    $endgroup$
    – Kuifje
    Jan 12 at 16:37










  • $begingroup$
    thanks hardmath, Kuifje
    $endgroup$
    – Mwana Hussein
    Jan 12 at 17:31














0












0








0





$begingroup$


I've been formulating an integer optimisation model for allocating students to projects where students give their preferences and rank them 1,2,or 3 with one being their best project preference.



Variables



$X_{i,j}$ = 1, if student i is allocated to project j and 0, otherwise



$C_{i,j}$ can take any value in set C where,C ∈ [1,2,3]



Constraints



$sum_{j=1}^{Tp} X_{i,j} = 1$



Each student is allocated to one project where Tp = total projects



$sum_{i=1}^{Ts} X_{i,j} = 1$



Each project is allocated to one student where Ts = total students



$sum_{j=1}^{Tp} C_{i,j} times X_{i,j} geq 1$



Each student is allocated a project that is one of their preferences



Objective Function



Minimize $sum_{i=1}^{Ts}sum_{j=1}^{Tp} C_{i,j} times X_{i,j}$



To minimize the sum of the rankings.



How can I code this integer optimisation problem in MATLAB or another way?



Thank you!!






optimization algorithms linear-programming integer-programming mixed-integer-programming







share|cite|improve this question











$endgroup$




I've been formulating an integer optimisation model for allocating students to projects where students give their preferences and rank them 1,2,or 3 with one being their best project preference.



Variables



$X_{i,j}$ = 1, if student i is allocated to project j and 0, otherwise



$C_{i,j}$ can take any value in set C where,C ∈ [1,2,3]



Constraints



$sum_{j=1}^{Tp} X_{i,j} = 1$



Each student is allocated to one project where Tp = total projects



$sum_{i=1}^{Ts} X_{i,j} = 1$



Each project is allocated to one student where Ts = total students



$sum_{j=1}^{Tp} C_{i,j} times X_{i,j} geq 1$



Each student is allocated a project that is one of their preferences



Objective Function



Minimize $sum_{i=1}^{Ts}sum_{j=1}^{Tp} C_{i,j} times X_{i,j}$



To minimize the sum of the rankings.



How can I code this integer optimisation problem in MATLAB or another way?



Thank you!!






optimization algorithms linear-programming integer-programming mixed-integer-programming




optimization algorithms linear-programming integer-programming mixed-integer-programming






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 12 at 16:55







Mwana Hussein

















asked Jan 12 at 16:10









Mwana HusseinMwana Hussein

12




12












  • $begingroup$
    Welcome to Math.SE! Our strengths will tend more to helping with algorithms, e.g. for your integer programming problem, rather than with advice about writing code. You might look up the Hungarian algorithm for assignment problems.
    $endgroup$
    – hardmath
    Jan 12 at 16:21










  • $begingroup$
    This is a good option : pypi.org/project/PuLP . Easy and effective
    $endgroup$
    – Kuifje
    Jan 12 at 16:37










  • $begingroup$
    thanks hardmath, Kuifje
    $endgroup$
    – Mwana Hussein
    Jan 12 at 17:31


















  • $begingroup$
    Welcome to Math.SE! Our strengths will tend more to helping with algorithms, e.g. for your integer programming problem, rather than with advice about writing code. You might look up the Hungarian algorithm for assignment problems.
    $endgroup$
    – hardmath
    Jan 12 at 16:21










  • $begingroup$
    This is a good option : pypi.org/project/PuLP . Easy and effective
    $endgroup$
    – Kuifje
    Jan 12 at 16:37










  • $begingroup$
    thanks hardmath, Kuifje
    $endgroup$
    – Mwana Hussein
    Jan 12 at 17:31
















$begingroup$
Welcome to Math.SE! Our strengths will tend more to helping with algorithms, e.g. for your integer programming problem, rather than with advice about writing code. You might look up the Hungarian algorithm for assignment problems.
$endgroup$
– hardmath
Jan 12 at 16:21




$begingroup$
Welcome to Math.SE! Our strengths will tend more to helping with algorithms, e.g. for your integer programming problem, rather than with advice about writing code. You might look up the Hungarian algorithm for assignment problems.
$endgroup$
– hardmath
Jan 12 at 16:21












$begingroup$
This is a good option : pypi.org/project/PuLP . Easy and effective
$endgroup$
– Kuifje
Jan 12 at 16:37




$begingroup$
This is a good option : pypi.org/project/PuLP . Easy and effective
$endgroup$
– Kuifje
Jan 12 at 16:37












$begingroup$
thanks hardmath, Kuifje
$endgroup$
– Mwana Hussein
Jan 12 at 17:31




$begingroup$
thanks hardmath, Kuifje
$endgroup$
– Mwana Hussein
Jan 12 at 17:31










2 Answers
2






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$begingroup$

First, a comment: I don't see the purpose of the third constraint ($sum_{j=1}^{T_p} C_{i,j} X_{i,j} ge 1$). Since $C_{i,j}ge 1$, this constraint is implied by the first one (assign every student to a project).



Second,regarding software, you could solve this in Excel (assuming a "reasonable" number of students and projects). Excel has a built-in linear programming solver, with limited capacity (but enough to do this for one class). There is also an open-source plug-in (OpenSolver) that works quite well and handles larger problem instances. If you are comfortable with spreadsheets but not an Excel user, OpenSolver also has a version for Google Sheets. To do it in MATLAB, you might start here: https://www.mathworks.com/help/optim/ug/first-choose-problem-based-or-solver-based-approach.html.






share|cite|improve this answer









$endgroup$





















    -1












    $begingroup$

    I agree with @prubin in both statements.
    There is no need for the third constraint and Excel + Solver may solve your problem.



    In case you are looking for something a bit more robust, I strongly recommend Google Colab (enviroment for Python notebooks): https://colab.research.google.com/



    Combine it with OR tools (https://developers.google.com/optimization/lp) and you will have a good tool to solve and teach linear programming problems right from the web browser.



    It can even have some interactive tools (forms, interface with spreadsheets, etc.).



    An short example with your code:
    https://colab.research.google.com/drive/1ukeA5Isx9COqHjAuDbUCecAlHhdUid8M



    An alternative could be Gusek (http://gusek.sourceforge.net/gusek.html).






    share|cite|improve this answer









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      2 Answers
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      2 Answers
      2






      active

      oldest

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      active

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      active

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      0












      $begingroup$

      First, a comment: I don't see the purpose of the third constraint ($sum_{j=1}^{T_p} C_{i,j} X_{i,j} ge 1$). Since $C_{i,j}ge 1$, this constraint is implied by the first one (assign every student to a project).



      Second,regarding software, you could solve this in Excel (assuming a "reasonable" number of students and projects). Excel has a built-in linear programming solver, with limited capacity (but enough to do this for one class). There is also an open-source plug-in (OpenSolver) that works quite well and handles larger problem instances. If you are comfortable with spreadsheets but not an Excel user, OpenSolver also has a version for Google Sheets. To do it in MATLAB, you might start here: https://www.mathworks.com/help/optim/ug/first-choose-problem-based-or-solver-based-approach.html.






      share|cite|improve this answer









      $endgroup$


















        0












        $begingroup$

        First, a comment: I don't see the purpose of the third constraint ($sum_{j=1}^{T_p} C_{i,j} X_{i,j} ge 1$). Since $C_{i,j}ge 1$, this constraint is implied by the first one (assign every student to a project).



        Second,regarding software, you could solve this in Excel (assuming a "reasonable" number of students and projects). Excel has a built-in linear programming solver, with limited capacity (but enough to do this for one class). There is also an open-source plug-in (OpenSolver) that works quite well and handles larger problem instances. If you are comfortable with spreadsheets but not an Excel user, OpenSolver also has a version for Google Sheets. To do it in MATLAB, you might start here: https://www.mathworks.com/help/optim/ug/first-choose-problem-based-or-solver-based-approach.html.






        share|cite|improve this answer









        $endgroup$
















          0












          0








          0





          $begingroup$

          First, a comment: I don't see the purpose of the third constraint ($sum_{j=1}^{T_p} C_{i,j} X_{i,j} ge 1$). Since $C_{i,j}ge 1$, this constraint is implied by the first one (assign every student to a project).



          Second,regarding software, you could solve this in Excel (assuming a "reasonable" number of students and projects). Excel has a built-in linear programming solver, with limited capacity (but enough to do this for one class). There is also an open-source plug-in (OpenSolver) that works quite well and handles larger problem instances. If you are comfortable with spreadsheets but not an Excel user, OpenSolver also has a version for Google Sheets. To do it in MATLAB, you might start here: https://www.mathworks.com/help/optim/ug/first-choose-problem-based-or-solver-based-approach.html.






          share|cite|improve this answer









          $endgroup$



          First, a comment: I don't see the purpose of the third constraint ($sum_{j=1}^{T_p} C_{i,j} X_{i,j} ge 1$). Since $C_{i,j}ge 1$, this constraint is implied by the first one (assign every student to a project).



          Second,regarding software, you could solve this in Excel (assuming a "reasonable" number of students and projects). Excel has a built-in linear programming solver, with limited capacity (but enough to do this for one class). There is also an open-source plug-in (OpenSolver) that works quite well and handles larger problem instances. If you are comfortable with spreadsheets but not an Excel user, OpenSolver also has a version for Google Sheets. To do it in MATLAB, you might start here: https://www.mathworks.com/help/optim/ug/first-choose-problem-based-or-solver-based-approach.html.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Jan 12 at 19:55









          prubinprubin

          1,765125




          1,765125























              -1












              $begingroup$

              I agree with @prubin in both statements.
              There is no need for the third constraint and Excel + Solver may solve your problem.



              In case you are looking for something a bit more robust, I strongly recommend Google Colab (enviroment for Python notebooks): https://colab.research.google.com/



              Combine it with OR tools (https://developers.google.com/optimization/lp) and you will have a good tool to solve and teach linear programming problems right from the web browser.



              It can even have some interactive tools (forms, interface with spreadsheets, etc.).



              An short example with your code:
              https://colab.research.google.com/drive/1ukeA5Isx9COqHjAuDbUCecAlHhdUid8M



              An alternative could be Gusek (http://gusek.sourceforge.net/gusek.html).






              share|cite|improve this answer









              $endgroup$


















                -1












                $begingroup$

                I agree with @prubin in both statements.
                There is no need for the third constraint and Excel + Solver may solve your problem.



                In case you are looking for something a bit more robust, I strongly recommend Google Colab (enviroment for Python notebooks): https://colab.research.google.com/



                Combine it with OR tools (https://developers.google.com/optimization/lp) and you will have a good tool to solve and teach linear programming problems right from the web browser.



                It can even have some interactive tools (forms, interface with spreadsheets, etc.).



                An short example with your code:
                https://colab.research.google.com/drive/1ukeA5Isx9COqHjAuDbUCecAlHhdUid8M



                An alternative could be Gusek (http://gusek.sourceforge.net/gusek.html).






                share|cite|improve this answer









                $endgroup$
















                  -1












                  -1








                  -1





                  $begingroup$

                  I agree with @prubin in both statements.
                  There is no need for the third constraint and Excel + Solver may solve your problem.



                  In case you are looking for something a bit more robust, I strongly recommend Google Colab (enviroment for Python notebooks): https://colab.research.google.com/



                  Combine it with OR tools (https://developers.google.com/optimization/lp) and you will have a good tool to solve and teach linear programming problems right from the web browser.



                  It can even have some interactive tools (forms, interface with spreadsheets, etc.).



                  An short example with your code:
                  https://colab.research.google.com/drive/1ukeA5Isx9COqHjAuDbUCecAlHhdUid8M



                  An alternative could be Gusek (http://gusek.sourceforge.net/gusek.html).






                  share|cite|improve this answer









                  $endgroup$



                  I agree with @prubin in both statements.
                  There is no need for the third constraint and Excel + Solver may solve your problem.



                  In case you are looking for something a bit more robust, I strongly recommend Google Colab (enviroment for Python notebooks): https://colab.research.google.com/



                  Combine it with OR tools (https://developers.google.com/optimization/lp) and you will have a good tool to solve and teach linear programming problems right from the web browser.



                  It can even have some interactive tools (forms, interface with spreadsheets, etc.).



                  An short example with your code:
                  https://colab.research.google.com/drive/1ukeA5Isx9COqHjAuDbUCecAlHhdUid8M



                  An alternative could be Gusek (http://gusek.sourceforge.net/gusek.html).







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Jan 23 at 2:36









                  SghatSghat

                  1




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