Question

A project-based course assigns students to project teams at the start of the term. For this purpose, each student is asked to examine the set of projects available and to identify three of the alternatives as preferred assignments (a preference of 3 represents the most preferred, 2 is the second choice, 1 is the third choice). After these preferences are collected, the instructor assigns the students to project teams, aiming for an optimal assignment of students to teams. The objective for the assignment is to maximize the total of the preferences assigned. This year, there are ten projects (P1 – P10) and sixteen students (S1 – S16). There is a maximum team size between 2 and 4 on each project, according to the nature of the work to be done (maximum sizes are listed in the table below), AND it is not permissible for a student to work alone on a project. The projects are submitted by outside organizations, and not all proposals are interesting to students, so not every project will be selected. In addition, P1, P3, and P8 have been submitted by the same organization, so the instructor wants to ensure that at most only one of these three projects is selected. The table below shows the student preferences and the limits for the team sizes. This problem blends elements of the Facility Location and Assignment Models (plus some other ideas/approaches); you will need to use Binary Decision Variables and Linking Constraints to solve this problem correctly (you might need to revisit some of the material from Topic 3 if you are having difficulty setting up all of the constraints for this problem). Construct and solve a Linear Optimization model for this problem that will maximize student preferences. a. Formulate an LP model for this problem b. Create a spreadsheet model for this problem and solve it using solver c. What is the solution S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 Max Size P1 3 3 3 3 2 3 P2 3 3 2 3 2 3 P3 2 2 2 2 2 3 P4 1 2 2 3 3 4 P5 1 1 2 1 3 3 4 P6 1 1 1 2 3 P7 2 3 2 3 3 3 3 P8 3 1 1 1 1 2 P9 1 2 2 2 P10 1 1 1 1 2

A project-based course assigns students to project teams at the start of the term. For this purpose, each student is asked to examine the set of projects available and to identify three of the alternatives as preferred assignments (a preference of 3 represents the most preferred, 2 is the second choice, 1 is the third choice). After these preferences are collected, the instructor assigns the students to project teams, aiming for an optimal assignment of students to teams. The objective for the assignment is to maximize the total of the preferences assigned. This year, there are ten projects (P1 – P10) and sixteen students (S1 – S16). There is a maximum team size between 2 and 4 on each project, according to the nature of the work to be done (maximum sizes are listed in the table below), AND it is not permissible for a student to work alone on a project. The projects are submitted by outside organizations, and not all proposals are interesting to students, so not every project will be selected. In addition, P1, P3, and P8 have been submitted by the same organization, so the instructor wants to ensure that at most only one of these three projects is selected. The table below shows the student preferences and the limits for the team sizes. This problem blends elements of the Facility Location and Assignment Models (plus some other ideas/approaches); you will need to use Binary Decision Variables and Linking Constraints to solve this problem correctly (you might need to revisit some of the material from Topic 3 if you are having difficulty setting up all of the constraints for this problem). Construct and solve a Linear Optimization model for this problem that will maximize student preferences.

a. Formulate an LP model for this problem
b. Create a spreadsheet model for this problem and solve it using solver
c. What is the solution

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 S14 S15 S16 Max Size
P1 3 3 3 3 2 3
P2 3 3 2 3 2 3
P3 2 2 2 2 2 3
P4 1 2 2 3 3 4
P5 1 1 2 1 3 3 4
P6 1 1 1 2 3
P7 2 3 2 3 3 3 3
P8 3 1 1 1 1 2
P9 1 2 2 2
P10 1 1 1 1 2

Added by Gema L.

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