1 Project Team Assignment. A project-based course assigns students to project te
ID: 380502 • Letter: 1
Question
1 Project Team Assignment. 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 altermatives as preferred assignments A preference of 3 indicates the most preferred projoct. When these preferences are collected, the instructor assigns the students to project teams,aiming for an optimal assignment of students to teams. Thecriterion for the assignment is to maximize the total of the preferences Thisyear, thereare 10availableprojectsand 16students enrolled. There is a maximum team size between 2 and 4 each project, according to the nature of the work to bedone. It is not permissible for a student to work alone on a project (that is, in a team of size I). The table below shows the student preferences and the limits for the team sines a. What is the best value of the criterion-that is, the maximum sum of assigned preferences? b. In the solution of part (a), how many students are assigned to their first choice? What is the maximum number of students who could be assigned to their first choice, if that were the only criterion?Explanation / Answer
(a) The Best Value of the criterion - The Maximum sum of assigned preferences:
From the table given in the question, we identify the total number of preferences under each project that are mapped to each student. From that perspective, there are totally 5 preferences for Project 1 from Students 2, 4, 6, 8 and 15. By this way, let us find the total preferences for all the 10 projects as shown below:
5+5+5+5+6+4+6+5+3+4 = 48 Preferences
(b) No. of students who are assigned to their first choice:
Based on the solution from part a, 5 students are assigned to their first choice. As they give most preference, the number of student is 4. Therefore, the maximum number of students who could be assigned to their first choice is 4. Here, we must assign the preferred project to the student by observing the given table criteria which is to choose the project for that student that is most prefered.
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