Question

In a new academic program, each master’s student is required to undertake an internship project at a company site. Since the projects are very important to the students and vary considerably by company, each student would like to undertake a project of his or her liking. To assure that the project assignments are fair, the program council has decided that each student ranks the projects by dividing 100 points over the projects (so ties in preference are possible). The objective is to assign students to projects to achieve the highest sum of total points of assigned projects. The project assignment has a few constraints. Each student must work on exactly one project and each project has an upper limit on the number of students it can accept. Each project must have an academic supervisor, drawn from a pool of eligible supervisors for this project. Finally each faculty member has upper and lower bounds on the number of projects that she or he can supervise. Formulate this problem as a Minimum Cost Flow problem.

Answer 1

The problem of assigning master's students to academic internship projects with the highest preference sum can be formulated as a Minimum Cost Flow problem, with constraints on student-project assignments, project capacity, and faculty supervision load.

Step-by-step explanation:

The academic internship allocation issue described can be formulated as a Minimum Cost Flow problem to achieve an efficient and fair distribution of internship projects among students. Each master's student is asked to rank the available projects by dividing 100 points among them to indicate their preferences. The objective is to maximize the total sum of points across all assigned projects. Key constraints include:

• Each student must be assigned to one project.
• Each project has a maximum number of students it can accept.
• Each project requires an academic supervisor from a pool of eligible faculty members.
• Faculty members have upper and lower bounds on the number of projects they can supervise.

By setting up the problem in this way, the program aims to ensure not only that students work on preferred projects but also that faculty workload is balanced and all projects are adequately supervised.