All students in the College of Business at State University are required to take a capstone course, Management 4394, the last semester of their senior year. This course consists primarily of a semester-long case project that pulls together all the business disciplines to test the students' knowledge in the major business areas of management, marketing, finance, accounting, quantitative methods, and operations. A difficult task for the course instructor is dividing the students in a class into equitable teams that will enhance the learning process and engender teamwork. The project teams should be relatively equal in terms of student ability and performance. Further, the teams should reflect different functional skills; that is, the teams should include a mix of different majors.
Also, the college would like the teams to be diverse in terms of gender and nationalities in order to prepare the students for working with diverse individuals when they graduate and take a job. Consider one course section of Management 4394 with 18 students. The instructor wants to divide the class into six project teams of three members each. The instructor's main objective for the teams is that they be relatively equal in terms of academic capability. Since the only means of assessing capability is a student's grade point average (GPA), the instructor has determined that one way to achieve this objective is for the teams to have a minimum average GPA of 2.80 while also striving to achieve the maximum overall average team GPA possible. It is also important that the teams have a mix of members with different majors to enhance the teams' functional capabilities, but the instructor does not want there to be more than two of the same major on any single team. In order to achieve some degree of diversity among team members the instructor wants there to be at least one female and one international student on each team, but not more than two females or two international students on a team. Following is a table that shows the breakdown of GPAs, majors, gender, and internationality of each student in the class.
Note that only two students are both female and international, and that student 2 is a double major. Formulate and solve an integer linear programming model for this problem to determine project teams that will meet the instructor€™s guidelines for team formation. How successfully do you think your model achieves the instructor€™s guidelines? In other words, do you consider the teams to be diverse and relatively equitable in terms of functional and academic capability? If not, how do you think you might need to change your model to better meet the team formationguidelines?