Instructions: Model the given problem as a linear program and solve it using the software of your choice. Include the linear program if you did not receive a solution from your instructor. Submit all code files as one zip folder onto the open portal on the e-learning system.
Each student is required to submit their own individual work. Your group is to help you brainstorm and understand.
Problem Statement:
A set of seven students are being funded by GJU to go to graduate school. The seven students consist of a couple and five single students. The couple wish to go to the same graduate program. GJU has agreements with six universities where they would like to send their students to for higher degrees where placing each student at a different university for diversity purposes. The students researched the set of universities that GJU has agreements with, and they created a score of five aspects of each university: rank/score of the program, size of the program, cost of living in the city, life in the city, and the weather year-round. They summed up the scores of each (out of a 100) as a result of their research, and Table 1 below summarizes those scores.
Table 1: Scores of the universities’ programs and cities, out of 100
University
Score of the Program
Size of the Program
Cost of Living
Life in the City
Weather in the City
The students have different preferences in terms of where they would like to go; some care about the score of the program while others care about the weather. Each student came up with a multiplying factor to the scores of the universities in each aspect. Table 2 summarizes the factor by which they value each aspect; if the factor is more than 1 then it is important, if it’s equal to 1 then they are neutral, and if it’s less than 1 then the factor is not very important.
Table 2: Multiplying factors to the five aspects of the universities to describe the students’ preferences
Score of the Program
Size of the Program
Cost of Living
Life in the City
Weather in the City
The students used their multiplying factors and the score of each aspect to formalize their preference of the universities they would like to attend. The students each created a rank list of the universities (1 being the most preferred and 6 being the least preferred) and gave it to GJU. Similarly, the universities reviewed the students’ applications and they sent GJU their ranking of the students as shown in Table 3 (one is the highest and 7 is the lowest).
Table 3: Universities’ rank lists of the students
GJU needs to use both rank lists, from the students and the universities, to match each of the students or the couple to a university for their graduate studies. They want to match them such that both the universities and the students are somewhat happy. The match process needs to yield that all six universities have a student or the couple from GJU, and every student placed at a university. Remember that the couple wants to attend the same university but their rank lists will be different.
First, you have to create the students’ rank lists of the universities. Second, define your decision variables. Third, which is the most challenging task, is defining your objective function.
Note: This is an application of a famous problem called Stable Marriage Problem. Think how this can be further complicated – here we included a couple to be matched with one university rather than a single.
The post IE 3315 Operations Research Lab 6 appeared first on My Assignment Online.