A Mathematical Model of Maximizing Matching Rate Between Students and Advisors

There are so many exciting things in college life, and matching with a “like-minded” pre-major advisor is definitely one of the most important things! For incoming students, pre-major advisors will be the first to provide them with unique perspectives about College of William and Mary; in addition, their academic experience will certainly influence students’ major decisions in future. We believe that every student wants to match with a pre-major advisor who shares similar interests, but sometimes not everyone can get matched to desired advisors: I paired with the Professor in English Literature department though I am more interested in math. Therefore, maximizing the satisfaction degree between both students and advisors becomes the intention of this project.

The goal of this research project is to use the linear operational model, specifically, the transportation problem algorithm to optimize the matching between freshman and pre-major advisors, and to maximize the satisfaction degree between these two groups (students who have specific interests toward certain majors are successfully assigned to advisors with the same indicated majors). The operational model can help the Office of Academic Advising (OAA) to improve the decision-making process and pairing between advisees and advisors. The results of the model can provide the optimal solution and enhance students’ educational experience by taking into the considerations of both groups’ specific interests, the number of advisees each advisor desires and the special population (transfer students, scholarship-sponsored students, undecided, red-flag students etc.).

The research project is based on the course Math323, Intro to Operational Research, and the algorithm of Transportation Problem, which was developed by Frank Lauren Hitchcock, a renowned American mathematician who is notable for vector analysis. The general formulation in Operations Research: Applications and Algorithms, Wayne L. Winston is:

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where the si is the maximum units could be supplied by supply point i; and dj represents that demand point j must receive at least dj units of the shipped good; cij stands for a variable cost when each unit produced at supply point i and shipped to demand point j (as pij ); xij stands for the number of units shipped from supply point i to demand point j. Since we assume that the cost objective function is linear, the total cost of this shipment is cij xij.

Winston, Wayne L. Operations research: applications and algorithms. PWS-KENT Publ. Company, 1987.