Optimal Admission and Scholarship Decisions: Choosing Customized Marketing Offers to Attract a Desirable Mix of Customers

Abstract

Each year in the postsecondary education industry, schools offer admission to nearly 3 million new students and scholarships totaling nearly $100 billion. This is a large, understudied targeted marketing and price discrimination problem. This problem falls into a broader class of configuration utility problems (CUPs), which typically require an approach tailored to exploit the particular setting. This paper provides such an approach for the admission and scholarship decisions problem. The approach accounts for the key distinguishing feature of this industry — schools value the average features of the matriculating students such as percent female, percent from different regions of the world, average test scores, and average grade point average. Thus, as in any CUP, the value of one object (i.e., student) cannot be separated from the composition of all of the objects (other students in the enrolling class). This goal of achieving a class with a desirable set of average characteristics greatly complicates the optimization problem and does not allow the application of standard approaches. We develop a new approach that solves this more complex optimization problem using an empirical system to estimate each student's choice and the focal school's utility function. We test the approach in a field study of an MBA scholarship process and implement adjusted scholarship decisions. Using a holdout sample, we provide evidence that the methodology can lead to improvements over current management decisions. Finally, by comparing our solution to what management would do on its own, we provide insight into how to improve management decisions in this setting.

Keywords: choice sets, college choice, utility on averages, statistical approximation, nonconvex optimization