As an example of how simulation can be used for operations research, consider
the following college enrollment model. A certain college wants to analyze the effect
of admissions and freshman retention rate on the college’s enrollment so that it can

predict the future need for instructors and other resources. Assume that the college
has estimates of the percentages of students repeating a grade or leaving school before
graduating. Develop a matrix equation on which to base a simulation model that can help
in this analysis . • Solution
Suppose that the current freshman enrollment is 500 students and the college decides
to admit 1000 freshmen per year from now on. The college estimates that 10 percent
of the freshman class will repeat the year. The number of freshmen in the following
year will be 0.1 (500) + 1000 ~ 1050, then it will be O.!(l (50) + 1000 = 1105, and
so on. Let xl(k) be the number of freshmen in year k, where k = 1,2,3,4,5,6, ….
Then in year k + 1, the number of freshmen is given by

xl(k + 1) = 10 percent of previous freshman class
repeating freshman year
+ 1000 new freshmen

=0.1x (k) + 1000

Because we know the number of freshmen in the first year of our analysis (which is
5(0), we can solve this equation step by step to predict the number of freshmen in the future. Let x2 (k) be the number of sophomores in year k. Suppose that 15 percent of the freshmen do not return and that 10 percent repeat freshman year. Thus 75 percent of the freshman class returns as sophomores. Suppose also 5 percent of the sophomores repeat the sophomore year and that 200 sophomores each year transfer from other schools. Then in year k + 1, the number of sophomores is given by

To solve this equation we need to solve the “freshman” equation (4.8-1) at the same
time, which is easy to do with MATLAB. Before we solve these equations, let us develop the rest of the model. Let x3(k) and x4(k) be the number of juniors and seniors in year k -, Suppose that 5 percent Qf the sophomores and juniors leave school and that 5 percent of the sophomores, juniors, and seniors repeat the grade. Thus 90 percent of the sophomores and juniors return and advance in grade. The models for the juniors and seniors are

we will see how to use MATLAB to solve such equations.