The Jackson Hole Higher Education Group
CyberCampus Technical Note 2.0
Simulation Engine: Overview
This note was prepared by William F. Massy to further the CyberCampus game development project, which is being funded by the Alfred P. Sloan Foundation. It is based on the author’s simulation engine prototype developed and coded in Mathematica for the same purpose. While inaccuracies and inconsistencies between the two are believed to be minimal, no warranty is offered. Our eventual game development partner will be expected to review these materials with the author, internalize them, and suggest corrections, changes, and improvements where needed, before finalizing the game design.
Contents are the property of The Jackson Hole Higher Education Group and may not be used or cited without permission. Limited distribution is provided to obtain comments and criticisms, and to assist potential collaborators. Copyright © 1997 by The Jackson Hole Higher Education Group.
1. Introduction
1.1. Purposes and Definitions
1.2. Market Segments
1.3. Institutional Segments
1.4. Institutional characteristics:
1.5. Student Levels
1.6. Student Market Segments
1.7. Student segment characteristics:
1.8. Program Modules and Sub-Modules
2. Enrollment Management Module
2.1. Primary Demand: Applications
2.2. Primary Demand: Institutional Admissions Offers
2.3. Primary Demand: Student Matriculations Decisions
2.4. Selective Demand: CyberCampus
2.5. Lessons Embodied in the Enrollment Management Module
3. Academic Operations Module
3.1. Student FTEs
3.2. Course Enrollment
3.3. Faculty FTEs
3.4. Course Offerings and Teaching Assignments
3.5. Faculty Research
3.6. Faculty Discretionary Time Distribution
3.7. Departmental Performance
4. Non-Academic Operations Module
5. Physical Plant Module
6. Resource Allocation Module
7. Implementation Details
7.1. Notation Used in the Prototype
7.2. Response Functions
7.3. Exponential Smoothing Function
7.4. Piecewise Linear Approximation to a Quadratic Program (PLQ)
This technical note provides an overview of the CyberCampus project and its evolving prototype engine elements. It also provides a sense of the kinds of issues and learning opportunities we hope to include in the CyberCampus design.
Market Segments
Few if any markets can be represented by homogeneous actors, either on the supply side or the demand side. Hence it is useful to model behavior at the market segment level, rather than for the market as a whole. One has considerable flexibility in defining market segments. The important thing is that behavior within the segment be as homogeneous as possible relative to the differences among segments.
CyberCampus will use the following market segment structure:
The definitions of the institutional market segments and student market segments won’t be known until the completion of empirical work now being performed at the University of Pennsylvania by the Institute for Research on Higher Education (IRHE). However, we offer the following tentative definitions to provide a context for thinking about what comes later.
The institutional segment definitions are:
"Medallion" institutions command market power by virtue of their names and associated prestige. They are highly selective and graduate a high proportion of those who matriculate. They also are well funded—often with substantial endowments or unusually high levels of state support, gift flows, and (for research universities) substantial income from sponsored research. At the other end of the spectrum, the "convenience outlets" are four-year schools with low selectivity, large part-time student populations, and low graduation rates. These schools often cater to students who want courses on specific matter rather than a degree. The middle group, the "generics," serve more traditional student groups than the convenience outlets but they lack the name-brand appeal of the medallions. The last segment, the "non-traditional providers," will represent a growing and important list of schools that cannot easily be accommodated elsewhere: e.g., the University of Phoenix and the Western Governors’ University.
The institutional segments will be characterized in terms of the aforementioned variables plus others that turn out to be relevant to the design of later simulation modules. In particular, we will include the following variables used to determine student preference:
Unless otherwise noted, the calculations assume that all institutions in a given segment have values equal to average for the segment.
CyberCampus will simulate activity at each of a number of student levels. All the student market segment and subsegment definitions, and all the primary and selective demand simulation modules, are defined in terms of student levels. We shall describe many of these using terms descriptive of the traditional undergraduate student. However, the same ideas should be understood to apply—with suitable modification in detail—to the other student levels. Our current thinking about the list of student levels to be included follows:
The "masters and professional" definition encompasses the MBA and JD degrees, and so-called terminal masters programs elsewhere, but not masters degrees achieved en route to or in lieu of the doctorate. (CyberCampus will have no medical school.) "Non-traditional" undergraduates are part-time, usually older students who are matriculated for the bachelors degree. "Non-traditional non-matriculated students" are those who take individual courses on a convenience basis or as part of a training program.
The prospective students at each student level will be classified as belonging to a student market segments. We plan to define approximately seven such segments:
Students also will be categorized in terms gender and whether the person qualifies as a minority under the eeoc definition. Each market segment will be broken down by gender and eeoc status, and we shall refer to the resulting categories as "student subsegments." The student segment cells are mutually exclusive but the subsegments are not. At times the model works with the hierarchy of all cell types: for example, "blue-chip, minority, males who prefer small institutions." For other purposes it deals only at the student segment level or at the level of student segment plus one or two subsegments: for example, {blue-chip, minority, female}; {blue-chip, minority}; or simply {blue-chip}.
The market segments and subsegments will be characterized according to the following variables:
For example, the blue chip segment will have the largest average academic rating and the largest non-academic rating, though not the largest athlete rating. Blue chip students also may be expected to have a larger average ability to pay than students in some of the lower segments. IRHE is working to collect data on as many of these relations as possible.
Except for "ability to pay," the calculations assume that all segment members’ values fall at the average. Because of the financial aid model’s particular requirements, ability to pay is distributed across the population of each segment and subsegment according a one-humped curve like the normal distribution but with a longer right-hand tail (we use a gamma distribution).
Suppose a prospective undergraduate student has decided to submit applications to a certain number of institutions. How many should go schools that will be easy to get into? How many should go to more attractive schools where the chances of admission are lower? The CyberCampus primary demand model simulates the way students go about answering these questions. The applicant profile for an institutional segment and student level can be obtained by adding up the applications for the student market segments and subsegments. The selective demand applications module, described in Section 3.4, calculates the player-managed institution’s applicant profile by determining how much the player-managed institution resembles each of the institutional segments.
As suggested above, we assume that the number of applications per students is determined exogenously—that is to say, outside the model. (The number may be different for the different student segments and subsegments, and it may vary over time.) In the language of modeling, our task is to allocate the fixed number of applications across the institutional segments. The allocation procedure, which simulates what we believe to be a reasonable representation of actual behavior, works in the following way.
The core idea is that students subjectively rate the typical school in each institutional segment. We simulate this result by means of a student preference function, which calculates an index that shows how the members of each student market segment and subsegment feel about the schools in each institutional segment. One of the game’s lessons is to internalize the idea that institutional actions affect student preference—and hence demand.
We assume that students distribute their applications among institutions in the following two ways:
The simulation blends the two methods according to a preset proportion (which may vary by student segment and subsegment) to produce the number of applications sent by a typical student to schools in each institutional segment.
The per-student application figures are multiplied by the number of prospective students in each market segment and subsegment. These results added up to produce the total number of applications received by each institutional segment.
In summary, the student applications module:
The next step is to simulate institutional admissions decisions. How do schools decide which of the applications they receive should be accepted? Because admitted students must know about financial aid before they can decide where to attend, the admissions model must take financial aid requirements and resources into account along with student academic, extracurricular, and athletic ability, and race and gender considerations. Gaining insight about how admissions deans balance these sometimes-conflicting factors represents another important CyberCampus lesson.
The admissions model starts with the idea of an institutional preference function, which rates academic, extracurricular, and athletic ability. Schools in the various institutional segments derive their ratings using different weights. Applying the preference function to the student attribute data produces a desirability rating for each student market segment and subsegment.
Institutions decide which applicants to admit based on a combination of the proportional and high-assay procedures described earlier, subject to certain ancillary requirements. First comes the obvious requirement that enough students be admitted to fill the entering class. This, in turn, requires that schools over-admit to allow for the fact that some admittees will decide to go elsewhere. The result is that schools admit a certain fraction of the applicants from each student segment and subsegment, subject to the requirement that the number of admitees divided by the expected yield rate equals the number of student places to be filled. The expected yield rate depends on the actual yield rate as calculated for prior years. The desired fraction of admitees depends on institutional preferences and the blend of proportional and high-assay calculation programmed into the simulation.
Schools also may apply race and gender as targets in the admissions process. For example, they may seek to maintain x% minority representation in the incoming undergraduate class. Such percentages are not treated as quotas, but rather as targets that may (or may not) alter the results of the proportional and high-assay calculations. The degree of weight applied to the target is a matter of school policy.
Student financial aid also enters a school’s decision about admissions offers. The model allows for two kinds of institution-supplied financial aid: (a) need-based grant aid; and (b) merit-based grant aid. Student loans and grant aid supplied by other entities are not modeled explicitly, though they can be considered as taken into account via the ability-to-pay variable described earlier. Need-based aid depends on ability to pay and the total cost of attendance. (We assume no need-based aid above the undergraduate level.) Merit-based aid depends on academic, extracurricular, or athletic ability, depending on the school’s policy. Need and merit aid can be blended, and the degree of emphasis can vary by institutional segment. For example, one kind of school might stress need-based aid, another merit aid targeted to academic ability, and a third merit aid targeted toward athletes. The amount of aid can also be varied. Schools can cover all or a fraction of calculated need, academic scholarships all or a fraction of tuition, and athletic scholarships the full cost of attendance.
Schools may decide to spend whatever is needed to provide the applicable amount of aid to all admitted students. Alternatively, they may limit total aid expenditures to a fixed sum, in which case their admissions offers will be adjusted so that the applicable aid falls within the budget.
In summary, the institutional admissions offer module:
The above procedure calculates the number of admissions offers received from schools in each institutional segment by applicants in each student market segment and subsegment. The admission rate for each institution-student segment can be determined from these results in a straightforward manner. The model also calculates the financial aid requirement based on each institutional segment’s financial aid policies and admissions profile, regardless of whether budget limits will apply.
Now the model turns back to the simulation of student behavior. By what process do prospective students decide among multiple admissions offers? The answer is that students accept an offer from a school in the most attractive institutional segment, where attractiveness is based on the student’s preference function. However, before writing the simulation we must transform the aggregate numbers of offers produced by the admissions module into the average numbers of offers received by individual students from schools in each institutional segment.
The transformation proceeds by calculating the average number of unduplicated offers per student within each institutional segment and the overlap of offers among segments. The following example shows why these quantities are important. Suppose an applicant receives four offers from private medallion research universities (segment 1) and two from medallion liberal arts colleges (segment 2), then decides to accept one of the university offers. This decision produces one university matriculation, three university rejections, and two liberal arts college rejections. Eliminating the university offers to this particular student (i.e., calculating the unduplicated offers for segment 1) prevents counting four matriculations when there can only be one. Eliminating the liberal arts college offers (i.e., calculating the overlap in offers between segment 1 and segment 2 institutions) prevents counting two matriculations when there can be none. The simulation uses probability theory to compute offer duplication and overlap.
As in the previous algorithms, student matriculation decisions are simulated by combining the proportional and high-assay approaches. In the present case, proportional allocation assigns the unduplicated offers across institutional segments as a function of relative student preference. The resulting matriculations are subtracted from the unduplicated offers for each segment, taking account of the overlap of offers among segments. Then the high-assay procedure assigns the remaining unduplicated offers to the segment with the largest preference value. These procedures can be performed separately for each student market segment and subsegment.
In summary, the student matriculation module:
The algorithm insures that the number of matriculations depends upon and does not exceed the number of applications for each institutional and student segment. Yield rates and financial aid commitments can then be calculated for each institution-student segment combination.
Like a real institution, the player-managed institution operates within the context of a marketplace that sorts prospective students with different characteristics into matriculations at one or another institution. The primary demand modules, just described, simulates the operation of that marketplace. Now it is time to describe the connections between the external student market and the player-managed institution itself: that is, how the number of applications, admissions offers, and matriculations for the player-managed institution are determined.
For applications and matriculations, the model compares the player-managed institution’s institutional attributes with those of the aforementioned institutional segments. In effect, we simulate how the player-managed institution looks to prospective students—through their eyes, using their student preference function. This makes sense because applications and matriculations decisions are made by the students themselves. If, for example, the player-managed institution looks like a private generic institution, one can expect that it will draw applications from the student market segments and subsegments at rates typical of that kind of institution. The same is true for yield rates.
The CyberCampus player’s degrees of freedom lie not in making the students’ decisions for them, but rather in taking actions that will change how the player-managed institution looks to prospective students. Thinking in terms of actions and marketplace reactions represents another important lesson to be embodied in the game.
The selective demand applications and matriculations modules operate as follows. First we determine the player-managed institution’s relative perceptual similarity to each institutional segment by comparing cost of attendance, financial aid, prestige, and the other performance values incorporated in the student preference functions, using the same weighting coefficients as the preference functions. The similarities, positive numbers that sum to one, are then used as the weights in a function that calculates the player-managed institution’s application and yield rates as a weighted average of the application and yield rates of the institutional segments. The student preference functions differ by student market segment and subsegment, so the player-managed institution’s application and yield rates also can be calculated on a segment-by-segment basis.
Because the application rates have the dimension "number of applications per student intake place," it is a simple matter to multiply by the player-managed institution’s intake places to get its total applications. The yield rates, defined as the fractions of admissions offers that are accepted, will be applied to the player-managed institution’s admissions offers to get total matriculations.
The player-managed institution’s admissions offer decisions will be simulated using the algorithm already described for primary demand. The player will be expected to provide inputs for the admissions and financial aid policy variables described in Section 3.3, and the selective demand applications module will provide the requisite applications figures. The output of the selective demand admissions module will feed into the matriculations module, where the aforementioned blended yield rates will be applied to obtain figures for the player-managed institution matriculations from each student market segment and subsegment.
The enrollment management module will help players understand student market structures and the effects of institutional positioning, price and price discounts, institutional performance, promotion, and admissions policies on student applications and yield rates. Marketing management texts stress the importance of segmentation, and the student and institutional segmentation structures built into the simulation should be interesting in their own right and also permit the player to access information at a rich level of detail. While more detail will be available than can be assimilated by an average player, users should be able to gain useful insights about the "great sorting" that takes place in the student-institution marketplace and about the kinds of strategies needed to manage enrollments effectively.
The following list provides some more specific insights we hope to offer the CyberCampus player. In addition to explaining the motivation behind the student intake algorithms, the listed items may help guide the game design and user interface. (For purposes of the list, "we" and "our" refer to the CyberCampus player.)
Institutional segmentation and market positioning:
• How do students’ perceptions sort institutions into segments? Why should we be alert to trends in student perceptions?
• Which are our peer institutions as seen by students?
• To what group of peer institutions do we aspire? What would it take to reposition ourselves?
Student segmentation and target markets
• How should one classify potential students? How can data on student market segmentation and greater specificity about our target markets aid enrollment management?
• What are the current profiles of our entering students? How do they differ from those of our peer institutions? Are we satisfied with the profiles? If not, to what profiles do we aspire and what would it take to get there?
• Do the profiles of applicants differ from those of entering students? For example, to what extent do yield rates indicate we’re a first-choice or backup school for each student segment? What if anything can be done to improve our profiles?
Competitive comparisons
• How do our sticker prices and financial aid awards differ from those of our actual and desired peer institutions? What are the trends? Can we do anything to improve matters?
• How do the various institutional performance indicators differ from those of our actual and desired peer institutions? What are the trends? Can we do anything to improve our performance?
• How do the various input measures differ from those of our actual and desired peer institutions? (Input measures include spending per student, student-faculty ratios, faculty quality indices, endowment, revenue mix.) How should we assess the impact of input-mix changes upon student preference—and hence upon our application and yield rates?
• How much improvement on the above dimensions can reasonably be achieved given the institution’s financial and other resources? How should we make tradeoffs among the various improvement options?
The student FTEs submodule allocates new-student interest across departmental programs (intDepts), for each stuLevel and intDept, simulates the movement of people into and out of the student population, and determines the numbers of degrees awarded, dropouts, continuations, and current student FTEs. The definition of intDept is as follows:
Interest department (intDept): the academic department in which a particular student concentrates. "Concentration" means different things for different student levels: for example, "major" undergraduates and "field" for masters and doctoral students. The intDepts for undergraduates who have not yet selected a major represent general areas of interest.
The submodule includes task-specific models that:
The course enrollment submodule determines the number of course enrollments by department (cseDepts), by level of course offered (cseLevel). The definitions of cseDept and cseLevel are:
Course department (cseDept): the academic department offering a courses in which the student actually enrolls. The list of cseDepts is the same as the list of intDepts, but the two constructs play different roles. The prototype uses only four departments, but ten or a dozen are anticipated for the final model.
Course level (cseLevel): the level of a course in which a student actually enrolls. The range of course levels is limited to "undergraduate" and "graduate." Doctoral and masters courses are not differentiated, and there are no special courses for non-traditional students. (Certain courses are tagged as being available for distance teaching; this will be discussed in a section.) Separating the cseLevel and stuLevel constructs permits the simulated students to take "out of level" courses: for example, an undergraduate may take graduate-level courses.
The faculty FTEs submodule: (a) determines the profile of new faculty hires for departments with an authorization to hire (from the resource allocation model); and (b) determines faculty departures and continuations. The submodels:
The course offerings and teaching assignments submodule determines course supply, and class sizes. Course offerings are determined for each department, course level, and course type.
The task-specific models:
The faculty research commitments submodule determines the amount of research effort required to meet sponsored research commitments. The submodule also determines the number of doctoral research assistants that will be available to faculty members. The models produce results for each department and faculty type.
The faculty discretionary time distribution submodule determines how faculty spend the time available after accounting for the student contact hours called forth by the teaching assignments. The discretionary time distribution is determined for each department and faculty type.
The departmental performance model determines educational value added, student satisfaction, sponsored research proposals and awards, research outcomes, faculty morale, and various other performance variables. The performance variables are available for reporting to the player and they will drive the aforementioned updating and allocation functions in the next simulated year.
The task-specific submodels:
(Eq 2.1)
where v is the input variable and m the norm for the input (v and m are usually lists of variables).
respF[ceiling, floor, m, v]; floor = 0, ceiling = 1, and m = 0:
respF[ceiling, floor, base, m1, m2 , v]; floor = 0, ceiling = 1, and m = 0:
(Eq 2.2)
where the smoothing parameter, l , must be between 0 and 1. This will be denoted by:
(Eq 2.3) ExpSm[z(x)]
xQ: list of variables included in f which are to be expressed in quadratic terms (xQ may be of any length <= number of variables in f; the variable names in xQ must be the same as those in f)
nQ: list containing the number of piecewise linear segments to be used in approximating each element of xQ
dQ: list containing the increment of each variable to be used in forming the piecewise linear segments (the first segment runs from 0 to dQi, the second from dQi to 2 dQi, and so on)
kQ: list containing multipliers to determine the amount of additional curvature, for each variable, to be applied in each piecewise linear segment (the multiplier for the first segment is 1, for the second segment it is kQi, for the third it is {1+kQi}2–1, and so on)
