This paper describes work in progress on the Higher Education simulation project funded by the Alfred P. Sloan Foundation. Contents may not be used or cited without permission. Limited distribution is provided to obtain comments and criticisms, and to assist potential development partners. Copyright © 1997 by JHHEG.

Resource allocation provides the central policy focus for Higher Education, for it is the creation and distribution of resources that drive most college and university functions. The term "resource allocation" as used here is synonymous with budgeting—the annual process that determines prices, salary guidelines, provisions for cost-rise, and net changes in the expenditure authorizations for academic and nonacademic operations. The resource allocation model converts player-generated policy inputs and changes in exogenous factors to the specific decisions needed to drive the simulation for the ensuing year. The resource allocation model’s main algorithms have been prototyped in Microsoft Excel^®. The model will run once per simulated year.

The model begins by defining the institution’s financial structure—its balance sheet and sources and uses of funds. The resulting financial statements will vary in structure and content depending on the player’s choice of institutional characteristics. The statements for public institutions will include state support. Wealthy institutions will have large endowments and cash reserves; struggling colleges might have none. The financial statements provide the initial conditions for the budget model that determines revenue and expense.

The budget model has three components. The first calculates the drivers of aggregate revenues and expenditures: e.g.,, tuition and financial aid, salary increases, and budget adjustments. (Budget adjustments, which will be defined presently, refer to expenditure changes over and above the effects of salary increases and cost-rise.) A second component allocates the budget adjustments among functions and activities: e.g., faculty, other departmental expense, libraries and information technology, athletics, and institutional advancement. The model’s third component, "faculty positions," allocates faculty salary expenditure adjustments among departments. By so doing, it also determines the number of new faculty that each department can hire.

Every spring Higher Education allocates resources for the next academic year. For simplicity, the model assumes accurate estimates for the current year’s financial outcomes. Because resource allocation takes place late in the fiscal year, this is not an unrealistic assumption. The current-year data provide the baseline against which budget adjustments will be considered. The player determines student intake targets as part of budgeting. (Actual admissions may deviate from the targets.) Therefore, the resource allocation model runs before the enrollment management model. The model also runs before the faculty hiring model even though, in real life, faculty hiring is not concentrated in the late spring. The new budget takes effect on July 1 and remains in effect for the next twelve months unless the player decides to rescind expenditure authorizations.

While actual revenues and expenditures tend to conform to the institution’s planned budget, deviations can be expected. The model uses the coming year’s budget as the initial condition for that year’s revenue and expenditure statement. Changes are introduced during the year as the result of endogenous, exogenous, and random events. For example, if the enrollment management model produces a shortfall or overflow of students (an endogenous event), tuition revenue and financial will be adjusted accordingly. A plunge in the stock market (an exogenous event) will produce variances in gift income and investment return. Small random deviations also will be programmed to affect most or all of the other revenue and expense items. The player can view the current revenue/expenditure statement and balance sheet at any time during the year, and it will be offered up for examination at year-end. Finally, the player can rescind amounts from some expenditure lines—for example, from student life or operations and maintenance—if the financial picture worsens during the year.

Because Higher Education is not intended to be primarily a financial exercise, its balance sheet and income statement contain only the elements needed to drive the rest of the simulation. For example, there is no general distinction between restricted and unrestricted funds for most income and expense categories, and some categories are highly aggregated. The revenue and expenditure statement also departs from normal usage in that it cross classifies expenditures by object of expense (faculty salaries, staff salaries, other expenses) and function or activity. The cross-classification is required for modeling purposes, and it will be instructive for the player to see the data displayed in this way. This system generally follows the strategic financial model developed previously by W. F. Massy.

Table 1 shows a sample balance sheet. It and subsequent sample tables display information needed by the simulation engine. They are not samples of player interface screens.

• Operating reserve: if the number is positive it represents sums available to fund operating deficits, if negative it represents bank loans; the reserve collects interest at the short-term interest rate and pays interest at the bank interest rate.
• Endowment, expressed at market value: changes from year to year due to investment return, new gifts to endowment, and endowment spending. Spending equals the endowment spending rate (a budget decision variable) times the endowment’s beginning market value.
• Buildings: value of physical plant, expressed in terms of replacement cost. New construction and renovation increment plant value and depreciation charges reduce it. (Depreciation charges affect the balance sheet but are not shown on the revenue and expense statement.)

• Capital reserve: money available to fund new building projects.
• General plant debt: funds borrowed to finance facilities other than residence halls. A fixed percentage (tentatively 4 percent) of the outstanding balance is repaid each year as part of debt service. (Debt service, which also includes interest on the outstanding balance, represents a call on general funds.) Pays interest at the long-term interest rate.
• Residence hall debt: funds borrowed to finance residence halls. A fixed percentage of the outstanding balance is repaid as a residence hall expense. Pays interest at the long-term interest rate.

Table 2 shows a sample revenue and expenditures statement. Most items are self-explanatory. Those items treated in an unusual way include:

• Gross and net tuition: gross tuition equals student FTEs times the tuition rate; net tuition equals gross tuition minus financial aid.

• Financial aid: sums paid from institutional sources; does not include student loans or external scholarships.
• Sponsored research: sums received from outside entities to support research. Faculty principal investigators control the "direct" portion. The "indirect" portion goes to the institution as general funds.
• Intercollegiate Athletics: income from intercollegiate athletics programs. Depends on the level of competition for football and basketball (e.g., NCAA Division IA); expenditures on athletics and athletics performance during the previous year. The level of income will be determined using the smoothed dual logistic function as described in Paragraph 2 of Technical Document 2.5.

• Academic departments: sums budgeted for academic department operations, excluding sponsored research. "AY Fac. Comp." represents sums paid from institutional funds for faculty salaries and benefits during the academic year. "Staff comp." and "Other exp." represent salaries and benefits and non-salary expenses for the whole year. The model calculates the total funds available under this heading and then allocates them among the ten simulated departments.
• Sponsored research: the direct portion of sponsored research revenues. Principal investigators may spend part of this amount to offset their academic year salaries—sums that otherwise would fall into the "academic departments line. They spend the remainder for staff compensation and other expenses.

Table 3 lists key financial factors that may vary exogenously over time, either at random or as part of preprogramed scenarios. Player decisions can influence the right-hand variables to some extent. For example, asset allocation might influence endowment total return. Expenditures on advancement and athletics might influence income growth for those categories. Heavy deficits requiring bank debt close to the credit limit might escalate the bank interest rate. Other income may be influenced by as yet unspecified institutional financial policies.

Table 4 presents the ten policy variables needed to determine aggregate revenues and expenditures. All percentages refer to the prior year’s base. Highlights include:

• Financial aid policy: fractional change in the amount of money to be allocated to financial aid in excess of any adjustments needed to accommodate changes in student numbers. In effect, this variable represents the change in the average aid per student.
• Endowment spending rate: fraction of the beginning-of-year endowment market value to be made available for current uses.
• Indirect cost rate: fraction of direct expenditures on sponsored research that is collected as overhead reimbursement.
• Faculty salary increases: growth rate of faculty salaries and fringe benefits. This does not necessarily represent the growth of total salaries, which will be affected by changes in FTE numbers as well as the compensation rates.
• Staff salary increases: growth rate of salaries and fringe benefits. The model does not track staff numbers.
• Budget adjustment: adjustments to the overall operating budget after taking account of cost-rise. For example, if the budget adjustment is 1 percent of the prior year’s base and salary increases and other cost-rise sum to 4 percent, the budget will grow by 5 percent overall.
• Transfer to plant: an allocation of current revenue to fund the capital budget. Uses of capital are handled in the physical plant model.

Two player-controlled policy parameters are associated with each policy variable.

• Target: the optimizer will try to achieve this figure. A * in the target field causes the program to set the target equal to the variable’s suggested value, which is defined below.
• Importance weight: represents the policy variable’s importance in the optimization. A * in the weight field cause the program to require the target to be achieved exactly.

Three model-determined figures also are associated with each policy variable.

• Upper bound: the optimizer will ensure that the policy variable remains below the upper bound.
• Lower bound: the optimizer will ensure that the policy variable remains above the lower bound.
• Reference value: Suggests a figure for the player to use as the target. The figures may vary over time due to endogenous or exogenous factors. The source of the information is displayed to the right of the "suggested value" field:

• tuition growth: an average of the recent growth in the player-generated institution’s peer institutions; the definition also applies to the indirect cost rate and faculty and staff salary growth;
• financial aid: the amount needed to fund the extra aid that will be triggered by the target tuition growth rate and any changes the player has made to financial aid policies.
• endowment spending rate: the value needed to achieve long-run financial equilibrium given the target cost-rise figures;
• other cost-rise: the projected growth rate of the "other expenditures" category;
• net operating budget growth: the value used in the aforementioned financial equilibrium calculations;
• transfer to plant growth: real cost-rise on construction projects;
• surplus/deficit: equals zero.

The model uses quadratic programming to minimize the weighted sum of squared differences between the actual values of the policy variables and their targets. The upper and lower bounds enter the quadratic program as inequality constraints. Equality constraints are added where necessary to handle any policy variables whose targets must be achieved exactly. Relationships among the policy variables and the underlying financial variables enter as additional equality constraints. For example, if the base year’s tuition rate is $10,000, the policy for real tuition growth is 2.5 percent, and inflation is 5 percent, the new tuition rate would be $10,750. The surplus or deficit implied by a given setting of the decision variables equals total revenue minus total operating expenditures, debt service, and transfer to plant.

It is anticipated that the game will be programmed to allow players to perform sensitivity analyses with different weights, targets, and bounds. Players should also be able to advance from year to year without having to change any of the policy variables. An automatic mode also may be offered that bypasses the budget screen(s) altogether.

The second step in allocating resources is to allocate budget adjustment amount, as calculated by the previous component, among alternative expenditure categories. The expenditure categories, called "functions" in university accounting jargon, are listed in Table 5. The table contains the same columns as Table 4, except that "suggested value" has been replaced by "absolute minimum value." The targets and bounds may be positive or negative, depending upon whether the function is to be expanded or contracted. The percentage changes represent shifts from the prior year’s levels of operation.

Most of the expenditure functions are self-explanatory, but the two involving departments require a brief explanation.

• Faculty FTEs: funds allocated to support faculty lines in both the regular and auxiliary faculty ranks. For example, a value of +1.5 percent would authorize an increase in faculty size of roughly that amount, depending on the rank and salary of the person hired. (The change is calculated in dollars, not FTEs, so its exact value depends on average salaries.) Negative values indicate decreases in faculty size.

• Non-faculty departmental expense: all funds flowing to departments except those for faculty lines. These expenses comprise the "staff" and "other expense" columns of Table 2’s "academic departments" line.

The model again makes use of quadratic programming to minimize the weighted sum of squared deviations of the allocations from their targets, subject to certain constraints. The primary constraint forces total net operating budget growth to equal the amount determined by the aggregate revenue and expenditure model. Both sums are evaluated as dollar quantities, not as percentages. The dollars may be positive or negative depending on whether the institution is expanding or contracting in real terms. The upper and lower bounds are applied as additional constraints, as are any requirements that the targets be achieved exactly, just in the aggregative revenue and expenditure model.

The quadratic program produces growth or reduction percentages for each expenditure function. These may be closer or further from their targets depending upon the targets’ consistency with the overall budget adjustment figure.

Applying these percentages to the prior year’s expenditure base gives the dollar value of the real budget increment or decrement for each function. The model assumes that the increment or decrement divides itself between salaries and other expenses in proportion to the existing base after adjustment for salary increments and cost-rise. (The exception is faculty salaries versus other departmental expenses, which are treated explicitly in the optimization.) Adding the real increments and decrements to the adjusted budget base produces the new budget, which can displayed according to the format of Table 2.

The aggregate revenue and expenditure model determines the overall level of faculty salary growth, but it is silent as to how this sum should be allocated across departments and faculty groups. The default will be to apply the same percentage increase figure everywhere. Depending on resources, we may consider allowing the player to override the default percentage and apply his or her own percentage to one or more departments, faculty groups, or department-group combinations. The remaining departments and groups will receive a new default percentage, determined by deducting the dollar values produced by the player-determined from the overall salary pool and then dividing by the remaining salary base. (To be designed, prototyped, and written up.)

The budget model’s remaining task is to allocate expenditures on faculty, as determined previously, among departments. In the aforementioned example, how much of the 6.5 percent increase in faculty expenditures should go to the English department? The Pphysics dDepartment?

The model’s first step uses average salaries to convert from expenditures to FTE numbers. Then it optimizes the number of FTEs to be assigned to each department, taking attrition, the continuing faculty base, and the expenditure limit into account. Finally, the number of new hires permitted each department can be determined by comparing the optimal FTE numbers with the continuing base.

The departmental allocations are based on the department’s teaching load, its relevance to institutional mission, its sponsored research volume, and the year-to-year change in faculty size.

• Teaching load: the difference between teaching loads as computed based on departmental enrollments and the department’s normal teaching load. Massy and Zemsky define departmental "utility," a construct that combines morale with concerns about faculty utilization, as a non-linear function of the ratios of teaching load and average class size to their norms. Practicality dictates that the Higher Education model approximate the above with the percentage deviation of teaching load from its norm, assuming the course mix as fixed and that all classes operate at their average class sizes. The teaching load deviation is recalculated according to the following procedure each time the optimization considers a new faculty staffing pattern. The calculations proceed as follows:

• Mission relevance: some departments will be viewed as critical to the institution’s mission, while others will be viewed as peripheral. The model reflects these differences by assigning a "mission relevance" parameter to each department. This will bias the hiring decision toward high-relevance departments, other things being equal. Suppose, for example, that chemistry is judged to be more mission-relevant than sociology. If the departments are about equal in teaching and sponsored research load, the incremental new hire would go to chemistry.

• Sponsored research performance: the ratio of sponsored research expenditures per regular faculty FTE during the base year to the average research norm for the department’s tenure-line faculty rank-age groups. The ratio, which does not change with the putative number of faculty, can be viewed as an adjustment to the mission relevance parameter.

• Year-to-year change in faculty FTEs: the percentage by which the putative staffing level would change the departmental faculty roster. Abrupt changes in a department’s FTEs can be highly disruptive so the model provides the player with an opportunity to smooth any transitions by deterring abrupt changes.

The budget model calculates the departmental teaching and sponsored research loads and the year-to-year staffing changes from data provided by the academic operations model. The mission relevance weights are policy parameters which are provided initially in the initial conditioins and which may be changed by the player at any time. The player can steer the allocation of new hires, including those that replace faculty who have departed, by adjusting importance weights for teaching load, mission relevance, sponsored research, and year-to-year staffing changes.

The faculty hiring optimization again is performed by quadratic programming. The following terms enter the objective function for each department:

• the squared percentage deviation of teaching load from its norm;
• the squared percentage change of FTE numbers from year to year;
• the mission-relevance parameter times the number of faculty;
• the ratio of per-faculty sponsored research dollars to its norm times the number faculty.

The first two terms are quadratic in the decision variable and the last two are linear. The quadratic terms enter the objective function with positive weights because the deviations from norms are to be minimized. The linear terms enter with negative weights because the program rewards mission relevance and sponsored research. The program minimizes the objective function subject to constraints.

The primary constraint requires that the expected total faculty salary cost equal the sum set aside for this purpose in the budget adjustment allocation. The resultant faculty size for each department also is constrained to be no less than the number of continuing FTEs. The number of new hires authorized for each department equals the resultant total faculty FTEs minus the continuing FTE base. The new hire figures are passed on to the faculty hiring component of the faculty FTE model, which produces the faculty roster for the year just budgeted.

While not part of the budget model, per se, this is an appropriate place to describe the asset allocation and total return model. (Total investment return is an input to the budget model.)

The player will be asked to describe how the institution’s endowment assets should be allocated among the following asset categories: (i) large-company stocks; small-company stocks; and (iii) bonds. This determination should be built into the player interface. Changes in asset allocation can be introduced any time, but they will not take effect until the beginning of the next fiscal year.

The allocation determines the expected real value and standard deviation of total return according to a function to be provided. The simulated total return for a given year will be determined by drawing a random number from a log-normal distribution with mean equal to the inflation rate plus the expected total return, and the given standard deviation. By managing asset allocation, players will learn that boosting total return—as may be achieved by upping the percentage of stocks (particularly small-company stocks)—comes at the price of increased risk.

The institution’s credit rating determines the total amount of debt that can be outstanding at a given time. For simplicity, we make no distinction between plant debt, residence hall debt, and bank debt. (Bank debt exists when the operating reserve balance is negative.) The institution’s borrowing limit represents the difference between its overall debt capacity and the debt currently outstanding.

Pending further research, the debt limit will depend on the four asset category balances shown on the left side of Table 1 and the fraction of total funds usage in Table 2 represented by debt service. The first quantity will be obtained by multiplying each asset balance will by a constant and summing. For example, the debt limit based on assets might be:

The borrowing limit based on debt service will be obtained by determining how much debt could be added without causing the debt service percentage to exceed a predetermined limit. The limit will be calculated and reported using both the long-term and short-term interest rates.

The player’s main budget decision comes near the end of each fiscal year and takes effect at the beginning of the next fiscal year. (The fiscal year runs from July 1 to June 30.) However, it may be desirable to follow established practice and give the play an opportunity to adjust the budget during the course of the year. This would allow a quick reaction to adverse circumstances or windfalls, thus speeding up the pace of response and helping the player maintain a sense of control.

Because the overall budget model is too complex to run more than once a year, the mid-year interventions will be constrained as follows.

1. Changes will be limited to the expenditure side of the budget; no changes in any revenue variables will be allowed.
2. Expenditure changes will be limited to variables that: (i) do not exert a direct effect on revenue; (ii) do not represent contractual commitments. This rules out expenditures on institutional advancement and intercollegiate athletics (because the functions that determine their effects on income run only at the beginning of the year); faculty and staff salary increases (which have already been implemented); sponsored research (governed by grant and contract requirements); faculty FTEs (which are governed by contracts with a minimum duration of one year); and debt service.
3. Players will be allowed to input dollar adjustments for any of the rows in Table 2 except those in the above list. This includes the transfer to plant. The changes will be prorated between staff other expenses (changes in the faculty column are precluded). They can be positive or negative, and they can be initiated at any time.
4. The changes will induce positive or negative effects on performance in the relevant functions—e.g., on the effectiveness of student life activities, administration, and O&M. The change in the relevant index values will take place immediately, and thus will influence the variables and events that depend on the indices. Examples include changes in student morale and adverse administrative outcomes.
5. Reduction in expenditures on staff will have an instantaneous adverse effect on staff morale (see paragraph 7.3 of Technical Document 2.5) because of the implications for workload expansion and possible layoffs. The morale shifts will affect all expenditure functions except those listed in (2). The size of the effect on morale will depend and the amount of time remaining before the end of the year as well as on the amount of reduction. For example, a 2 percent overall cut eight months into the year will require a 6 percent expenditure reduction during the remaining four months.
6. The midyear budget adjustments will affect the surplus-deficit for the year. If the adjustment involves the transfer to plant, the plant balance also will be updated. (The program should reject a downward transfer to plant adjustment if that would cause the plant balance to become negative.)
7. The mid-year budget adjustments also will affect the continuing budget base used to launch the following year’s resource allocation process. Changes in circumstances that might trigger a mid-year adjustment also will be reflected. For example, an enrollment drop may induce the player to initiate a mid-year administrative expenditure reduction. The reduction will be reflected in the ongoing expenditure base and the enrollment drop will be reflected in the revenue forecast. Alternatively, players may wish to plan for a modest budget surplus that can be eaten up during the year as they allocate "one-time money" to respond to problems. The changes will be reflected the next year’s continuing expenditure base.

1. See paragraph 2.5 of Technical Document 2.2.
2. See William F. Massy, Endowment: Perspectives, Policies, and Management (Washington, D.C.: Association of Governing Boards of Universities and Colleges, 1990), or David S. P. Hopkins and William F. Massy, Planning Models for Colleges and Universities (Stanford, CA: Stanford University Press, 1981).
3. The deviation for the surplus/deficit is scaled to be a percentage of the prior year’s total expenditures.
4. Sponsored research requires special treatment because it is an exogenous variable determined by the market rather than directly by institutional policy. The actual amount of sponsored research will be calculated by the academic operations model after the aggregate revenue and expense model determines the indirect cost rate. However, the budget model must project the indirect cost rate’s effect on sponsored research volume because this sum is included in total revenue. Then it uses the indirect cost rate to divide projected total sponsored research into its direct and indirect components. Both the direct and indirect components count in total revenue. However, only the direct component counts on the expenditure side of the surplus/deficit calculation.

The model considers a certain portion of direct sponsored research expenditures to be used to offset academic year faculty salaries. The offsets are shown in the "faculty" column of Table 2’s sponsored research line. This amount needs to be escalated by the growth rate of faculty salaries. However, the growth rate of direct sponsored research expenditures may not equal the faculty salary growth rate. The dollar value of any such difference reverts back to general funds in the surplus-deficit calculation. Suppose, for example, that the offsets would have to grow by 5 percent because of salary increases, but direct sponsored research will grow by only 4 percent. The resulting gap, which is 1 percent of the $5,143 (thousand) shown in Table 2, amounts to a little over $50 thousand. The model will add this to the "departmental" line before calculating the surplus/deficit.

5. New hires will be costed according to the average salary for the department’s existing faculty base. A more precise method would use the weighted average salary by rank-age grouping using by the relative hiring preference for the rank-age groupings, discussed in Technical Document 2.2, as weights. Either way, the hiring model will produce inhires in the specific rank-age categories. Each inhire will have a specific salary, which may or may not correspond to the costing figure used in the resource allocation model. Consistent with real life, such discrepancies will result in small budget variances the following year. The difference in methods also will produce small variations.
6. William F. Massy and Robert Zemsky, "A Utility Model for Teaching Load Decisions in Academic Departments" (Economics of Education Review, November/December, 1997, forthcoming).
7. See Section 4.2 of Technical Document 2.2.