Modeling Cost and Performance for Military Enlistment Report of a Workshop (1994) / Chapter Skim
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Part III: The Cost/Performance Trade-off Model
Part III: The Cost/Performance Trade-off Model
Pages 101-158
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From page 101... ...
The cost/performance trade-off model has been developed as a tool to aid analysts and policy decision makers in answering questions about recruit quality needs and in justifying the costs associated with selected quality mixes. Here we provide a context for the personnel planning process.
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From page 102... ...
More selective recruiting policies tend to reduce the effective size of the youth labor market from which the Services may recruit, raising recruiting costs. Presumably, the investment in higher recruiting costs resulting from a more selective policy yields a return in the form of a more capable recruit one who is more likely to complete training successfully and to perform well on the job.
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From page 103... ...
Therefore, the Services attempt to set recruit quality goals that balance the higher performance and lower attrition costs of high-quality individuals with their increased recruiting costs. Figure 1 depicts the trade-off between costs and performance that the Department of Defense faces in setting recruit quality goals.
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From page 104... ...
104 Military Performance Personnel Costs Low ~Recruit Quality Total L FIGURE 1 Accession quality cost/performance trade-off. PART III ~ High _ , Recruiting Attrition
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From page 105... ...
. It builds directly on the results from the Joint-Service Job Performance Measurement/ Enlistment Standards (JPM)
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From page 106... ...
(1993~. The second section uses the model in two different types of validation tests: comparing model results against actual accession cohorts and varying individual elements in the scenario defining an optimization run.
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From page 107... ...
Without using what must be arbitrary performance valuations, the model can be used to define the efficient cost and performance combinations, an improvement in the information currently available to policy makers.2 In mathematical terms, the model is a constrained minimization problem with the three elements: accessions by recruit quality category and occupation, which are the variables for which we solve; performance and personnel strength goals, which define the constraints on the problem; and personnel costs, which comprise the objective function. We describe the model in terms of these three elements.
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From page 108... ...
For example, all Services track enlistments separately by gender because some occupations, by regulation or statute, cannot be filled by women. Although the model would be more useful to accession planners if its recruit categories were also defined by gender, there is little research measuring the linkage between female accession quality and recruiting costs.
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From page 109... ...
Definition of Performance In the model, performance for an occupation group is the sum of expected hands-on performance test scores over the first term of service for 4 The one-digit DoD occupation codes included in the model are: infantry, gun crews, and seamanship specialists; electronic equipment repairers; communications and intelligence specialists; health care specialists; other technical and allied specialists; functional support and administration specialists; electrical/mechanical equipment repairers; craftsmen; and service/ supply handlers. 5 Specifically, a performance index based only on occupation characteristics is constructed from the performance equations described below.
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From page 110... ...
The performance value for an occupation group is the result of two calculations. The term in parentheses is the survival-weighted sum of predicted performance test scores over the first term for individuals from a particular recruit category enlisting in that occupation group.
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From page 111... ...
Measuring Performance Constructing performance values in the model would be straightforward if observations on hands-on performance test scores were available for all occupations, by recruit category and time in service. However, the cost of developing and administering hands-on performance tests limited the data available from the JPM Project.
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From page 112... ...
In contrast to the hands-on performance test scores, obtaining survival rates for the performance equation is relatively simple. Longitudinal personnel records, sorted by occupation group and recruit category, can be used to estimate the probability of survival to various time in service points.
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From page 113... ...
The job performance test data available from the JPM Project include only tests of first-term personnel within a limited range of years of service. These data are not sufficient to develop the qualityperformance relationships that would be required for members of the career force.l2 In addition, we have shown elsewhere that the accession programs generated by this type of model can depend arbitrarily on the number of fiscal years modeled, which is obviously not a desirable characteristic.
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From page 114... ...
In particular, because of the nature of recruiting costs, one must jointly solve for the cost-minimizing level of recruit quality in all occupation groups; a group-by-group approach will not work. The requirement to find a simultaneous solution to recruit quality goals increases i4Hogan et al.
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From page 115... ...
The prices of recruiting resources are i5To understand this point, consider the analytical process of finding the minimum cost level of recruit quality in a single occupation with just two recruit quality categories-high and low. Among the mixes of high- and low-quality recruits that satisfy the performance goal, the model will select that mix for which the cost per unit of performance is the same for high- and low-quality recruits.
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From page 116... ...
The advantages of determining recruiting costs from the underlying production function are threefold. First, the cost function estimates minimum recruiting costs for a particular mix of enlistments costs, a necessary input in determining the minimum personnel costs for a given set of performance goals.l6 Second, the cost function correctly captures the increasing average cost nature of recruiting costs.~7 This is particularly important given today's recruiting policy issues.
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From page 117... ...
In this section, we will use the model in two types of validation tests. Setting performance goals equal to the performance expected from the cohorts entering each Service in fiscal 1990, we compare the accession cohorts selected by the model to meet these goals at minimum cost with the actual cohorts accessed.
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From page 118... ...
To provide a common framework for comparison, "actual" man-years and personnel costs are calculated by applying the survival rates and cost functions in the model to the actual distribution of accessions by quality category and occupation group in fiscal 1990. To generate the model's selected cohort for each Service, we set performance goals for each occupation group equal to the performance expected from the actual fiscal 1990 accession cohort, constrained total man-years to equal the man-years generated by the fiscal 1990 cohort, and established minimums of 40 percent high quality for each occupation group.
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From page 120... ...
First, inaccuracies in measuring either the quality-performance relationship or recruiting costs at the occupation group level, both potential problems in the model, would cause the model to select the wrong quality content. Second, the Services' processes for setting quality goals by occupation, which are not driven solely by performance and cost considerations, may not be producing the cost-effective solution either.
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From page 122... ...
On a performance-to-cost basis, high-quality individuals are now more attractive, and the model selects a higher average quality level for the accession cohort. Mirroring this result, relatively more resources are allocated to recruiting with the lower performance goals, as recruiting budgets decrease by less than the reduction in performance goals.
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From page 123... ...
Building on the results from previous research into military job performance measurement and enlistment supply, performance equations and recruiting cost functions were estimated and incorporated, along with other information on attrition and training/compensation costs, into a nonlinear optimization model for each of the Services. Initial tests of the model are promising.
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From page 124... ...
ALTON SMITH AND PAUL F HOGAN TECHNICAL APPENDIX This appendix describes the optimization problem underlying the Accession QualityCost/Performance Trade-off Model and outlines the derivation of the recruiting cost function.
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From page 125... ...
The parameters of the quadratic are estimated by ordinary least-squares regression on a data set generated by the "true" recruiting cost function. Because recruiting costs are quadratic, we can use quadratic program
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From page 126... ...
If, during the optimization process, the trial solution varies significantly from the data used to approximate the recruiting cost function, a new approximation is calculated and the optimization is restarted. Recruiting Cost Function The recruiting cost function estimates the minimum costs of recruiting a specified number of individuals in each of the three recruit quality groups defined above.
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From page 127... ...
Substituting the first-order conditions into the recruiting budget formula, the first line in equation (6) , yields the recruiting cost function Minimum Cost Budget = c~Z(CH)
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From page 128... ...
Fernandez, Richard L., and Garfinkle, Jeffrey B 1985 Setting Enlistment Standards and Matching Recruits to Jobs Using Job Performance Criteria.
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From page 129... ...
In its primary formulation, the model solves for a recruit quality mix that is able to meet desired first-term performance goals, by occupational category, at the lowest cost. It does so by trading the additional recruiting costs for the higher expected performance levels and lower expected attrition costs associated with higher-quality recruits.
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From page 130... ...
Within this framework, a clear, formal definition of an "optimal" recruit quality mix is provided something that has been absent from much of the debate on enlistment standards and recruit quality. The model solves for a stylized optimal recruit quality mix one that minimizes the personnel costs of meeting first-term performance goals.
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From page 131... ...
In general, the higher the proportion of high-quality recruits, the greater the recruiting resources required to achieve the goals, and the larger the numbers of applicants who want to enlist but who are denied. Congress, as an agent of the taxpayers and of the citizens who are applicants for military service, must, in its oversight role, be convinced that enlistment qualification standards and quality goals are fair to the taxpayer and to the applicant.
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From page 132... ...
Over the years, it has been clear that the failure to present to Congress a rigorous method for determining recruit quality goals, based on empirical linkages between enlistment qualification criteria and subsequent job performance, has, during periods of stringent budgets, made recruiting resources and the recruit quality those resources represent a target for reductions. Without a vision of exactly what is sacrificed when recruit quality declines, the case for preserving recruiting budgets is weakened.
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From page 133... ...
First, the model provides a logical framework for discussing the determination of recruit quality goals. In the model, quality goals are determined by tradeoffs between the greater performance contribution made by higher-quality recruits, the reduced training costs that result, and the higher recruiting costs associated with higher-quality recruits.
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From page 134... ...
This linkage should shift congressional interest from a narrow focus on the recruiting budget to the broader implications of recruit quality for training costs and other personnel costs. Saving an additional $5 million in the recruiting budget by lowering recruit quality standards will be more difficult to justify if it results in an additional $7 million in training costs.
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From page 136... ...
The training costs in this highly technical area are the highest in the Army, and the differences in expected performance between higher- and lower-scoring recruits in these areas are relatively large. Hence, we find that higher-quality personnel in this category reduce the costs of achieving the overall performance goals.
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From page 137... ...
· The optimal quality mix depends, inter alla, on the state of the recruiting market, training costs, the distribution of openings among jobs, and the differences in expected performance among recruit quality categories. These propositions and others are illustrated by the preceding example, by the examples that follow in this section, and by the section on program development and evaluation.
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From page 138... ...
HOGAN AND DICKIE A HARRIS TABLE 2 Implications of a Hypothetical Reduction in the Navy Recruiting Budget Fiscal 1996 Navy Case 12% Reduction in Recruiting Budget Recruiting costs $345.1M $302.4M Accessions 68,O66 68,066 Staff years 216,813 216,813 Percent high quality 51% 38.9% Expected performance 61% 55.3% per staff-year graduates.
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From page 139... ...
This includes recruiting, training, and compensation costs of an entry cohort of about 84,900 accessions, providing approximately 245,049 staff-years of service over the first term, with an average expected performance per staff-year of about 56.2 percent. Using the model again to estimate the cost of an accession cohort with a performance level that is percent above this cohort's level, the total cost rises to $6,562.1 million.
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From page 140... ...
Do the recruiting resources programmed represent the most efficient combination of recruiting resources (recruiters, bonuses, advertising, and education incentives) to achieve programmed recruit quality goals?
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From page 141... ...
The economic assumptions for the recruiting market in fiscal l99Y are that the unemployment rate will be about 6.5 percent and the ratio of military starting pay to wages in the civilian youth labor market will be about 0.89. Given these assumptions, the recruiting cost function component of the model indicates that a recruiting budget of about $383.6 million will be necessary if the Army is to achieve a 62.2 percent high-quality mix for 67,522 accessions in the projected fiscal l99Y recruiting market.
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From page 142... ...
However, the model's solution suggests that the same level of expected performance over the first term of service can be obtained from an accession cohort that is approximately 525 accessions less and about $60 million less in recruiting costs. The reason the model is apparently able to do as much with less is that it distributes highquality recruits among the various occupational categories much differently than does the Army program.
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From page 143... ...
The recruiting cost function portion of the model can be used to analyze the effect of changes in the economic environment on required recruiting budgets. For example, the recruiting budget is based on the assumption that the civilian unemployment rate in fiscal l99Y will be about 6.5 percent and the ratio of military pay to the pay of civilian youth will remain at about 0.89.
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From page 144... ...
We illustrate its use as a development tool using a hypothetical Navy accession program. Setting Recruit Quality Goals and Resources In building the Navy accession program for fiscal l99Z, the initial guidance is that the overall level of first-term performance should be about that of the actual fiscal 1990 accession cohort, except that it should be about 20 percent smaller.
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From page 145... ...
Compared with the unconstrained case, the second case results in slightly lower quality and a slightly higher total cost. However, the differences are small and recruiting costs are actually lower in case 2.9 As a result, it is decided that the plan shown as case 2 will be brought to the Admiral for approval.
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From page 146... ...
Recruit quality, as a percentage, is higher, and expected performance per staff-year increases to 61.5 percent. The recruiting budget goes up, slightly, even though total accessions and required performance go down, because high-quality recruits become somewhat less costly at the slightly lower level of accessions.
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From page 147... ...
SETTING ENLISTMENT STANDARDS: ANALYSIS OF OCCUPATION-LEVEL ENLISTMENT STANDARDS Thus far, the applications of the model have focused primarily on higherlevel program decisions the overall recruit quality mix, recruiting resources, the nature of the trade-off between budgets and performance, and the effects of the environment on these quantities. In these areas, the model is potentially helpful in formulating recruit quality goals and the resources necessary to achieve those goals, and in understanding the linkages between recruit quality goals and measures of job performance.
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From page 148... ...
How fies, but appears especially well qualified based on his or her composite scores. Actual classification decisions also take into consideration the current staffing of the occupation, the convening dates for training classes, and the recruit's preferences, so that the matches that are made are less than perfect from the more narrow criterion of classification efficiency.
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From page 149... ...
Hence, in general, for a given composite, the higher the cutoff score, the higher the average quality of recruits entering that occupation, as measured by the AFQT. We are able to analyze the effect of job-specific enlistment standards, defined by minimum cutoff scores on relevant composites, by approximating the effect that the cutoff scores would have on the minimum proportion of high-quality recruits entering that occupational group.
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From page 150... ...
HARRIS . Comparisons of the proportion of high-quality recruits in each occupational category prescribed by the model to the proportion that occurs under current enlistment standards, under otherwise similar conditions; · The implications for overall recruit quality goals and for the costs of imposing a minimum proportion of high-quality recruits implied by current enlistment standards; and The implication for overall recruit quality goals and for the costs of raising (or lowering)
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From page 151... ...
are not in terms of AFQT scores, but rather are in the form of the proportion of high-quality recruits the proportion of AFQT Category I-IIIA high school graduates. Moreover, one of the important outcomes of enlistment standards by occupational group is the proportion of high-quality recruits that enters that occupational category, partly as a result of the standard.
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From page 152... ...
HOGAN AND DICKIE A HARRIS TABLE 14 AFQT-Equivalent Average Enlistment Standards by DoD Occupation Code Average Implied AFQT Cutoff Scores DoD Occupation Marine Air Code Army Navy Corps Force (0)
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From page 153... ...
The performance goals and performance equations in the model do not capture all of the factors that influence readiness and job performance. Enlistment standards, represented by externally imposed, minimum cutoff scores for entry into an occupation, may capture factors affecting performance and readiness that are not included in the model.
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From page 154... ...
Both the performance goals and the accession goals are held constant in the analysis. The average expected performance per staff-year in fiscal 1990 was 56 percent.
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From page 155... ...
With the reduction in enlistment standards there is a concomitant reduction in costs and the proportion of high-quality recruits accessed. Recruiting costs fall by about $72 million, compared with the case in which the original standards are imposed, and the proportion of high-quality recruits falls by about 7 percentage points.
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From page 156... ...
An implication of these results is that inefficiently high enlistment standards in one or more occupations raises the cost of high-quality recruits to other occupations, potentially reducing the proportion of high-quality recruits in those occupations below what would have been optimal in the unconstrained case. SUMMARY We have examined some potential applications of the Accession Quality Cost/Performance Trade-off Model from several different perspectives: · As a vehicle for explaining to Congress the rationale for an accession program and its relation to personnel readiness over the first term of service; .
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From page 157... ...
Clifton, D., and Sola, M 1992 Accession Quality, Job Performance, and Cost: A Cost/Performance Trade-off Model" Report No.
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