A Decision Support Model for Salary Structure Design

Introduction

At the core of many organizations’ compensation system is a salary structure, whose design involves balancing market and internal considerations.^1,2,3 To take proper account of market considerations, it is important to use current and accurate market data to compare internal salaries against market salaries for comparable jobs and to gauge and establish an organization’s relative pay position vis-à-vis the market. ⁴ Internally, making pay equitable to the internal worth of jobs, as assessed, for instance, based on job evaluation, is a major consideration. There is, however, a degree of tension between market and internal considerations, with the consequence that organizations may need to “sacrifice their ideals (if they have them) of internal equity to the realism of the marketplace.”^5(p97)

Generally, given an organization’s grade structure and a market reference salary for each grade, designing a salary structure to achieve market position and internal equity objectives involves defining salary levels, salary range spread, midpoint salary differential and overlap.^6-9 Salary range spread defines the width of a salary range and is measured by the percentage difference between a grade’s maximum and minimum salaries. It defines the scope that should be allowed for performance, contribution or career progression within grades. ¹⁰ Whereas range spread refers to the horizontal salary difference within the same grade (holding the job size constant), midpoint differential refers to the degree of salary difference between a grade above and a grade below (i.e., for different job sizes). It is measured by the percentage difference between the midpoint salaries of two successive grades. In principle, midpoint differential should be proportional to the change in scope of responsibility, contribution, talent scarcity and effort between consecutive jobs.^11,12 Finally, overlap measures the extent to which the salary ranges of two adjacent grades coincide. Ideally, it should be proportional to the extent to which a highly experienced employee at the top end of the range in the grade below can contribute more than a junior employee in the grade above.

These structural parameters determine the degree of equity and the premium for various job and personal attributes. For instance, wide spread can lead to lack of equity; while narrow spread can limit career progression and recognition of performance. Similarly, too low differential may make promotion to higher grades unattractive, whereas too high differential may result in paying too much for insignificant change in responsibility.^13-15

The appropriate levels of the parameters may differ from organization to organization, subject to the attributes of each organization, such as organization size, culture, industry and so on.^16-21 Furthermore, organizations may require the parameters to be in certain patterns, such as when salary range spreads should not decrease with grade.^22,23 Such requirements add more complexity to the salary structure design problem.

Several studies indicate that organizational pay policies and the resulting pay variations can significantly influence individual and organizational performance.^24-30 Furthermore, the salary structure serves as a foundation for the design of other compensation and benefit plans. These observations show the value to be had from careful design of the salary structure. Surprisingly, this aspect seems to be given little attention in management science research, ³¹ leaving practitioners with limited tools to address the aforementioned design issues.

To enhance clarity and make more reasonable trade-off between internal and market considerations, or more generally to improve efficiency and quality in salary structure design, it is important to develop models that are easy to implement. This article develops one such model, the essence of which is best summarized by Armstrong’s^32(p98) description of the pay management process:

The pay management process must cope as best it can when the irresistible force of market pressures meets the immovable object of internal equity. There will always be some degree of tension in these circumstances and, while no solution will ever be simple or entirely satisfactory, there is one basic principle that can enhance the likelihood of success. That principle is to make explicit and fully identifiable the compromises with internal equity that are made and have to be made in response to market pressures [emphasis added].

Previous work on the development and implementation of models for salary structure design is rare. To our best knowledge, an exception is Bruno, ³³ who formulated a model for positon–salary design in school districts. The main purpose of his model was to derive weights for job-relevant factors to be used in determining salaries for different job categories. This is different from the aim of the model presented in this article. More important, Bruno’s model didn’t incorporate market considerations, whereas the trade-off between market and internal equity considerations is the focus of the model we present in this article. Despite these key differences, Bruno’s early interest in the area and his good initial model seem to be overlooked.

The remainder of the article is organized as follows. The model for salary structure design is presented in the Model Formulation section. In the Application section, the actual application of the model in one organization is discussed. In the Conclusion section, concluding remarks including potential extensions to our model are forwarded.

Model Formulation

We start by defining the grade structure and related parameters.

Note that grades are usually defined based on job evaluation scores and reflect internal worth (size) of jobs, where jobs within the same grade are assumed to have equivalent size. On the other hand, the market reference salary is based on the market rate of jobs within a grade and reflects the external worth of the jobs. As often happens to be the case, there can be a mismatch between the internal and external values of jobs, which brings conflicting considerations in salary structure design.

The two primary variables for our purpose are as follows:

Using these, we define four related variables: midpoint salary, range spread, differential and overlap.

The midpoint salary in a grade is the average of the grade’s maximum and minimum salaries:

A j = ( L j + U j ) / 2 A j = Midpoint salary in grade j ∈ J

A grade’s salary spread measures the width of the grade’s salary range. Mathematically,

μ j = ( U j − L j ) / L j μ j = Range spread in grade j ∈ J

Midpoint differential is the difference between the midpoint salaries in a grade above and a grade below:

α j = ( A j − A j − 1 ) / A j − 1 α j = Midpoint differential between two successive grades j , j − 1 ∈ J , j > 1

Our final variable is overlap. A common measure of overlap between two successive grades is the difference between the maximum salary in the grade below and the minimum salary in the grade above expressed as a percentage of the difference between the maximum and minimum salaries in the grade below. ³⁴ This measures the percentage of the salary range in the grade below that coincides with the salary range in the grade above. Alternatively, we can use the difference between the maximum and the minimum salaries in the grade above as the denominator to get a measure of overlap that is interpreted as the maximum percentage that the salary of a highly experienced staff in the grade below can go into the salary range in the grade above. We prefer this alternative measure and its interpretation. Using our alternative measure, the overlap between two successive grades is thus:

σ j = ( U j − 1 − L j ) / ( U j − L j ) σ j = Overlap between two successive grades j , j − 1 ∈ J , j > 1

To provide context, we present first the original salary structure design problem, which is a direct translation of the verbal description of the problem and is to be distinguished from the reformulations that we present later. Model I below is the original salary structure design problem.

Minimize θ 1 = ∑ j = 1 n S j A j

(1a)

subject to

M j ( 1 − δ j l ) ≤ A j ≤ M j ( 1 + δ j u ) , for ∀ j ϵ J

(1b)

R j ( 1 − γ j l ) ≤ μ j ≤ R j ( 1 + γ j u ) , for ∀ j ϵ J

(1c)

D j ( 1 − β j l ) ≤ α j ≤ D j ( 1 + β j u ) , for ∀ j , j − 1 ϵ J , j > 1

(1d)

O j ( 1 − τ j l ) ≤ σ j ≤ O j ( 1 + τ j u ) , for ∀ j , j − 1 ϵ J , j > 1

(1e)

μ j − 1 ≤ μ j , for ∀ j , j − 1 ϵ J , j > 1

(1f)

α j − 1 ≤ α j , for ∀ j , j − 1 ϵ J , j > 1

(1g)

A j , μ j , α j ≥ 0 δ j l , γ j l , β j l ϵ [ 0 , 1 ] and δ j u , γ j u , β j u , τ j l , τ j u ≥ 0

The parameters in the last line are the possible deviations from the targets for the corresponding policy parameters. We allow them to assume the technically feasible set of values only for the sake of generality. In practice, the restrictions on the possible deviations from the policy targets are usually very tight.

The objective is to minimize total salary costs. Equation (1b) defines the requirement that the midpoint salary should fall within a defined range of the target midpoint salary for each grade. Equation (1c) to Equation (1e) similarly define the values allowed for the salary range spread, midpoint differential and overlap, respectively. Equations (1f) and (1g) specify the requirement that the salary range spread and the midpoint differential, respectively, cannot decrease with grade.

It may be difficult to fulfill all the requirements in Model I, as no feasible solution may exist that satisfies all the restrictions. Our next reformulations allow us to avoid this difficulty and solve the problem more efficiently. Our main strategy is to reformulate the problem into a goal-programming model. For this, we need the following deviational variables and associated penalties.

Model II below is a reformulation of the salary structure design problem.

Minimize θ 2 = ∑ j = 1 n S j A j + ∑ j = 1 n c j + p j + + c j − p j − + ∑ j > 1 n w j + d j + + w j − d j −

(2a)

subject to

A j + p j − − p j + = M j , for ∀ j ϵ J

(2b)

A j − ( 1 + D j ) A j − 1 + d j − − d j + = 0 , for ∀ j , j − 1 ∈ J , j > 1

(2c)

A j − k 1 M j ≥ 0 k 1 ≥ 0 , for ∀ j ∈ J

(2d)

A j − k 2 A j − 1 ≥ 0 k 2 > 1 , for ∀ j , j − 1 ∈ J , j > 1

(2e)

A j − 1 A j + 1 − A j 2 ≥ 0 , for ∀ j ∈ J , j > 1 , j < n

(2f)

p j + , p j − , d j + , d j − ≥ 0

The model objective function (Equation 2a) has three components: total salary cost (the first term), costs associated with deviations from market competitiveness goals (the second term) and, finally, the third component that captures the penalties/costs associated with deviations from the internal equity (midpoint differential) goals. In the next section, we describe our approach for deriving the penalties associated with the two goals.

Equations (2b) and (2c) define the midpoint salary and midpoint differential goals, respectively. Equations (2d) and (2e) specify minimum acceptable midpoint salaries and differentials, respectively. Exclusion of either or both of these requirements does not do much damage to solution quality if the weights for the goals are carefully chosen. They can be viewed as minimal requirements for an acceptable salary structure and can be used to ensure that the midpoint salary and midpoint differential goals are not pursued beyond what could be reasonably acceptable to the organization. Equation (2f) defines the requirement that midpoint differentials should not decrease as grade increases. We use it in the application presented in the next section, but it may be appropriate only when it is required by the particular organization. Note that we have not incorporated the range spread and overlap-related requirements that appeared in the original problem. It is easy to show that range spreads can be freely determined according to organization policy once we derive optimal solution for midpoint salary and differential (see below). Moreover, once differential and range spread are defined, overlap is fully determined.

Model II is a nonlinear model, only because of the requirement that the differentials should not decrease with grade (Equation 2f). By dropping this requirement, we can get a simple linear model with fewer constraints. We will refer to this as Model III and compare it with Model II in the application presented in the next section. Model III may suffice for most practical purposes, unless the differential pattern requirement is critical.

After the optimal midpoint salaries and midpoint differentials are obtained using either model, we can choose the desired spreads freely and then determine the minimum (L) and maximum (U) salaries as follows:

where the bars on the variables indicate that these are the optimal values.

Alternatively, for the original target range spread (R), which was defined relative to minimum salary, we could have defined an equivalent range spread relative to midpoint salary by the following relationship:

ρ j = R j / ( 2 + R j ) ρ j = Range spread defined as a percentage of midpoint salary of grade j ϵ J

In this case, the minimum and maximum salaries can be determined as follows:

L ¯ j = A ¯ j ( 1 − ρ j ) U ¯ j = A ¯ j ( 1 + ρ j )

In practice, going from the range spreads relative to minimum salary to the range spreads relative to midpoint salary rather than simply beginning with the latter may be appropriate. For many managers, defining the range spread relative to the minimum salary is the more convenient and customary one. Curiously, it is not uncommon to speak to managers who are accustomed to defining range spreads relative to midpoint salaries. The relationships shown above are thus useful when designing salary structures in both environments.

Last, overlap can be determined using the midpoint differential and salary range spreads by the following relationships:

σ ¯ j = ( U ¯ j − 1 − L ¯ j ) / ( U ¯ j − L ¯ j ) = ( R j − 1 + R j ( 1 + R j − 1 ) − d ¯ j ( 2 + R j − 1 ) ) / ( R j ( 1 + d ¯ j ) ( 2 + R j − 1 ) ) j ∈ J , j > 1

Similarly, to obtain the implied overlap target (O), rather than the implied solution (σ), one can use the second formula above after replacing the model derived midpoint differential (d) by the target differential (D).

The fact that overlap can be determined once midpoint differential and range spread are chosen does not mean that organizations need not bother about the degree of overlap in their salary structures. Instead, managers should recognize that while setting targets for midpoint differential and salary range spread, they are implicitly setting their targets for overlap. More generally, when setting targets for the three parameters, there are only two degrees of freedom. While managers may prefer to set their overlap targets directly, this principle still holds: The targets for overlap and one of the other two parameters can be freely set, and the remaining parameter’s target is implicitly defined.

Application

This section presents key results from an application of the model in developing one organization’s salary structure. The input data used in this application are shown in Table 1.

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Table 1.

Input Data Used for Designing the New Salary Structure.

Grade	Target midpoint salary (M; currency unit)	No. of employees (S)	Target range spread (R; %)	Target midpoint differential (D; %)	Target overlap (O; %)
18	84,261	1	95	15	73
17	66,578	4	95	20	64
16	51,666	3	90	15	72
15	45,206	12	90	20	65
14	38,676	33	90	20	63
13	31,836	17	85	20	64
12	26,383	84	85	20	64
11	22,271	18	85	20	64
10	18,277	50	85	20	62
9	15,255	83	80	20	63
8	12,720	78	80	20	63
7	10,531	132	80	20	63
6	8,493	396	80	20	63
5	7,087	219	80	20	63
4	5,840	41	80	20	63
3	4,993	37	80	20	63
2	4,004	159	80	20	63
1	3,374	90	80	NA	NA

Note. Target overlap is implicitly derived based on the target range spread and target midpoint differential, using the relationships discussed earlier. NA = not applicable.

The target midpoint salaries (the reference salaries) are average salaries paid in the market for comparable jobs in relevant benchmark organizations that operate in the same industry or region as the focal organization. The existing salaries paid in the organization were significantly below the market salaries paid for comparable jobs. Competitors were offering generous salaries to attract key employees, and in fact, the organization was losing increasing number of key employees to competitors. This led to the need for redesigning the organization’s salary structure. Since the organization was also undergoing restructuring, the management used the opportunity to correct anomalies in aspects of their existing salary structure such as differential and range spread.

Perhaps the main practical challenge in implementing the model lies in defining the weights for the subgoals in the objective function. Though our approach to weight assessment is less sophisticated, for completeness, we briefly describe it as follows.

We began by assessing the priority weights for the three component objectives in the objective function: salary costs, deviations from target midpoint salary and deviations from target midpoint differential. Our approach roughly resembles the well-known analytic hierarchy process for weight determination.^35,36 We assessed the relative importance of the three objectives on a rating scale and used these ratings to derive priority weights. For convenience, we normalized these priority weights relative to the weight for the salary cost minimization objective (thus, the normalized weight for salary cost minimization objective is 1).

Moving down one level on the objective hierarchy (in the fashion of analytic hierarchy process), we next specified weights that captured differences in the importance accorded to grades with respect to each of the three component objectives. For instance, if deviation from target midpoint salaries (the second subgoal) are less acceptable for higher grades than for lower grades, then the corresponding penalty weights should be greater for higher grades. To this end, we used a fixed number of points (n − 1 points for the midpoint differential objective, and n points for the remaining objectives) for each of the three objectives and allocated them across grades: giving us the within-objective priority weight for each grade. For the salary cost minimization objective, this is straightforward: We simply assigned 1 point to each grade (every extra expense is equally unacceptable regardless of the grade incurred by it). For the remaining goals, any desired preferential treatment of some grades with respect to a goal is taken care of by allocating greater points to these grades (and proportionately smaller points for the other grades) and ensuring that the total points allocated to all grades equal the fixed number of points corresponding to each goal. For instance, if deviations from target midpoint salaries are equally (un)acceptable for all grades, the n points are allocated in such a way that each grade receives 1 point. On the other hand, if deviations from targets are less acceptable for some grades, then these grades get more than 1 point (and to compensate for this, some other grades get less than 1 point).

Last, we derived the final penalty weights corresponding to each grade for each of the three objectives/goals. This involved multiplying three numbers for each grade: the objective weight (Step 1), the within-objective point allocated to a grade (Step 2) and the number of employees in a grade. Obviously, number of employees is the only penalty parameter corresponding to each midpoint salary variable in the salary cost minimization objective (since we normalized the weights for the three objectives relative to the salary cost minimization objective weights, the objective weight for the salary cost objective is 1, and the within-objective weight is also 1 point for each grade). For the other two goals, the final penalty for each grade depends on the number of employees in a grade and the within-objective points allocated to a grade. Also, for these two goals, when there are differences in the desirability of positive deviations and negative deviations from target, we discount the final penalty weights by a certain percentage for the more acceptable deviation.

One of our anonymous referees suggested to us to provide guidance on how to construct the salary policy parameters. Since this is a well-developed topic, for the sake of brevity, we rather refer the reader to Armstrong ³⁷ and Armstrong and Cummins ³⁸ for detailed guidelines on how to set the relevant policy targets such as market pay position, midpoint differential and range spread.

Turning now to the solutions, we solved the two models using the AMPL-Minos package. AMPL provides an interactive command environment for setting up and solving mathematical programming problems. For each of our models, AMPL reads the commands and model elements from the respective text files and the relevant data from intermediary Excel files. By using the solve command in AMPL, the required processes can be invoked. First, the command causes AMPL to generate specific instances of optimization problems and data that were supplied. After the optimization problem has been generated, AMPL enters a presolve phase in which it tries to simplify the problem for the solver, thus making it easier for the optimizer to find solution. Next, AMPL sends the generated optimization problem, possibly modified by presolve, to the Minos solver. The solver works with the preprocessed optimization problem and generates optimal solution values. ³⁹

Table 2 shows the solutions for the two models. For each grade, minimum, midpoint and maximum salaries, as well as range spread, midpoint differential and overlap are indicated. The minimum salary in a grade is what entry level employees make. The midpoint is the rate for a fully competent individual who is completely qualified to carry out the job. An employee’s salary can go up to, but not beyond, the maximum salary.

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Table 2.

Salary Structures Derived From the Solutions to Models II and III.

Grade	Model II						Model III
	Min salary (L)	Midpoint salary (A)	Max salary (U)	Range spread (µ; %)	Midpoint differential (α; %)	Overlap (σ; %)	Min salary (L)	Midpoint salary (A)	Max salary (U)	Range spread (µ; %)	Midpoint differential (α; %)	Overlap (σ; %)
18	57,126	84,261	111,396	95	24	60	57,126	84,261	111,396	95	27	57
17	45,987	67,831	89,674	95	21	63	45,138	66,578	88,018	95	25	58
16	38,768	56,213	73,659	90	21	64	36,809	53,373	69,937	90	15	72
15	32,128	46,585	61,043	90	20	64	32,008	46,412	60,815	90	20	65
14	26,673	38,676	50,679	90	20	63	26,673	38,676	50,679	90	20	63
13	22,533	32,110	41,687	85	20	63	22,618	32,230	41,843	85	22	61
12	18,708	26,658	34,609	85	20	63	18,515	26,383	34,252	85	20	64
11	15,532	22,132	28,733	85	20	63	15,429	21,986	28,543	85	20	64
10	12,895	18,375	23,855	85	20	61	12,846	18,306	23,766	85	20	62
9	10,897	15,255	19,614	80	20	62	10,897	15,255	19,614	80	20	63
8	9,047	12,665	16,284	80	20	62	9,085	12,720	16,354	80	21	61
7	7,511	10,515	13,519	80	20	62	7,522	10,531	13,540	80	24	57
6	6,236	8,730	11,224	80	20	62	6,075	8,505	10,935	80	20	62
5	5,177	7,248	9,318	80	20	62	5,062	7,087	9,112	80	20	63
4	4,298	6,017	7,736	80	20	62	4,219	5,906	7,594	80	18	65
3	3,568	4,996	6,423	80	20	62	3,567	4,993	6,420	80	23	57
2	2,962	4,147	5,332	80	20	63	2,892	4,049	5,206	80	20	63
1	2,469	3,456	4,444	80	NA	NA	2,410	3,374	4,338	80	NA	NA

Note. Max = maximum; Min = minimum; NA = not applicable.

The differences in the salary figures under the two models indicate how policy differences can lead to significant consequences. In Grade 16, for instance, the starting salaries under Models II and III are 38,768 and 36,809, respectively. Not a small difference, especially from employees’ perspective. Generally, depending on the importance attached to the different policy goals, salaries based on the two models can be more or less different. Thus, the chosen configuration of a few policy parameters determines the amount of money employees make, which is likely to influence employees’ attitudes and behaviors and ultimately the organization’s success. ⁴⁰ In fact, with limited salary budgets, which is implicit in our model, Bloom’s^41(p26) observation is commendable, though it paints a somewhat darker picture: “Since an organization has limited compensation resources, the distribution of pay within it is inherently a zero-sum matter.” This is why we insist on the need for a more explicit, structured and principled approach for salary structure design. We believe the model presented in this article contributes to further development toward such an approach.

To assess the extent to which the targets for the structural parameters were met under the two models, we compared the model-derived solutions with the targets. Summaries are presented in Table 3.

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Table 3.

Deviations From Targets Under Models II and III.

	Model II (nonlinear) (deviation from target)				Model III (linear) (deviation from target)
Summary Statistics	Midpoint salary	Range spread	Midpoint differential	Overlap	Midpoint salary	Range spread	Midpoint differential	Overlap
Average (%)	1.6	0.0	7.8	(2.7)	0.5	0.0	8.4	(3.1)
Maximum (%)	8.8	0.0	61.5	0.0	3.3	0.0	77.1	4.4
Sum of absolute deviations percentages	31.5	0.0	131.8	45.6	11.0	0.0	160.7	61.4
Weighted average a (%)	1.8	0.0	2.0	(1.0)	0.2	0.0	2.4	(1.1)
Weighted sum of absolute deviation percentages a	2,776.2	0.0	2,885.6	1,390.3	370.9	0.0	4,190.4	2,019.4
Total salary costs (CU)	16,550,100 CU				16,361,800 CU

Note. CU = currency unit.

a

Calculations using number of employees in each grade as weights. The general conclusions based on the measures with and without weights are similar.

For midpoint salary, Models II and III deviated by an average of 2% and 0.5% from target, respectively. Based on the sum of absolute deviations from targets (which is a more reasonable measure of performance in this context), Model III did well. This is not unexpected. In Model II, the goals for midpoint salary are pursued only when they do not contradict the restriction on the midpoint differential pattern, and this can lead to relatively lower performance on the midpoint salary goal.

The targets for range spreads, on the other hand, were fully met in both the models. This should not be surprising because the range spreads were freely determined after the optimal midpoint salaries were known.

With regard to midpoint differential, each model produced an average deviation from the target of 8%. However, Model II fared slightly better based on sum of absolute deviations.

When it comes to overlap, since overlaps are fully determined once midpoint differentials and range spreads are specified, the performance of the two models against the overlap targets is linked to their performance on the other parameters. Specifically, the differences in the midpoint differentials produced by the two models explain the differences in the overlaps. Thus, the overlap percentages from Model II were relatively closer to the overlap targets, mirroring the relative performance of Model II on midpoint differential targets.

Finally, remember that Model II includes the constraint on differential patterns. Even if this is not the actual restriction we had for this particular application, the solutions derived based on our hypothetical restrictions are instructive. The differential patterns for the two models can be seen in Table 2. The midpoint differentials based on Model II were in the desired pattern (do not decrease with grade). This contributed to the lower performance on midpoint salary targets and the marginal (around 1%) extra salary costs under Model II.

Overall, the targets were reasonably well achieved for our present application because of the good correlations between internal worth of jobs as indicated by their grades and their external worth as indicated by the market average (reference) salaries. Usually this may not be true when, for instance, there is a mismatch between the internal and external worth of jobs. In such cases, the trade-offs between the two considerations may be more difficult to make. Our model proves to be even more valuable under such difficult situations. Considering the reasonable quality of the solutions together with the simplicity of the model, Model III is a good choice if the differential pattern requirements are not critical. The model structure and size summaries in Table 4 offer some insight on the relative complexity of the two models.

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Table 4.

Summary of Model Size and Structure.

Model	Variables		Constraints			Objective		Iterations
	Linear	Nonlinear	Linear	Nonlinear	Nonzeros	Type	Nonzeros
Nonlinear model (Model II)	70	18	52	16	204	Linear	88	1,567
Linear model (Model III)	88	0	52	0	156	Linear	88	42

Note. The number of variables and constraints shown are after the presolve stage of AMPL. For both the models, only two variables and no constraints were eliminated by presolve. We solved the two models after excluding the minimum salary requirements specified by Equation (2d).

We conclude by noting that managers sponsoring salary design projects often prefer to have at least two alternative salary structures anchored on alternative parameter configurations. This is not difficult to do: Just solve the model with the alternative parameter configurations and obtain alternative salary structures that can be submitted to higher level bodies that make final approval decisions. Actually, the evaluation of alternatives and the making of approval decisions can be significantly streamlined with the aid of the approach presented here.

Conclusion

Compensation design in general, and salary structure design in particular, is perhaps one of the few most important aspects of human resources management in modern organizations. A well-designed salary structure can support better attraction, motivation and retention of talent. Since the salary structure is often the basis for other compensation elements, its importance is significant. In view of this, a more structured and disciplined approach to the design of an organization’s salary structure has much to recommend it.

This article presented a simple model for salary structure design, which permits more explicit and reasonable trade-off between internal and market considerations. The model can be extended or modified in many ways. For instance, a cap on total salary budget or a total salary budget goal constraint can be incorporated, if desired. Rather than minimizing all deviations from the goals, it is also possible to minimize the maximum deviations from the goals as a separate model or in addition to the objectives already included in our model. In contrast to the model presented here, this formulation ensures that the deviations from the market and internal equity goals are more evenly spread across grades. Furthermore, to address more complex relationships between differential, salary level and range spreads, it may necessitate that range spreads are explicitly incorporated into the model. Another interesting extension will be to modify the model for the purpose of designing total pay structure to support in defining appropriate target pay mix (proportion of variable pay relative to salary) and total pay level and other structural attributes addressed in this article. Significant improvements might consider a model for determining optimal number of grades, midpoint salaries, salary and job size ranges for each grade, taking into consideration market pay rates and internal size of jobs.

Finally, as suggested to us by one of our anonymous referees, an interesting and important research direction would be based on the uncertainty surrounding the market reference salaries and the (uncertain) human resource consequences expected from salary adjustments (e.g., the risk of losing key employees in case the model-derived salaries are below the true market reference salaries; the risk of overpaying relative to the true market pay rate, which could be known only probabilistically when the salary structure is designed). To address these issues, researchers may use a combination of simulation/sensitivity analysis and stochastic programming.