Computers ind. Engng Vol. 14, No. 2, pp. 147-152, 1988 0360-8352/88 $3.00+0.00 Printed in Great Britain Pergamon Press plc

A G O A L P R O G R A M M I N G A P P R O A C H T O J O B E V A L U A T I O N

JATINDER N. D . GUPTA a n d NAZIM U . AHMED

Department of Management Science, Ball State University, Muncie, IN 47306, U.S.A.

(Received for publication 1 May 1987)

Al~araet--Job evaluation refers to a systematic determination of the relative values of jobs in an organization. Often, jobs are evaluated based upon subjective judgement. By considering each job to consist of certain levels of different job factors, this paper develops a goal programming model to evaluate various levels of job factors. The main constraints in such a formulation are obtained by using some existing benchmark jobs. The model development and application in evaluating new jobs are illustrated by solving an example problem consisting of four factors and six levels of each factor.

INTRODUCTION

Job evaluation refers to a systematic approach to determine the relative values or worth of each job in an organization [1, p. 209]. These relative values, when translated by the organization's pay structure determine salaries paid for performing various jobs. The main goal of a job evaluation effort is to eliminate pay inequalities which may exist because of illogical structures [2, p. 361]. To achieve this goal, the job evaluation process must satisfy the following requirements: (1) provide a consistent measure of job worth which can easily be understood; (2) involve managers from its inception through its administration and subsequent revisions; (3) protect employees from favoritism, biases, and resultant pay inequalities; (4) measure the job and not the performance of the employees doing the job; and (5) adapt to broad job clusters within functional groups [3,4].

The development and administration of job evaluation program is often subjective, though several attempts have been made to make it as objective as possible [5]. For example, Charnes et al. [6] describe a linear programming model to determine executive salary. This method is extended by Llewellen [7] to develop relative weights to be assigned to points given various factors in the point system of job evaluation. However, these methods fall short of solving the practical problem because of multiple goals that need to be satisfied in practice. Further, the selection of job evaluation compensable factors is treated as a matter of management judgement based upon factors deemed necessary and appropriate to the company and the job itself. To remedy this situation, Ahmed and Waiters [8,9] propose using the linear programming approach to evaluate the relative worth of various levels of job factors by assuming that the number of steps in each job factor is finite and a linear combination of factor weights represents the worth of a job.

This paper treats the job evaluation problem as a managerial decision making situation involving multiple objectives. Extending the analytical work of Charnes et al. [6], Llewellen [7] and Ahmed and Waiters [8,9], a linear goal programming model is proposed for determining the relative worth of various levels of job factors comprising the significant portion of a job. The development and use of the proposed model are illustrated by solving the multiple objective case of the numerical example used by Ahmed [8].

PROBLEM ASSUMPTIONS AND MODEL FORMULATION

The formulation of the job evaluation problem as a goal programming model assumes that all possible factors which comprise any given job in an organization can be explicitly

147

148 JATINDER N. D. GUPTA and NAZIM U. AHMED

stated and clearly identified. Further, it is assumed that these factors are present in all jobs in a finite number of levels (or steps). In addition, it is assumed that a number of benchmark jobs are available for which management has already made some judgement as to their approximate worth. With these assumptions, consider a simple example where an organization's jobs may be evaluated in terms of the following four factors:

Factor A: Factor B: Factor C: Factor D:

Complexity of duties Education Necessity of supervision Mental and/or visual demands

Further, assume that each factor has six levels as follows:

Al, A2, A3, A4, As, A6, B l, B2, B3, B4, Bs, B6, C1, C2, C3, C4, C5, C6, DI, DE, D3, Da, D5, D6.

where the notation Xi means the relative worth of the i-th level (step) of factor X. The higher the level of a factor in a job, the more complex the task. Thus, Ai means

least complex and A 6 means most complex, B1 means that the job needs minimum education, B6 means that the educational needs are greatest. C~ means maximum amount of supervision necessary and C6 means least amount of supervision necessary, D t means least mental and/or visual demand necessary and 0 6 means most visual and/or mental demand needed.

After defining the factors and levels, the next step is to select some benchmark jobs with known levels of different factors associated with each benchmark job. Assume that the top labor grade job in that organization consists of factors and levels A6, Bs, C6, D6. Let the total score for this top grade job be 100. Then, the sum of scores for various levels of factors comprising this top labor grade job must satisfy the following equation:

A 6 + B s + C 6 + D 6 = 100 (1)

which means that the scores A6, B5, C6, D6 adds up to 100 points. In a similar fashion, equations for four other known jobs can be written as:

A5 + B5 + C4 + D5 = 88.4 (2) A4 + B4 + C4 + D3 = 73.8 (3) A 3 + B 3 + C 3 + D 3 = 64.7 (4) A1 + B2 + C3 -Jr- D 2 = 58.7 (5)

where equation (2) means the second benchmark job consists of the 5th level of factor A, the 5th level of factor B, the 4th level of factor C, and the 5th level of factor D. Also, the total compensation for the second job is 88.4% of the first job. Amongst the five benchmark jobs, job 1 is paid the highest while job 5 being paid the lowest.

Now, it is unlikely that the score structure in an organization absolutely satisfies equations (1) through (5). These are the goals for each of the jobs, but some deviations will invariably exist. These deviations from goals have to be permissible for an organiz- ation to function. Let d~, d~, d~, d~, d~ be the positive deviationai variables indicating that the total job scores stated in equations (1) through (5) are the least acceptable scores. Then, the system of equations (1) through (5) can be written as the goal programming constraints as below:

A 6 + B 5 + C 6 + D 6 - d ~ ' - - 100 As+Bs+C4+D3-d~" =88.4

A goal programming approach to job evaluation

A4 -4- B4 + C4 + D3 - d~" = 73.8 A3 + B3 + C3 + D3 - d~" = 64.7 A1 + B2 + C3 + D2 - d~" = 58.7

149

(P1)

Equat ion set (P1) indicates that the factors should be evaluated so that each equation is satisfied with as small values of deviations as possible (or the total scores for the five benchmark jobs are as close to their respective minimal goals of 100, 88.4, 73.8, 64.7, and 58.7 as possible).

In addition to the deviations on total job scores of the benchmark jobs, some deviations are acceptable in the individual score of each of each level of a job factor. The goal programming constraints comprising these constraints are as follows:

A ~ - d ~ = 5 BI - d~" = 5 C1 - d~ = 5 D1 - d ~ " = 5

(P2)

A6 + di-0 = 35 B 6 + di-~ = 35 C6 + di-2 = 35 D 6 + d~ 3 = 35

(P3)

A2 - A1 - di~4 = 2 A3 - A2 - d~5 = 2 A4 - A3 - di~6 = 2 As - A4 - d~7 = 2 A 6 - A 5 - di~8 = 2

(P4)

B 2 - B 1 - d~9 = 2

B 3 - B 2 - d~-0 = 2

B 4 - B 3 - d~-i = 2

B 5 - B 4 - d~-2 = 2

B 6 - B 5 - d~-3 = 2

(P5)

C 2 - C I - d~4 = 2 C3 - C2 - d ~ = 2 C4 - C3 - d~6 = 2 C5 - C4 - d~'7 = 2 C6 - C5 - d~-8 = 2

(P6)

D z - D l - d ~ l = 2 D3 - D2 - d~o = 2 D4 - D3 - d~'l = 2 D 5 - D 4 - d ~ ' 2 = 2 D6 - D5 - d~'3 = 2

(P7)

The equat ion set (P2) indicates that the lowest levels of factors A, B, C, and D should be at least worth five points and d~, d~, d~, d~- are the positive deviational variables associated with the constraints in equation set (P2). Equat ion set (P3) indicates that the highest level of factors A, B, C, D should not be more than 35, and di-0, d~l, di-2, di-3 are the negative deviational variables associated with equation set (P3).

Equat ion sets (P4), (PS), (P6), and (P7) indicate that the worth of a factor at a particular level should be at least two points higher than that of the same factor at an immediately preceding level. Here d~-4, d~5 . . . . d~3 are the positive deviational variables associated with equat ion sets (P4), (P5), (P6), and (P7).

150 JATINDER N. D. GUFrA and NAZIM U. AHMED

Now, in the job evaluation problem, it is desirable that the benchmark jobs satisfy equations (1) through (5) as well as is possible without making the scores negative. Further, the significance of various goals stated in equation sets (P1) through (P7) may be different. For example, it may be more important to meet the goals of the benchmark jobs as close to their assigned values as possible even though the deviation of the actual worths of various levels of job factors may increase. These conditions are handled by assigning different priorities to various goal sets above. The highest priority is assigned to that goal which is most important to management. Taking these arguments into account, the objective function, Z, of the goal programming model can be stated as follows:

Minimize:

z = P, (d; + d; + d~ + d; + d;) + P2 (d~ + d~ + d; + d~) + P3 (d lo+ d~-i + d~-2 + di-3) + P4 (d~'4 + d~-5 + d~16 + d~-7 + d~-8 + d~-9 + d~2o + d~'l + d~2 + d~'3

+ d~, + d~ + d~6 + dI7 + d~s + d~9 + d~0 + d~, + d~2 + d~3)

Here the top priority P~ is assigned to minimize the deviations from the goals in equation set (P1). The next priority, P2, is assigned to minimize the deviations in the constraints in equation set (P2) and then the priority P3 is assigned to minimize the deviations in equation set (P3). Priority P4 is assigned to deviational variables associated with equation sets (P4), (P5), (P6) and (P7). Depending upon actual situations, the above priority scheme can be changed as judged appropriate by management. However, for illustrative purposes, the above priority scheme will be used to solve the foregoing example problem.

The complete goal programming model representing the job evaluation problem then is one of minimizing Z given above subject to the constraints (P1) through (P7).

SOLVING THE GOAL PROGRAMMING PROBLEM

Once the job evaluation problem is formulated, it can be solved by using any one of the several available goal programming algorithms [10-12]. The best approach to solve the goal programming problem described is to use the preemptive goal programming technique [11].

Basically, the preemptive goal programming approach consists of successively solving the problem by assuming that the problem has been optimized for the highest priority goal. Thus, for the above example, the preemptive goal programming approach would first solve the problem by assuming that Pl = 1 and P2=P3=P4=Ps=O. Once the solution to the corresponding integer programming problem is found, the attainment for the highest priority goal P~ is stated as a constraint to be satisfied at its optimal level. Then, the objective function is modified to exclude the highest priority goal and the problem now solved by assuming P2 = 1 with all other priority goal values to be zero. This process is continued until a feasible and optimal solution is found that satisfies all goals in the hierarchy of the goal priorities. (Details of the preemptive goal programming approach are discussed by Ignizio [11] who also proposes several refinements to reduce computa- tional burden.)

EVALUATING A NEW JOB

The solution to the above goal programming problem provides scores for each factor at different levels. So, for any new job requiring different levels of factors, the total score can readily be obtained by adding the scores for levels of different factors in that job. Later, the total score can be directly converted into the salary structure.

To illustrate this procedure, the above example problem was solved using a pre- emptive linear goal programming computer code developed by Sang Lee. This code is

A goal programming approach to job evaluation

Table 1. Optimal worth of compensation factors

151

Levels

1 2 3 4 5 6

A 5 7 9 12.1 24.7 26.7 Factors B 5 7 9 11 13 35

C 5 27 29 31 33 35 D 5 17.7 19.7 21.7 23.7 25.7

Table 2. Goal attainment in the benchmark job constraints

Benchmark Goal Deviation job Goal attainment Deviation in percent

l I00.0 100.4 0.4 0.4 2 88.4 88.4 0 0 3 73.8 73.8 0 0 4 64.7 66.7 2 3.1 5 58.7 58.7 0 0

written in FORTRAN IV and solves integer goal programming problems by using the branch and bound procedure. Table 1 depicts the optimal worth of various compensation factors at different levels.

The goal attainments in the benchmark jobs, reflecting the quality of the solution obtained are shown in Table 2.

From Table 2, it is clear that the goals in benchmark jobs 1 and 4 were exceeded by only 0.4 and 3.1 respectively while the goals for benchmark jobs 2, 3, and 5 were attained exactly. The average deviation from the goal was 0.62%.

Suppose the benchmark job in equation (1) has a base rate of ten dollars per hour, and the management is to evaluate another job comprising the levels of various factors as: A3, B5, C6, D 4. Then, using the optimal worths of various factor levels in Table 1, the total score of this job will be: A3 + B5 + C6 -I- D4 = 9 + 13 + 35 + 23.7 = 80.7. Thus, the base rate for this job will be 80.7 x (10/100) = $8.07 per hr.

The above example illustrates that having determined the optimal worth of various levels of different factors, the base rate for any other job can be established by comparing the levels of factors involved in that job to that of a benchmark job.

D E T E R M I N I N G T H E B E N C H M A R K JOBS

The application of the above goal programming approach requires that a number of benchmark jobs be determined and used. This can be accomplished through a procedure where a manager is asked questions, often more than once, regarding the factors that make-up a specific job and the levels of factors needed for acceptable performance. The total score can also be determined by asking questions as to the relative worth of the jobs in questions. For example, it may be possible for the management to conclude that a given job is worth half as much as another known job. Knowing this information, the goal programming model can be constructed and used for evaluating other jobs in an organization.

The problem of determining the benchmark jobs is similar, in many ways, to the determination of the probabilities by management. Hertz and Thomas [13, pp. 155-170] discuss several methods for such an effort. Each of those methods can also be used for the determination of benchmark jobs to be used in the job evaluation model. However, the effort needed may require that some methods are more appropriate than others. Furthermore, the larger the number of benchmark jobs, the better will be the quality of the job evaluation model solution. Therefore, this point should be explicitly considered in the selection of the method to be used in the identification and determination of the worth of the benchmark jobs.

152 JATINDER N. D. GUFTA and NAZIM U. AHMED

CONCLUSION

Job evaluation is an attempt to systematically and objectively determine the relative values of jobs in an organization. Compensation literature discusses the importance of objectivity and exactness in developing pay structures and evaluation plans. Deter- mination of factor level scores, however, frequently focuses on subjective judgements being made by management tailored to special requirements of each organization. This paper has illustrated the use of a linear goal programming approach to systematically determine factor scores according to an established pay pattern. Use of such an analytical approach would hopefully improve the objectivity with which an ongoing job evaluation plan is administered.

The proposed approach to modeling the job evaluation problems and the use of pre- emptive goal programming solution technique also has some added advantages. The changes in the goal priorities can easily be handled by just defining the hierarchical structure of the objective function in the resulting goal programming model. Further, parametric changes in the benchmark jobs can be incorporated by using the sensitivity analysis concepts in goal programming. This enhances the utility of the job evaluation process particularly in times of labor negotiations and collective bargaining agreements.

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