USE OF FUZZY MATHEMATICAL QUADRATIC PROGRAMMING APPROACH IN JOB EVALUATION

Purpose of study: The current paper is the based on mathematical model of the job evolution system. Methodology: The proposed method is the fusion of quadratic programming and fuzzy logic where quadratic programming is used to optimize objective function with related constraints in the form of non-linear formulation. Fuzzy logic is used to control uncertainty related information by estimating imprecise parameters Main Finding: The optimal solution of the job evaluation based on fuzzy environment where goal is imprecise. Application of this study: It is used in the areas where information is not exact. The originality of this study: The novelty of the method is the fusion of quadratic programming and fuzzy logic.


INTRODUCTION
Modeling in Job Evaluation is the important tool that facilitates the solution of non-bench mark jobs by reference to the evaluation of benchmark job It is the systematic process to determine the worth of one job in relation to other jobs in any orgation an enterprise. It is required to arc the relation worth of many jobs be paid depending upon the worth of the job. It focuses is typically on the duties and responsibilities assigned to a job, not on the credentials or charters tic the jobrelated person nor the quality or quantity of the incumbent's performance.
Employment Assessment Goals The following are some examples: 1 To obtain and retain a complete, correct, and impersonal description of each specific job or occupation in the factory.
2 To provide a consistent method for calculating the relative worth or importance of each job in a factory.
3 Establish a just and equal rate of pay for each job in comparison to other jobs in the factory, society, and industry. 4 To ensure that all eligible employees on similar jobs are paying the same salary.
5 Allow workers to be eligible for promotion and relocation fairly and correctly. 6 To provide a factual basis for comparing pay prices for related occupations both Geographically and Nationally.
The following are the requirements: (a) Determining the work system and architecture. (c) Ensuring that market analysis is conducted successfully prior to work review.
(d) Ensuring that all parties, labor, workers, and management are included on the committee.    (i) The active participation of a labor union and employers is important.
(j) Access to business prices (via a Labour sector survey) in order to determine current wage prices.
(k) Determining which classes of workers and jobs will be evaluated by the scheme.
Job evaluation helps in developing and maintaining pay structures by comparing the relative similarities and differences in the content and the value of jobs. If in an organization the pay structure is illogical then the pay inequalities may exist.
The purpose of job evolution is to eliminate the pay inequalities Leep, T. L. and Michael D. Crino (1990) and Milkovich, G.T. and Boudreau, W. (1990).
In this paper, an attempt has been made to solve the job evaluation problem using the fuzzy goal programming approach. Since practically it is difficult for the decision-maker to fix the goals absolutely for the benchmark jobs. So, it is considered that the scoring goals as fuzzy in nature. The concept of fuzzy set developed by Bellman 2001) to illustrates the achievement of the fuzzy logic. In the proposed approach the worth's of the different factor levels of each factor which are components of the benchmark job may be computed. With these computed worth's of various factor levels, it will be possible to compute the scores for different types of jobs and thus jobs may be evaluated. A sample problem has been solved using the proposed approach.

MODEL ANALYSIS
Let x i is a job factor. It has a finite number of levels x ij , i ϵ [1, n]. The management of the organization identifies K benchmark jobs y n (x), n ϵ [1, K] whose levels and scopes (s n , n ϵ [1, K]) are known. Similarly, the score constraints for the lowest levels for each factor are known, and also the differences of scores of each level of a factor from the previous levels are also known. These constraints have been considered as rigid constraints.
Fuzzy mathematical model for the above-mentioned job evolution problem may be developed as:

MATHEMATICAL MODEL
Determine an action x=(x 11,…….. x 1m ; x 21………. x 2m ; x m1 …….. x mn ) Such that y i (x) s n where ' ~ ' sign denotes fuzziness. For defuzzification, linear membership function is used as: µ n( z n) = ……. (1) where, ȳ and y are the maximum and minimum values of y n (x). The first membership function is non decreasing function whereas the second membership function is non increasing function. The membership function for Fuzzy inequality greater or equivalent may be obtained.

NUMERICAL PROBLEM
The management of the organization has four factors each job with six levels of each factor and identified five benchmarks' jobs with fuzzy worth's Mathematical analysis x 16 Where the first benchmark job represents the top labor grade job in that organization. The fuzzy worth's of the highest levels of each factor (with a limit of tolerance) the know scores for lower levels of each factor and the known amount by which by which a particular level is higher than the preceding level are decided as. On the solving (QP) using Lingo Software, the following numerical values worth of various factor at different levels are obtained as: Hence, the benchmark jobs are computed and tabulated as given below