Manufacturing workforce assessment using AHP and TOPSIS logic

To perform a given activity by two individuals having the same qualification, the performanceof achievement varies, which introduces the concept of individual competence level. This article presents an assessment method of multi-skilled workforce. In this paper wewill discuss how to consider the differences and similarities between acquired level and required level. For a compound competence, the objective of our method is to present a quantified assessment method usingAHP technique and TOPSISlogic which allows calculating the degree of excellence in the use of all individual competencies in execution of all activities. Keywords-Assessment,Individual competence, Performance, AHP, TOPSIS.

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A. Chara
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IV.
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CHARACTER
As an illustrative example, we consider four alternatives A1, A2, A3 and A4; the three proposed criteria (raw material cost (Cmp), Profit margin (Pm) and Complexity (C)). We suppose the following input data shown in Table 1.  Thus, the criteria weight value is calculated as follow:

2) Calculation of activities' weight
In this segment, we proposed to use a pair-wise comparison based on ratios calculated from quantitative input data.We assume the input data shown in Table 1.
For instance, when we should express ajudgment when activity A2 is compared to activity A1 in terms of raw material cost. The corresponding comparison assumes the value of 1.2. And, when activity A1 is compared to activity A2, the corresponding comparison assumes the value of 0.83. A similar interpretation is true for the rest. The next step consists in calculating the relative importancefor each activity relative to each criterionas shown in Tables 3(a), 3(b) and 3(c). For the first criterion "raw material cost (Cmp)", the judgment matrix with the pair-wise comparisons is calculated as follow (2): For the second criterion "Profit margin (Pm)", the judgment matrix with the pair-wise comparisons is calculated as follow (4): 1 For the third criterion "complexity (C)", the judgment matrix with the pair-wise comparisons is calculated as follow (5):

3) Ranking of activities
The relative importance of eachcriterionis determined previously using pair-wise comparisons. And the activities are compared with each other in terms of each criterion.The final priorities denoted by are determined according to the following formula (6): The previous priority vectors resulting from the previous pair-wise matrixes are used to form the entries of the decision matrix. The final priorities are calculated according to formula (8). Table 4 illustrates the global weights of activities.

A. Chara
The  With, : Number of components required to produce one unit of the activity (i); k : Index of component; : Number of the component (k) required to produce one unit of the activity (i); : The amount of component (k) consumed by the operator (j) to produce Qp .

B. Calculation of the degree of importance of each assessment criterion
For the weighting of the three adopted sub-criteria (WP, EQ and CR), which reflect the individual performance, we have used the AHP technique. In the same manner as weighting activities, we proposed to use a pair-wise comparison based on ratios calculated from quantitative. To avoid subjectivity and in order to compare the different criteria in a quantitative way, we will determine the relationships between the three criteria and the different production costs (manufacturing cost, cost of non-quality and cost of waste).In this section, we will formulate the extra cost resulting from the assignment of a given activity (i) to a given operator (j) whose initial performance is not optimal. The demonstration presentsthree costs: the first one contains the extra cost due to additional time related to the working speed; the second one discussesthe extra cost due to noncompliant products, the third one isthe extra cost due to the loss of components which are improperly handled.

1) First cost due to the additional time
If the work performance (WP) is less than 1, this means there is an extra time in addition to the standard time. The extra time (Ta) is defined as the difference between the standard time (Ts) required achieving a given activity and the real time (Tr) spent on its achievement. So, there is an extra cost resulting from the assignment of a given activity (i) to a given operator (j) whose work performance is (WP). The extra time (Ta) to produce the quantity demanded ( ) is defined as: Ta 1 WP . Tr (10) Let,

Ts
Ts . Ts . EQ Replacing (11) in (7), we get: Substituting (12) in (10), the extra time due to the additional time is: The extra cost (Cat) due to the additional time Ta to produce Qd is equal to: Therefore, 1 WP WP * EQ . Ts . AHR We can deduce that (Cat) is related to (WP), when (WP) decreases the value of (Cat) increases. As a result, the value of (Cat) is inversely proportional to (WP).
2) Second cost due to poor product: If the execution quality (EQ) is less than 1, this means there are wrong products. Assume that (Cnq Qp ) corresponds to the cost of non-quality incurred when producing the planned quantity (Qp ) of the activity (i). Let, We considered that ( corresponds to the production cost and it's equal to the sum of the raw material cost é and the manufacturing cost ( ), so: 1 .
Therefore, we can deduce that when (EQ) decreases, (Cnq) will increase. As a result, the value of (Cnq) is inversely proportional to (EQ).
3) Third cost due to damaged components: If the consumption ratio (CR) is less than 1, this means there are damaged components due to improper use. Assume that (C Qp ) corresponds to the cost of "damaged components" incurred when producing the planned quantity (Qp ) of the activity (i) and (Cmp ) corresponds to the raw material cost needed to produce one unit, with: Cmp é ∑ n . Cmp , where (Cmp ) corresponds to the purchase cost of components (k), then (C Qp ) is: . We can deduce that (Cd) is related to (CR), when (CR) decreases the cost (Cd) will increase. As a result, the value of (Cd) is inversely proportional to (CR).
For weighting the three sub-criteria (WP, EQ and CR) in an objective manner, we have used the three factors (Cat, Cnq and Cd) because they are homogeneous and they are all inversely proportional to the three evaluation criteria. As an illustrative example we assume the following input data shown in Table 5. The next step is to extract the relative importance of each assessment criterion (WP, EQ and CR) by reference to each activity. Tables 6(a), 6(b), 6(c) and 6(d) represent comparison matrixes of the three criterions respectively for the four activities.
For the first activity (A1), the judgment matrix with the pair-wise comparisons is calculated as follows 23 : In the same way, we develop the three comparison matrix for the others activities:   The Table 7 summarizes the calculation made previously:

THE PROPOSED MODEL FOR ASSESSMENT OF MULTI-SKILLED WORKFORCE USING
TOPSIS LOGIC TOPSIS (Technique for order performance by similarity to ideal solution) [11] is a practical and useful technique for ranking and selection of a number of alternatives through distance measures. [11]further proposes that the ranking of alternatives will be based on the shortest distance from the positive ideal solution and the farthest from the negative ideal solution. It originates from the concept of a displaced ideal point from which the compromise solution has the shortest distance [2] [27]. TOPSIS has been successfully applied to various areas such as transportation [12], product design [13], manufacturing [15], plant location analysis [24], etc.In our case we have used the TOPSIS logic for order workers according to their relative closeness, and to provide an aggregated evaluation.The major weaknesses of TOPSIS technique are in not providing for weight elicitation, and consistency checking for judgments [20]. Tomake an objective assessment, we suggest an integrated approach that simultaneously uses the AHP technique for weighting and TOPSIS logic for ranking.
For TOPSIS technique, a decision matrix is required at the beginning of the process. The decision matrix contains competitive alternatives (activities), with their attributes' ratings. Originally TOPSIS utilizes Euclidean distances; the best alternative should be at the shortest distance from the ideal solution and the farthest distance from the anti-ideal solution.The detailed procedure is illustrated with an example in the following sections.

A. Construct judgment matrix
The structure of the matrix can be expressed as shown in Table 8: where denotes the operators (j) , ∈ ; denotes activity (i), ∈ ; represents sub-criterion c , ∈ . indicates the performance rating of operator with respect to activity and assessment criterion . The performance rating is calculated using the three formulas (7), (8) and 9.

B. Calculation of the degree of importance of each activity and each assessment criterion
Using pair-wise comparisons, the relative importance of each activity andassessment criterion was previously computed. The Table 9 summarizes the calculation made previously with:

C. Determination of the ideal levels and anti-ideal levels
By analogy with the TOPSIS method, we choose for each activity the best and the worst performance rating as ideal and anti-ideal performance level.
, … , , … , 24 Where: ∀ ∈ ; ∀ ∈ 25 And: , … , , … , 26 Where: The idea is to minimize the gap between the required performance level and the acquired performance level. The Table 10 summarizes the ideal and anti-ideal performance level.   VII. CONCLUSION This approach seems more meaningful since it involves a decision process using AHP and TOPSIS techniques for assessment of multi-skilled workforce in an objective way. In themanufacturing industryhuman resources areconsidered as a keyelement of performance. In this context,wehave defineddifferent criteria and we have useddecision making techniquesto providean operational tool for assessment ofmulti-skilled workforce. In this paper, we have proposed a method using AHP technique and TOPSIS logic for classification of workers; we have expressed the worker's efficiency through tangible results. We have used AHP technique as decision support tool for weighting assessment criteria and activities. On the other hand, we have also used TOPSIS logic as a decision support tool for distance measuring between acquired levels and required levels. The model proposed in this study is meaningful for aggregation, simple to use for real-world applications and allows the companyto better determine theavailable performance levels of human resources they possess.