## Defining the Concept of Productivity

In attempt to quantify employee productivity, the authors propose two models to represent this combination: (1) the additive model, which considers productivity to be the sum of efficiency and effectiveness and (2) the multiplicative model which considers productivity to be the product of these two. To compare the two models, an example of a grocery clerk is used. Productivity levels of the grocery clerk are determined using additive and multiplicative models for 5 different cases of varying levels of efficiency and effectiveness.

Comparison suggests that multiplicative model is a better way to define productivity in measurable terms, as it overcomes the limitations in the additive model. Introduction Organizations strive to maximize productivity. One way they can do this is to seek out and maintain high performing employees. Another option is to reward individuals for higher levels of productivity and punish those with low. For example, supervisors at General Electric Company rank order their employees by their level of performance each year and fire those who fall in the bottom 10% (GE, 2001).

In order to make appropriate appraisal decisions, it is essential that we know how to accurately assess employee productivity. The Additive Model In the additive model, productivity is

The effectiveness index can assume a value from 0 to 1 in this equation, whereas the efficiency index can assume a value of greater than 1 for employees performing faster than the set norms. This can be depicted by the following equation: Productivity Index (PI) = [Efficiency (? ) + Effectiveness Index (EI)]*100 / 2 Additive model: PI = [45 / 50 + 0 /100] * 100/2 = 45 Multiplicative model: PI = 45 / 50 * 0 /100 * 100 = 0 Case 5: Very low efficiency and high effectiveness Case 5 represents a scenario that is the opposite of case 4.

The grocery clerk here demonstrates a high level of effectiveness by scanning all the items correctly (100% accuracy), but a very low level of efficiency by only scanning 5 items in 10 minutes. Additive model: PI = [5 / 50 + 100 /100] * 100/2 = 55 Multiplicative model: PI = 5 / 50 * 100 /100 * 100 = 10 Limitations of the multiplicative model 1. Quantifying effectiveness and efficiency for all jobs may not be possible especially for managerial jobs. 2. The model assumes that the equipment, machinery and resources required to perform the given task are available to the employee and are working properly.

This may not be always true, particularly when there are multiple workers sharing the resources. 3. Since efficiency cannot be zero (it might take on infinitesimally small values though, as even starting the work will have some value) the pane 1 in the figure can never be completely opaque. Defining Productivity, Efficiency, and Effectiveness Pritchard (1992) defined organizational productivity as “how well a system uses its resources to achieve its goals” (p. 455). Building on this definition, Payne (2000) defined individual productivity as “how well an individual uses available resources to achieve his/her goals” (p. ). Pritchard further defined productivity as a combination of efficiency (quality of resource use) and effectiveness (achievement of goals). Traditionally, efficiency is defined as the ratio of output over input. It has also been defined it as the “skillfulness in avoiding wasted time and effort” (Hyperdictionary, 2003). Effectiveness, on the other hand, is the evaluation of the results of the performance (Campbell, 1990). Efficiency and effectiveness might also be thought of as “doing things right” and “doing the right things,” respectively.

The Multiplicative Model In the multiplicative model, productivity is defined as a product of efficiency and effectiveness indices. The multiplicative model also follows the associative and commutative laws. A multiplicative factor of 100 is used so the final productivity index is scaled to 100. The efficiency and effectiveness indices can assume values similar to those in the additive model. This can be depicted by the following equation: Productivity Index (PI) = Efficiency (? ) * Effectiveness Index (EI) * 100

Comparing the models Both models are very straightforward and very easy to compute. They are equally accurate and flawless in representing the first three cases and permitting comparisons between them. However, for all 5 cases, the additive model overestimates productivity. Also, in case 4, when effectiveness is zero, the productivity index equals 45 using the additive model. This suggests that it is possible to be somewhat productive even when one is not at all effective. This is inconsistent with our previous conceptual arguments.

The multiplicative model handles these extreme circumstances more accurately and is therefore a better model than the additive one. A pictorial depiction of this model is shown below: Factors affecting Productivity Factors affecting Efficiency 1. Speed of work which is a function of dispositional preferences and motivation. 2. Knowledge of different ways (methods) to get the job done. 3. Access to different aides/ tools for doing the job Factors affecting Effectiveness 1. Goal clarity 2. Task priority

Productivity as a Combination of Efficiency and Effectiveness If productivity is a combination of efficiency and effectiveness, this implies that demonstrating one but not the other is either partially productive or not productive at all. This depends on how efficiency and effectiveness are combined. This can be done one of the two ways: (1) by adding them together (the additive model) or (2) by multiplying them together (the multiplicative model). We argue that some level of each component is necessary for any level of productivity and if either one is zero, productivity is zero.

Cases with different levels of efficiency and effectiveness Case 1: High efficiency and high effectiveness Case 1 with high efficiency and effectiveness can be represented as the grocery clerk scanning 45 items in 10 minutes, as compared to the standard of 50 items per 10 minutes, and on an average scans 90% of the items correctly. Additive model: PI = [45 / 50 + 90 /100]* 100/2 = 90 Multiplicative model: PI = 45 / 50 * 90 /100 * 100 = 81 Case 2: Low efficiency and high effectiveness Case 2 describes a scenario of low efficiency and high effectiveness.

This would be a case where the grocery clerk scans only 25 items in 10 minutes, but with the same level of effectiveness, 90% accuracy. Additive model: PI =[25 / 50 + 90 /100] * 100/2 = 70 Multiplicative model: PI = 25 / 50 * 90 /100 *100 = 45 Case 3: High efficiency and low effectiveness Case 3 describes a scenario of high efficiency and low effectiveness. The grocery clerk demonstrates a high level of efficiency by scanning 45 items in 10 minutes, but lower level of effectiveness, a 50% accuracy rate.

Additive model: PI =[45 / 50 + 50 /100] * 100/2 = 70 Multiplicative model: PI = 45 / 50 * 50 /100 * 100 = 45 Case 4: High efficiency and zero effectiveness Case 4 represents a scenario that is extreme. The grocery clerk here demonstrates a high level of efficiency by scanning 45 items in 10 minutes but a zero level of effectiveness by scanning all the items incorrectly. Discussion • The multiplicative model overcomes the limitations of the additive model. The multiplicative model is more robust but at the same time sensitive enough to the extreme values efficiency and effectiveness can take on.

It is a more realistic and objective way to calculate productivity. The multiplicative model can be used by supervisors to calculate each employee’s level of productivity. It provides for a common index to make comparisons and a final number to base personnel decisions like raises, promotions, and termination. Returning to example mentioned earlier of the worker manufacturing defective goods at a speed greater than the standard norms, it can be argued that efficiency itself is a function of effectiveness.

This argument is based on the fact that if a significant amount of time is lost in rectifying defects; overall efficiency is reduced. However, this applies only to those items for which rectification is possible. Secondly the process of rectification can be considered a job activity in and of itself and will have a level of efficiency and effectiveness of its own. These models assume that work can be quantified in into efficiency and effectiveness indices. This may be difficult in white collar jobs. In this case, the job activities can be broken into elements that are quantifiable, which can be assessed with the multiplicative model.

Future research might explore an adaptive productivity index to accommodate other model limitations. Example A primary task for a grocery clerk is to scan products quickly and accurately. We propose that the efficiency criterion for this task is the ratio of time taken by the grocery clerk to scan products to the standard time set by industry norms to scan that number of products (a slight deviation from the traditional definition of efficiency). The effectiveness criterion here is the ratio of number of products accurately scanned to the total number of the products scanned.

Thus a productive grocery clerk is an employee who scans a high number of the products with no errors. • Effort Efficiency Pane Effectiveness Pane Productivity Screen • In this model, the light bulb represents the total effort expended on the job by the employee. On the job, pane 1 is the efficiency pane, which is a rectangular glass pane. The pane becomes increasingly darker as the efficiency (? ) decreases. That is for 100% efficiency the pane is completely transparent and for 0 % efficiency the pane is completely opaque.

The second pane, pane 2, is the effectiveness pane. The effectiveness pane is similar to the efficiency pane; it is completely transparent when an employee achieves maximum effectiveness and the opacity of the pane increases as effectiveness decreases. The last screen used to denote productivity is an opaque screen. The observed productivity demonstrated by the employee on the job is represented by the final amount of light falling on screen or in simple words the brightness of the Screen. To get any amount of productivity, effectiveness cannot be zero.

In other words to have any light falling on the Screen, pane 2 cannot be completely opaque. Here the best employees, are the “brightest. ” Assumptions of Models 1. Work is readily available and remains available. 2. Resources required to perform the task are available to the employee. 3. The equipment and machinery required to perform the given task are available to the employee and are working properly. 4. The employee has the knowledge of at least one method for performing the task. 5. The output of the work done can be quantified in terms of both effectiveness and efficiency. • •

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