## HR 3D Matrix

Human resource management has been considered as an abstract concept for the last few decades. Any aspect of HRM has been left immeasurable, baffling all when it comes to practice. Overall, HRM is considered as something “logical” than “scientific”, forget Mathematics.

In this whitepaper, we deal with measurements in HRM, through an **universal** tool, which we call the **HR 3D Matrix**. This tool is universal, which means it can be used in multiple situations which then acts as a major assistant while taking HR decisions. Situations include:

- Clustering expected employees
- Evaluating to-be employees
- Measuring current employee performance
- Taking action on the employee performance (train, motivate, terminate,…)
- Compensation

Firstly, what is the HR 3D Matrix? This has two meanings in two different contexts. The first context is the recruitment stage and the second context is the performance stage. We begin with the first context.

The HR 3D Matrix, as it’s name sounds is a three dimensional matrix, with the x,y,z axes as usual and

- The x axis represents level of experience in years
- The y axis represents level of innovation
- The z axis represents level of communication skill

One thing you must note is that communication skills are not language skills. This skill is the ability to understand an object and document the object. For example, if there is an issue in the requirements document, a person who understands that issue and documents that issue in a way that conveys the issue clearly to the requirements team has communication skills.

We define a **HR Point** as a point in the matrix whose co-ordinates are (x,y,z) and that point represents the employee, as in, the x co-ordinate represents his experience, the y co-ordinate represents his level of innovation and finally the z co-ordinate represents his communication skill. Overall, we are visualizing the position of an employee (not necessarily current) as a point in space.

This looks great to hear, but unfortunately this is just the tip of the iceberg. The problem begins now, how do we measure the levels of experience, innovation and communication? To make this a sensible question, let us first understand the context of this measurement. We sure are in the recruitment stage, but there are two sub-stages:

- Selecting the target employee cluster
- Evaluating to-be employees

Since they are in order, we begin with the first. Basically, we want to select the cluster of HR points, or the cluster of employees we expect to be in our organization, and if any to-be employee, after being placed his HR point is out of our cluster, he will simply be rejected. No hypothesis, pure mathematics.

Now we answer your question, how do we decide the expected experience, innovation skill and communication? That depends on the future plan of ours. And how do we first measure these quantities? Experience is trivially in years, but what about the other two? Here is where we use another tool of ours, the **Need and Plan Diagram**. Let us brief this tool out for you. This tool is an extension of the **5 What’s Analysis** which is by asking “What’s” repeatedly to an expectation and reaching the root need. Here is an example:

- Albert wants to write a program – Expectation
- What does he need? – A laptop – Need
- What does he need there? – Linux OS – Need
- What does he need there? – VI Editor – Root need

The need and plan diagram classifies the set of all needs, then moves on individually to each of those needs and then classifies those individual needs into more sets of needs and so on until the set of all root needs is classified.

How can we use this for our purpose? The level of innovation depends on the skillset we expect. So, we create a need and plan diagram and find out the root skillset that we expect from the employee. The cardinality of that set would be our y co-ordinate. Similarly, we can evaluate the z co-ordinate. Our cluster now is the set:

S = {(x,y,z) | x ≥ x_{0},y ≥ y_{0},z ≥ z_{0}}

Moving on to the next sub-stage, we want to evaluate the to-be employee. Finding out his x co-ordinate is a cake. We now need to evaluate his y and z co-ordinate. The y co-ordinate can be evaluated by the lead, who asks technical questions and the number of right answers in that scheme per se shall be his y co-ordinate. Finally, the z co-ordinate can be evaluated by the lead and the HR team together, by asking more questions based on documentation styles and understanding power. If his/her HR point is in our cluster, accept him, else reject him.

We now move on to the second context. Albeit the HR 3D Matrix is universal, since we’ve changed the context, we need to slightly adjust the axes and their orientation. We re-define the HR 3D Matrix now as:

- The x axis represents level of experience in years
- The y axis represents his/her overall result
- The z axis represents level of communication skill

Measuring the latter two axes requires a slightly different orientation. Here is where we introduce the concept of **Waste**. Waste is anything that adds on extra cost which could have otherwise been eradicated. In the next few texts, we will be talking about waste as a whole and not specify the axes for a while.

Assume that we have derived root wastes: w_{1},...,w_{n} Then the overall waste W is determined by the partial differential equation:

W = f

δW

δW_{1}

,...,

δW

δW_{n}

From this PDE, we can determine the overall waste committed by the employee, and then we use the equation

Result = Efforts - Waste

To determine the y,z co-ordinates.

Why are we doing this? There are two reasons:

- Keep the employees on track always
- Compensation

In order to keep the employees on track, we need to measure their performance continuously, and so we do this. If we find any abnormality in performance, the HR team will do one of these:

- Train
- Motivate
- Terminate

depending on the scenario.

The greatest use of this tool comes into picture now, compensation. Compensation has been regarded as a highly hypothetical and un-scientific aspect. But with this tool, we can mathematically evaluate compensation, by solving the partial differential equation:

C =

δC

δx

X x +

δC

δy

X y +

δC

δz

X z

Note that this only tells us about how much money we should spend on the employee, not about where to spend it. To figure out where to spend it, we determine the employee’s motivation factors and allocate the money according to what motivates him the most.

All in all, we conclude that the **HR 3D Matrix** is an universal tool, consistent and is a beautiful mix of concepts such as waste, the need and plan diagram to be able to measure abstraction. As we know, where all the are measurable quantities.

Abstraction = f(m_{1},...,m_{n})

where all the m_{i} are measurable quantities.