Markov Chain - Simple and powerful model for organization dynamics
Introduction
In this article, I will describe a statistical model called Markov Chain. Unlike the perceived image through the name, the concept will look very simple to you. However, the theory is applied to many use cases across domains. Let’s explorer its application to workforce data!
How is Weather Forecasting modeled?
To describe the concept of the Markov Chain, I take daily weather as an example. Suppose that if it rains today, then it will rain tomorrow with probability . If it does not rain today, then it will rain tomorrow with probability . The system of weather is formulated as a matrix of the four probabilities.
Table 1
Formulation of Transition Probability for tomorrow’s weather
This matrix is called as one-step transition probability. We calculate probability of transitioning from one state to another for multiple time windows so that we can calculate probability to be rainy two days later in case it is rain at the first day. We obtain two-step transition probabilities P(2) by multiplying one-step transition probability.
if then the two-step transition probabilities are calculated as follows.
Table 2 explains there is 61 percent chance to rain day after tomorrow in case it rains today. The idea behind this calculation is that an event is happened based on the sequences of the previous states over time and the probability is depending on the previous state. This is core concept of Markov Chain.
Table 2
Example of two-steps Transition probabilities for tomorrow’s weather
What is Markov Chain?
Markov Chain is a type of stochastic process in which an individual subject can move from one state to another state in a fixed probability. In this process, state at the next day depends only on the current state independent of the past state. The concept is simple but powerful to represent behavior of a lot of natural or social phenomena. In the weather forecast example above, the weather tomorrow depends solely on the previous day’s weather. Markov Chain Model is used for several purposes: Weather Forecasting, Predicting stock price, Predicting machine failure, and so on.
Application of Markov Model to Workforce Planning
Let's think of an individual employee as a subject that is similar to today’s weather. Also, let's think of his or her position in your organization as a state. Then the decision around his/her promotion or resignation can be modeled as Markov Chain. The benefit of modeling employee progressions on Markov Chain is its simplicity. You can track only the history of individuals. Unlike complicated machine learning techniques, it is not always necessary to define additional explanatory variables. At the same time, it allows us to forecast the long-term evolution of cohort members if enough amount of data is processed.
Transition Probability Matrix as a hidden secret source
How can we model your organization on Markov Chain? Let’s explore with a simple example. A workforce system is given as vector of number of three job title A, B and C at time 0.
In this scenario, suppose following transition probability matrix P and number of recruited people R(T) are given:
The cell P11 (0.90) means that it is 90 percent chance for an employee at job title A remains the same job title. The cell P12(0.10) means that it is 10 percent chance to promote from job title A to B. Number of employees for each job title at time T=1 is calculated:
In the similar manner, number of employees can be forecasted in Table 3.
Table 3
Example of forecasted number of employees by job title
Maintaining accurate transition probability is like a secret source to make an economic impact on Human Resources process. Given the reliable statistics at reasonable granularity, you will be able to simulate structural changes in your organization and find a gap with the required deployment. Also, the statistic will help you to care individual level. For instance, you can pinpoint a team member who is at risk of leaving your firm because of spending more than average years in the current position. You can come up with action items to retain the person.
Figure 1
Example of Transition Matrixes
Conclusion
If your business is people intensive such as consulting, it is worth investing in collecting work history data in your organization. The benefit is accurate outlook of future personnel deployment and its consecutive financial outcome. The Markov Chain is a powerful analysis to model dynamics of your workforce. In the next article, I will explore additional refinement called Semi-Markov Model for a more realistic situation.
References
Ross, S.M. (2014). Introduction to Probability Models Eleventh Edition. Academic Press.