Markov analysis is a technique that deals with the probabilities of future occurrences by ­analyzing presently known probabilities.¹ The technique has numerous applications in business, including analyzing market share, predicting bad debt, forecasting university enrollment, and ­determining whether a machine will break down in the future.

Markov analysis makes the assumption that the system starts in an initial state or condition. For example, two competing manufacturers might have 40% and 60% of the market sales, respectively, as initial states. Perhaps in 2 months the market shares for the two companies will change to 45% and 55% of the market, respectively. Predicting these future states involves knowing the system’s likelihood or probability of changing from one state to another. For a particular problem, these probabilities can be collected and placed in a matrix or table. This matrix of transition probabilities shows the likelihood that the system will change from one time period to the next. This is the Markov process, and it enables us to predict future states or conditions.

Like many other quantitative techniques, Markov analysis can be studied at any level of depth and sophistication. Fortunately, the major mathematical requirements are just that you know how to perform basic matrix manipulations and solve several equations with several unknowns. If you are not familiar with these techniques, you may wish to review Module 5 (on the Companion Website for this book), which covers matrices and other useful mathematical tools, before you begin this chapter.

Because the level of this course prohibits a detailed study of Markov mathematics, we limit our discussion to Markov processes that follow four assumptions:

1. There are a limited or finite number of possible states.

2. The probability of changing states remains the same over time.

3. We can predict any future state from the previous state and the matrix of transition probabilities.

4. The size and makeup of the system (e.g., the total number of manufacturers and customers) do not change during the analysis.