Markov case study

Markov Analysis and Forecasting The Doortodoor Sports Equipment Company sells sports clothing and equipment for amateur, light sport (running, tennis, walking, swimming, badminton, golf) enthusiasts. It is the only company in the nation that does this on a door‐to door basis, seeking to bypass the retail sporting goods store and sell directly to the customer. Its salespeople have sales kits that include both sample products and a full line catalog they can use to show and discuss with customers. The sales function is composed of full‐time and part time salespeople (level 1), assistant sales managers (level 2), and regional sales managers (level3). The company has decided to study the internal movement patterns of people in the sales function, as well as to forecast their likely availabilities in future time periods. Results will be used to help identify staffing gaps (surpluses and shortages) and to develop staffing strategy and plans for future growth.
To do this, the HR department first collected data for 2010 and 2011 to construct a transition probability matrix, as well as the number of employees for 2012 in each job category. It then wanted to use the matrix to forecast availabilities for 2013. The following data were gathered:

Based on the above data:
1.Describe the internal labor market of the company in terms of job stability (staying in same job), promotion paths and rates, transfer paths and rates, demotion paths and rates, and turnover (exit) rates.
2. Forecast the numbers available in each job category in 2013.
3. Indicate potential limitations to your forecasts.