Markov Analysis and Forecasting

The Doortodoor Sports Equipment Company sells sports clothing and equipment for amateur, light sport (running, tennis, walking, swimming, badminton, and golf) enthusiasts. It is the only company in the nation that does this door-to-door, 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 the products and discuss them 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 (level 3).

The company has decided to study the internal movement patterns of people in the sales function, as well as forecast their likely availabilities in future time periods. The 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 2014 and 2015 to construct a transition probability matrix. as well as the number of employees for 2016 in each job category. It then wanted to use the matrix to forecast availabilities for

2017. The following data were gathered:

Transition Probabilities Transition Probabilities (2014-15) Current Sales, Full-time Sales, Part-time Assistant Sales Regional Sales Exit Workforce (2016) Job Category (L1) (L1) Mgr (L2) Mgr (L3) Sales, Full-time (L1) 0.50 0.10 0.05 0.00 0.35 500 Sales, Part-time (L1) 0.05 0.60 0.10 0.00 0.25 150 Assistant Sales Mgr (L2) 0.05 0.00 0.80 0.10 0.05 50 Regional Sales Mgr (L3) 0.00 0.00 0.00 0.70 0.30 30 Forecast of Supply (Availabilities) in 2017 Fill in the following table: 2017 Current Workforce (2016) Sales, Full-time Sales, Part-time Assistant Sales Regional Sales (L1) (L1) Mgr (L2) Mgr (L3) Job Category Sales, Full-time (L1) 500 Sales, Part-time (L1) 150 Assistant Sales Mgr (L2) 50 Regional Sales Mgr (L3) 30