Question

Question 18

1. A large corporation collected data on the reasons both middle managers and senior managers leave the company. Some managers eventually retire, but others leave the company prior to retirement for personal reasons including more attractive positions with other firms. Assume that the following matrix of one-year transition probabilities applies with the four states of the Markov process being retirement, leaves prior to retirement for personal reasons, stays as a middle manager, and stays as a senior manager.
   

Leaves-	Middle	Senior
	Retirement	Personal	Manager	Manager
Retirement	1.00	0.00	0.00	0.00
Leaves-Personal	0.00	1.00	0.00	0.00
Middle Manager	0.03	0.07	0.80	0.10
Senior Manager	0.08	0.01	0.03	0.88

The company currently has 640 middle managers and 280 senior managers. How many of these managers will eventually leave the company for personal reasons? Please calculate the N & NR matrices to the nearest three decimal places!

		579
		225
		341
		287
		5

Answer 1

ANSWER: 341

Steady state is computed as below:

We stop the iterations, because states are almost stabilized.

We see that steady state for L = 341

and for R = 578

EXCEL FORMULAS:

H6 =$H5*B$4+$I5*B$5+$J5*B$6+$K5*B$7 copy to H6:H75

I6 =$H5*C$4+$I5*C$5+$J5*C$6+$K5*C$7 copy to I6:I75

J6 =$H5*D$4+$I5*D$5+$J5*D$6+$K5*D$7 copy to J6:J75

K6 =$H5*E$4+$I5*E$5+$J5*E$6+$K5*E$7 copy to K6:K75