Selected Topics in Operations Research
MSC 522
Turn-in Problem #8
Markov Processes
Staffing Model (winter 2007)
The ORS Goode Company is a small business that primarily does contract work for the
government. All new employees begin as a trainee. The Company has 6 classes of workers
(including trainee) with annual promotion opportunities as shown in Table 1. All promotions
occur on an annual basis effective the beginning of the calendar year.
Worker
Class
Percent
Promoted to next
worker class
Trainee
50
Level 1
15
Level 2
5
Level 3
5
Level 4
4
Level 5
Table 1. Promotion Rates
In addition, a certain percentage of these workers leave the worker class annually as shown in
Table 2.
Class
Percent
Percent
Quit
Fired
Trainee
20
20
Level 1
7
3
Level 2
5
5
Level 3
1
3
Level 4
1
1
Level 5
1
2
Table 2. Worker Exiting Percents
Percent
retire
0
0
0
1
5
13
Percent promoted
to management
0
0
0
0
1
4
Each year, a worker who is not promoted nor leaves his level for one of the above reasons will
remain at his current level.
Construct a Markov transition matrix to reflect the movement of workers within the company and
answer the following questions:
1. For a new trainee, what is the probability of making level 2 in exactly two years? Within 3
years?
2. What is the probability a level 4 will be promoted to management within five years? Retire
within 4 years?
3. The Company has 173 workers. The current number of workers in each level is shown in
Table 3.
Trainee
Level 1
21
31
Table 3. Current Worker Distribution
Level 2
42
Level 3
38
Level 4
27
Level 5
14
Selected Topics in Operations Research
MSC 522
Turn-in Problem #8
If no new trainees are hired during the next three years as a result of a hiring freeze (downsizing),
what is the expected number of workers in each working class and each exiting class at the end of
the third year? (Do not round-off)
4. For a level 1 worker, determine the expected number of years remaining with the company as
a worker (i.e. level 1 through level 5) before being fired, promoted to management, retiring, or
quitting.
5. For a worker in each class, determine the percent that will eventually quit, be fired, retire, and
promoted to management.
6. From the current 173 workers, how many are expected to eventually retire? How may are
expected to end up in management?