Applications of Stationary Population Ideas

1. Applications of Stationary Population Ideas (Session 16)

2. Learning Objectives – this session At the end of this session, you will be able to • appreciate the wider application of LT ideas in manpower planning • utilise Life Table algebra in a more practised way, to contribute to elementary forms of manpower planning calculation

3. Example questions: 1 Shows type of Q. below. Others will not give you the answers in class! Work them out. Q1. In terms of standard Life Table algebra, what is the amount likely to be paid out by a company which has sold an insurance to 1000 people (aged exactly 20) that undertakes to pay out $1000 to the family if an individual dies before reaching age 50? A1. 1000 x 1000 x (l20 – l50)/l20

4. Introduction The stationary population is one replenished to remain at constant size. The example below looks at an (unrealistic, simplified) population: employees who age & either die or retire are “replaced” by new recruits to maintain population. Questions for classroom practice give first indication of use of stationary pop.n in manpower planning. Real worker pop.ns are grade-structured & subject to promotion, resignation, separate M & F LTs etc.

5. Scenario I A company recruits 100 men per year, uniformly over the year, at exact age 18, and retires everybody at age 60. Assume no other men are recruited at any other age, and no-one leaves the employment other than through retirement or death. Assume they are all subject to mortality as per the UK 0305 single year of age interim LT used in earlier practicals.

6. Example questions: 2 Q2. What is the total number of men on the staff of the company above.

7. Example questions: 3, 4 Q3. How many pensioners (surviving retired employees) would the company have on its books? Q4.How many staff would the company have on its books aged between 40 and 60?

8. Example questions: 5, 6 Q5. How many staff retire each year? Q6. How many die each year while still in service on the staff?

9. Example questions: 7, 8 Q7. How many pensioners die each year? Q8. How many pensioners die each year aged 70-80?

10. Scenario II Q9. A company staff in a stationary state is maintained by 1,000 entrants each year continuously recruited so they start evenly across time. They are recruited at exact age 20. 10% leave at age 23 after a 3-yr contract. 5% remaining leave at age 26 after a second 3-year contract. The rest are taken on permanent contracts: 40% of those who reach age 60 retire then; all who reach 65 retire then.

11. Example questions: 9, 10 Q9. What is the total number on the staff? Q10. What is the total no. of pensioners?

12. Example questions: 11, 12 Q11. How many pensioners are there aged 60 – 65? Q12. How many staff are there between ages 25 and 40?

13. Example question: 13 Q13. What is the average number of years expected to be worked with the company by a new recruit aged 20?

14. Example questions: 14, 15 Q14. What is the average number of years expected to be worked with the company after age 40 by an employee currently aged 25? Q15. What is the probability that a member of staff aged exactly 25 will still be on the staff at age 63?

15. Generalisations Above type of argument gets more complex with the further structures mentioned in the introduction, when salaries go up according to pay scales, when inflation changes financial measures through time, and when the value of money is computed at different time points (e.g. net present values).

16. Some other examples The following can all employ the same fundamental method. When items are sold a retailer needs to replenish stocks. Similarly a factory with many machines may seek to maintain a stock of parts that are liable to fail. A hospital ward carrying out routine surgery may have a similar throughput, except that “sales” or “failures” are replaced by the departures of patients who have recovered from their operations.

17. Some practical work follows …