Replacement Models : Staffing Problem

In the previous sections, we discussed about replacement problems, which were not related to human resources working in an organization.

The replacement models can also be used to solve the problems of staff replacement. This section focuses on the problem of replacing staff in an organization. Staff replacement is essential due to the following factors:

Inefficiency
Resignation
Retirement
Unexpected events (like accident, death, etc.)

"Companies that sensibly manage their investment in people will prosper in the long run." - Tom DeMarco & Tim Lister

Assumption

The life distribution for the service of staff in an organization is predetermined.

Consider the following illustrations

Example 1

A team of software developers at www.universalteacher.com is planned to rise to a strength of 50 persons, and then to remain at that level. Consider the following data:

Year	Total % who have left upto the end of the year
1	5
2	30
3	50
4	60
5	70
6	75
7	80
8	85
9	90
10	100

On the basis of above information, determine:

What is the recruitment per year necessary to maintain the strength? There are 8 senior posts for which the length of service is the main criterion. What is the average length of service after which new entrant can expect his promotion to one of these posts?

Solution.

Calculating values for table 1

The values in column (c) are obtained by subtracting the corresponding elements of column (b) from 100.
The values in column (d) are obtained by dividing the corresponding elements in column (b) by 100.
The values in column (e) are obtained by dividing the corresponding elements in column (c) by 100.

Table 1

On small screens, use horizontal scrollbar to view full calculation

Year	No.of persons who leave at the end of the year	No. of persons in service at the end of year	Prob. of leaving at the end of the year	Prob. of in service at the end of the year
a	b	c	d	e
0	0	100	0	1.00
1	5	95	0.05	0.95
2	30	70	0.30	0.70
3	50	50	0.50	0.50
4	60	40	0.60	0.40
5	70	30	0.70	0.30
6	75	25	0.75	0.25
7	80	20	0.80	0.20
8	85	15	0.85	0.15
9	90	10	0.90	0.10
10	100	0	1.00	0
Total		455

From table 1, we find that with a recruitment policy of 100 persons every year, the total number of persons serving in the organization would have been 455. Hence, if we want to maintain a strength of 50 persons then we should recruit

100 x 50
----------
455

1000
-------
91

10.98

= 11 persons/year

Every year 11 persons should be recruited to maintain a strength of 50. Number of survivals after each year can be obtained by multiplying the various values of column (e) by 11.

"New people are recruited to replace the old ones." - Vinay Chhabra & Manish Dewan

Table 2

Year	Number of persons in service
0	11
1	10
2	8
3	6
4	4
5	3
6	3
7	2
8	2
9	1
10	0

Now there are 8 senior posts. From table 2, it can seen that there are 3 persons in service during the sixth year, 2 in seventh year, 2 in eighth year, and 1 in ninth year. Hence, promotions of new recruits will start by the end of sixth year and will continue upto seventh year.

Example 2

The Railway Ministry requires 200 private assistants, 300 private secretaries, and 50 section officers. Persons are recruited at the age of 21, if still in service, retire at the age of 60. Given the following life table, determine

How many persons should be recruited every year ?
At what age promotions should take place ?

Use horizontal scrollbar to view full calculation

Age	21	22	23	24	25	26	27	28
No. in service	1000	600	400	380	311	260	229	206
Age	29	30	31	32	33	34	35	36
No. in service	190	180	174	166	162	155	150	146
Age	37	38	39	40	41	42	43	44
No. in service	145	135	131	125	120	112	105	100
Age	45	46	47	48	49	50	51	52
No. in service	94	86	80	73	65	60	53	46
Age	53	54	55	56	57	58	59	60
No. in service	40	32	26	23	19	13	11	0

Solution.

If a policy of recruiting 1000 persons every year is followed, then the total number of employees in service between the age 21 to 59 years will be equal to 6403. But the requirement of organization is 550 (200 + 300 + 50) employees.

Therefore, to maintain a strength of 550 employees, the organization should recruit:
(1000 X 550)/6403 = 86 (approx.) persons every year.

Private assistants

Out of a strength of 550, there are 200 private assistants. Hence, out of a strength of 1000 there will be
(200 X 1000)/550 = 364 private assistants.
From the above life table, 364 is available upto 24 years. Therefore, the promotion of private assistants will take place in 25th year.

Private secretaries

Out of a strength of 1000 there will be
(300 X 1000)/550 = 545 private secretaries.

Section officers

Number of section officers = 1000 - (364 + 545) = 91.
From the above life table, we find that at the age of 46 only 86 will survive. Therefore, promotion of private secretaries will take place in 46th year.

In this chapter, you were introduced to the problem of replacement that is experienced in systems (both machines and men) where efficiency of items worsen over their life span or sometimes fail completely. The chapter focussed on the following categories: