TITLE:
Manpower Systems Operating under Heavy and Light Tailed Inter-Exit Time Distributions
AUTHORS:
R. Sivasamy, P. Tirupathi Rao, K. Thaga
KEYWORDS:
Manpower System; Recruitment Policy; Inter-Exit Time; Wastage; Waiting Time to Breakdown; Heavy Tailed Inter-Exit Time Distribution and Light Tailed Distribution
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.2,
January
20,
2014
ABSTRACT: This paper
considers a Manpower system where “exits” of employed personnel produce some
wastage or loss. This system monitors these
wastages over the sequence of exit epochs {t0 = 0 and tk; k = 1, 2,…} that form a recurrent process and admit
recruitment when the cumulative loss of man hours crosses a threshold level Y, which is also called the breakdown
level. It is assumed that the inter-exit times Tk = tk-1 - tk, k = 1, 2,… are independent and identically distributed random variables with a
common cumulative distribution function (CDF) B(t) = P(Tk t) which has a tail 1 – B(t) behaving
like t-v with 1 v as t → ∞.
The amounts {Xk} of wastages incurred during these inter-exit times {Tk} are
independent and identically distributed random variables with CDF P(Xk X) = G(x) and Y is distributed, independently of {Xk} and {tk}, as an exponentiated
exponential law with CDF H(y)
= P(Y y) = (1 - e-λy)n. The mean waiting time to break down of the system has been obtained assuming B(t) to be heavy
tailed and as well as light tailed. For the exponential case of G(x), a comparative study has also been made
between heavy tailed mean waiting time to break down and
light tailed mean waiting time to break down
values. The recruitment policy operating under the heavy tailed case is shown
to be more economical in all types of manpower systems.