Manpower systems operating under heavy and light tailed inter-exit time distributions

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 re- current 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 < 2 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 man- power systems.