Mean and Variance of the Time to Recruitment in a Two Graded Manpower System with Two Thresholds for the Organization

Abstract

In this paper, a two graded manpower system which is subject to exit of personnel due to the policy decisions taken in the system is considered. There is an associated loss of manpower if a person quits. As the exit of personnel is unpredictable, a new recruitment policy involving two thresholds – one is optional and the other one mandatory is suggested to enable the organization to plan its decision on recruitment. Based on shock model approach, two mathematical models are constructed using a univariate policy of recruitment. The analytical expression for the mean and variance of the time to recruitment are obtained when i) the loss of manpower processes in grades 1& 2 form separately a sequence of independent and identically distributed exponential random variables ii) the inter-decision times are independent and identically distributed exponential random variables and iii) the optional and mandatory thresholds in both the grades follow exponential, exponentiated exponential distribution and the distribution having SCBZ property respectively. The results are numerically illustrated for both the models and relevant conclusions are made.