A semi-Markov model of a manpower system

A semi-Markov model which views a manpower system globally in the sense that it has single grade only, therefore internal promotions and other aspects are ignored and the interest is centered on the total number of vacancies available in the entire organization. To be specific, a manpower system with a single grade allowing wastages and recruitment is considered. Wastages occur according to a Poisson process. Recruitment is made instantaneously as and when the number of vacancies reaches a level s. At the time of each recruitment, the number of vacancies filled up is a random variable following a binomial distribution with parameters s and p, where p is the probability that a vacancy is filled by recruitment. It is further assumed that the value of p depends on the elapsed time since the last recruitment. Identifying the underlying stochastic process as a Markov-renewal process, the distribution of the vacancy level at any time is obtained and the stationary behavior of the system is discussed in this paper. A numerical example also illustrates the results obtained.