A Three Graded Manpower Planning Model with Bulk Recruitment at First Grade and Poisson Recruitment at Second Grade

This is a manpower model with three hierarchical grades. At first grade direct recruitment is assumed to be bulk and bulk sizes are assumed to follow geometrically distributed and bulks arrivals are assumed to follow Poisson. In addition to this a direct Poisson recruitment is assumed at second stage. It is further assumed that the promotion processes from grade-I to grade-II and grade-II to grade-III and leaving process from all the three grades are all Poisson. The transient behavior of this system is analyzed through differencedifferential equations. The system characteristics of the model like mean and variances of number of employees in each grade and covariance between different grade sizes are explicitly derived. The limiting behavior of the model under equilibrium is also analyzed by obtaining the system size joint probability distribution. The sensitivity of the model with respect to model parameters is also discussed.