Personnel planning is an important function for many firms. Consider a company’s department with a desired headcount of 100 positions. Suppose that employees leave their positions at a rate of 3.4 per month, and that it requires an average of 4 months for the firm to fill open positions. Analysis of past data shows that the number of employees leaving the firm per month has the Poisson distribution, and that the time required to fill positions follows Weibull distribution. What is the probability that there are more than 15 positions unfilled at any point in time? How many jobs within the department are filled on average? How many positions should the firm have in order for the head count of working employees to be 100 on average?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Personnel planning is an important function for many firms. Consider a company’s department with a desired headcount of 100 positions. Suppose that employees leave their positions at a rate of 3.4 per month, and that it requires an average of 4 months for the firm to fill open positions. Analysis of past data shows that the number of employees leaving the firm per month has the Poisson distribution, and that the time required to fill positions follows Weibull distribution. What is the probability that there are more than 15 positions unfilled at any point in time? How many jobs within the department are filled on average? How many positions should the firm have in order for the head count of working employees to be 100 on average?
Given data is
Desired headcount = 100
Leave rate(arrival rate) = 3.4 per month
Filling rate(service rate) = 4 months
The given problem is an M/G/infinite queue model because after the employee leaves the company and the search for a new employee starts immediately and the accurate model I would have infinite servers.
The expected number of positions unfilled is
Now, the probability of more than fifteen unfilled positions is Poisson variable(random) such that mean of 13.6 exceeds 15. From the table of cumulative Poisson probabilities, one can find the corresponding value of 0.29.
Hence, the probability that there are more than 15 positions unfilled is 0.29 and there are 86.4 jobs filled on average in the department.
Step by step
Solved in 3 steps
