Question

Explain the relationship between Utilization, Little's law, spending and cost per unit for a manufacturing company. Using of diagrams is preferred.

Answer 1

Little’s Law states that in a queuing system under steady state conditions. the average items in the system is same as the average of item arrival in the system multiplied with the average time it spends in the system.

                        L=lambda * W

Waiting line theory is based on the premises of Little’s Law. This theory estimates the percentage of time a system is busy or is under utilization based on the number of tasks been processed and the number of customers waiting in the queue.

n(t) 1s departure in T Nharrival in T A(T) 1st arrival in T Time period T

The probability of arrivals in the system in given time period is given by the following equation:

(AT)"AT n! where: P-probability of n arrivals in T time periods A arrival rate T number of time periods

Based on above, the utilization of the system can be given by the ratio of arrival rate and service rate.

where: ρ-: average utilization of the system λ arrival rate μ service rate