Question

Larry Ellison starts a company that manufactures high-end custom leather bags. He hires two employees. Each employee only begins working on a bag when a customer order has been received and then she makes the bag from beginning to end. The average production time of a bag is 1.8 days with a standard deviation of 2.7 days. Larry expects to receive one customer order, per day on average. The arrival process follows a Poisson distribution. What is the expected duration, in days, between when an order is received and when production begins on the bag

Answer 1

12.55 days.

Step-by-step explanation:

Arrival time (a) = 1 day

Coefficient of variation of arrival (CVa) = 1

Processing time (p) = 1.8 days

Standard deviation for processing = 2.7 days

Coefficient of variation for processing = Standard deviation for processing/ Processing time

Coefficient of variation for processing (CVp) = 2.7/ 1.8

Coefficient of variation for processing (CVp) = 1.5

Given, number of servers (m) = 2

Utilization of system (u) = p/(m×a)

Utilization of system (u) = 1.8/(2×1)

Utilization of system (u) = 0.9

Let waiting time in the queue = Tq

Formula for waiting time in queue is quite complicated to write it here. SO, I have attached in the attachment below. Please refer to the attachment to see the formula for Tq.

SO, after plugging in the values in to the formula, we get:

Tq = 12.55 Days

Therefore, the Expected duration between when an order is received and when production begins = 12.55 days