Question

: Larry Ellison starts a company that manufacturers 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 inter-arrival times of orders have a coefficient of variation of 1. What is the expected duration, in days, between when an order is received and when production begins on the bag (i.e. include the time waiting to start production but do not include the time in production)

Answer 1

Expected duration between when orders begin and production begins = 12.55 days

Explanation:

Expected duration between when an order is received and the start of production:

Average production time for a bag, P = 1.8

Standard deviation,
`\sigma_(p) = 2.7 days`

Number of employees, m = 2

Larry expects one customer order a day, a = 1

Coefficient of variation of arrival,
`v_(a) = 1`

Coefficient of variation of processing,
`v_(p) = (\sigma_(p) )/(P)`

`v_(p) = (2.7)/(1.8) \\v_(p) = 1.5`

Utilization,
`v = (p)/(ma)`

`v = (1.8)/(2*1)`

`v = 0.9`

Expected time of wait =
`((P)/(m) * (v^(√(2(m+1))-1 ) )/(1 -v) )* ((v_(a) ^(2)+ v_(p) ^(2) )/(2) )`

Expected time of wait =
`((1.8)/(2) * (0.9^(√(2(2+1))-1 ) )/(1 -0.9) )* ((1 ^(2) + 1.5 ^(2) )/(2) )`

Expected time of wait = 12.55 days