Question: You are responsible for a machine that makes widgets for your company. The time to process each lot of widgets through your machine is 4

You are responsible for a machine that makes widgets for your company. The time to process each lot of widgets through your machine is 4 hours. There is 1 hour of setup time and 3 hours of run time required for each lot. The process times for the lots are exponentially distributed. The machine is available 80 hours per week.

Widgets are ordered by the manufacturing lot and average number of lot/orders per week is 18. The orders arrive randomly in time and the arrivals can be characterized as a Poisson process.

a. What is the expected cycle time for each lot of widgets?

b. If the lead time you are quoting for each order is 1 week, what is the probability that your customer deliveries are on time? ((assume LT has a exponential distribution: Prob(t-lT where l= 1/avg cycle time)

c. What is the probability that your customer deliveries are on time if you could reduce setup time to 10 mins instead of 1 hour, again with a 1 week lead time?

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