# Question

Vistaprint produces monitors and printers for computers. In the past, only some of them were inspected on a sampling basis. However, the new plan is that they all will be inspected before they are released. Under this plan, the monitors and printers will be brought to the inspection station one at a time as they are completed. For monitors, the interarrival time will have a uniform distribution between 10 and 20 minutes. For printers, the interarrival time will be a constant 15 minutes.

The inspection station has two inspectors. One inspector works on only monitors and the other one only inspects printers. In either case, the inspection time has an exponential distribution with a mean of 10 minutes.

Before beginning the new plan, management wants an evaluation made of how long the monitors and printers will be held up waiting at the inspection station.

(a) Formulate a simulation model for performing a simulation to estimate the expected waiting times (both before beginning inspection and after completing inspection) for either the monitors or the printers.

(b) Considering only the monitors, use the interactive procedure for simulation in your IOR Tutorial to interactively perform this simulation over a period of 10 arrivals of monitors.

(c) Repeat part (b) for the printers.

(d) Use the Queueing Simulator to repeat parts (b) and (c) with 10,000 arrivals in each case.

(e) Management is considering the option of providing new inspection equipment to the inspectors. This equipment would not change the expected time to perform an inspection but it would decrease the variability of the times. In particular, for either product, the inspection time would have an Erlang distribution with a mean of 10 minutes and shape parameter k = 4. Use the Queueing Simulator to repeat part (d) under this option. Compare the results with those obtained in part (d).

The inspection station has two inspectors. One inspector works on only monitors and the other one only inspects printers. In either case, the inspection time has an exponential distribution with a mean of 10 minutes.

Before beginning the new plan, management wants an evaluation made of how long the monitors and printers will be held up waiting at the inspection station.

(a) Formulate a simulation model for performing a simulation to estimate the expected waiting times (both before beginning inspection and after completing inspection) for either the monitors or the printers.

(b) Considering only the monitors, use the interactive procedure for simulation in your IOR Tutorial to interactively perform this simulation over a period of 10 arrivals of monitors.

(c) Repeat part (b) for the printers.

(d) Use the Queueing Simulator to repeat parts (b) and (c) with 10,000 arrivals in each case.

(e) Management is considering the option of providing new inspection equipment to the inspectors. This equipment would not change the expected time to perform an inspection but it would decrease the variability of the times. In particular, for either product, the inspection time would have an Erlang distribution with a mean of 10 minutes and shape parameter k = 4. Use the Queueing Simulator to repeat part (d) under this option. Compare the results with those obtained in part (d).

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