GLOBAL OPERATIONS MANAGEMENT
1. At the Airport
Metro Airport is required to randomly screen checked luggage for some of its passengers. The current method of screening checked luggage is for a single screener to search each piece by hand. It takes an average of 4 minutes per piece of luggage, and the hand search time is exponentially distributed. The airport is considering leasing an automatic luggage-screening machine to replace hand screening. The new luggage-screening machine will only take an average of 3 minutes per piece of luggage, with a standard deviation of 2 minutes.
The airport has an average of 30 flights per day, with an average of 125 passengers per flight, and each passenger has an average of 1 piece of checked luggage. The airport is required to screen 5% of all passengers. Passenger arrivals are Poisson, and the average rate of arrivals is constant throughout a 15-hour day of flights.
a) At what rate do pieces of luggage requiring screening arrive (in pieces of luggage per hour)?
Arrival rate ______________ pieces of luggage needing screened per hour
b) What are the utilizations for the current system and the automatic system?
Current system utilization _____________
Automatic system utilization _____________
c) What is the amount of time an average passenger spends waiting & being screened (combined) under the current system and under the automatic system (in minutes)?
Current system _____________ minutes
Automatic system _____________ minutes
d) If the airport is willing to spend up to $4000 more per month (30 days) for the new system (vs. what the old system costs, including labor), what value are they implicitly placing on a minute of passenger time spent with screening (waiting plus screening time)?
Value of one minute of passenger time ___________
e) If the airport goes with the automatic system, what is the average number of passengers that will be waiting in the line?