Q$3\mathrm{.}9($Paris Airport$)$ Kim Opim, an enthusiastic first$-$year MBA student, is on her flight

over from Philadelphia $($PHL$)$ to Paris $($CDG$),$ where she will spend some time at

INSEAD in Fontainebleau, France. Kim reflects upon how her educational experiences from

her operations courses could help explain the long wait time that she experienced before

she could enter the departure area of Terminal A at PHL$.$ As an airline representative

explained to Kim, there are four types of travelers in Terminal A:

$$ Experienced short$-$distance $($short$-$distance international travel destinations are

Mexico and various islands in the Atlantic$)$ travelers: These passengers check in online and

do not speak with any agent nor do they take any time at the kiosks.

$$ Experienced long$-$distance travelers: These passengers spend $3$ minutes with an agent.

$$ Inexperienced short$-$distance travelers: These passengers spend $2$ minutes at a kiosk;

however, they do not require the attention of an agent.

$$ Inexperienced long$-$distance travelers: These passengers need to talk $5$ minutes with an

agent.

$123$

All passengers must pass through security, where they need $0\mathrm{.}5$ minutes independent of their type. From historical data, the airport is able to estimate the arrival rates of the different customer types at Terminal A of Philadelphia International:

$$ Experienced short$-$distance travelers: $100$ per hour

$$ Experienced long$-$distance travelers: $80$ per hour

$$ Inexperienced short$-$distance travelers: $80$ per hour

$$ Inexperienced long$-$distance travelers: $40$ per hour

At this terminal, there are four security check stations, six agents, and three electronic kiosks. Passengers arrive uniformly from $4$ p$.$m$.$ to $8$ p$.$m$.,$ with the entire system empty prior to $4$ p$.$m$.($the $$midafternoon lull$)$ and no customers arriving after $8$ p$.$m$.$ All workers must stay on duty until the last passenger is entirely through the system $($e$.$g$.,$ has passed through security$).$

a$.$ What are the levels of implied utilization at each resource?

b$.$ At what time has the last passenger gone through the system? Note: If passengers of one type have to wait for a resource, passengers that do not require service at the resource can pass by the waiting passengers!

c$.$ Kim, an experienced long$-$distance traveler, arrived at $6$ p$.$m$.$ at the airport and attempted to move through the check$-$in process as quickly as she could. How long did she have to wait before she was checked at security?

d$.$ The airline considers showing an educational program that would provide information about the airport's check$-$in procedures. Passenger surveys indicate that $80$ percent of the inexperienced passengers $($short or long distance$)$ would subsequently act as experienced passengers $($i$.$e$.,$ the new arrival rates would be $164$ experienced short$-$distance, $112$ experienced long$-$distance, $16$ inexperienced short$-$distance, and $8$ inexperienced long$-$distance $[$passengers$/$hour$]).$ At what time has the last passenger gone through the system?