Elevator

Our building has six floors. Floor 0 is used to enter and exit the building, and floors 1-5 each have the same number of residents.  There is one elevator and it is used by the residents only to leave the building (going from their floor to floor 0) or to return to their floor (starting at floor 0). The problem is how to program the elevator.

Half of all calls are from floor 0 going to each resident floor with equal probability 1/5. The other half are from the resident floors (with equal probability 1/5) and they all go to floor 0.

Why do we need a program? Well, we need to decide what the elevator should do once it has delivered a resident to a destination. Of course it could stay right where it has landed and wait there for the next call. But we might also want it to go and park somewhere else to wait, somewhere that might be more “cost-effective.” That would arise if the residents were crazy busy people and they put a cost on their time. In economics, such costs are called “opportunity costs.” 

This is an interesting modeling problem, certainly more complex than we usually find in school, but what it really draws on is careful organized thinking. It’s also the kind of activity our students will encounter in that big world to come.

As a bonus there’s an interesting app that the kids can use to test different policies.