Estimation: right-sizing the elevators in a typical office building

Estimate how many elevators an average office building should have. Explain how you break the problem down, label each assumption as you make it, and finish with a count you can defend and a sense of how far it would move if your assumptions are off. ```hint Split demand from supply Work out how many riders the elevators must move in the window you size them for, then how many riders one car can carry in that window once you know how long its round trip takes. ``` ### Clarifying Questions - Does "average" mean the typical building by count, which may be only a few stories, or a typical city-center office tower, and how many floors and people per floor should I assume? - Is it one company with shared start times, or several tenants, possibly with shifts or public spaces such as a rooftop restaurant or ground-floor retail? - Should the count cover passenger elevators only, or also service and freight cars and any cars that serve parking levels? - What service level should the elevators meet: a cap on how long people wait in the lobby, or a time limit for getting everyone to their floor? ### What a Strong Answer Covers - A concrete picture of the building (floors, people per floor, tenant mix) stated as labeled assumptions - The demand window the count is sized for, why that window is the binding one, and the arrival rate it implies - A round-trip model for one car (loading, stops, doors, travel) that turns into riders moved per car in that window - Unit-consistent arithmetic from demand and per-car capacity to a count, checked against a wait or interval target - A range from varying the shakiest inputs, plus how the count shifts with building height, service cars and redundancy ### Follow-up Questions - How would your count change for a building twice as tall, and at what point would you split the floors into separately served zones? - If a lobby system had riders enter their destination floor before boarding, how would that change your estimate? - If the building added a second shift whose start overlaps the first shift's end, which inputs would you revisit?