Sunday, December 17, 2006

Xmas Cracker Puzzle for grown-ups

Here’s today’s problem:

You are the Building Manager of a 100-storey office block. The block is occupied by about 120 different companies of various sizes who, between them, have 12,000 employees in your building. All these companies officially start their working day at either 9.00 or 9.30am and finish at 5.30 or 6.00pm respectively.

On top of the building there is a viewing platform, open to the general public, which is very popular because of the panoramic views of the city it provides. The 100th floor is occupied by a restaurant and a couple of cafes and bars which are very popular with both locals and visitors alike.

Somewhat bizarrely, floors 36 to 39 are occupied by the Anlar School, the most exclusive in the city, whose remote sports campus is state of the art. The school has 800 pupils.

Your building is serviced by 40 lifts, each of which has a capacity of 20 people. When full, each lift makes an average of 10 stops, each of 30 seconds duration which contribute to an average “round-trip” time of 7 minutes. In other words, the maximum lift capacity is 800 people every 7 minutes or 6,860 per hour.

Every working day begins and ends with large numbers of workers milling around the various banks of lifts. Younger employees on the first 6-7 floors tend to use the stairs in the morning rather than endure the delay of getting a lift. Departing in the evening, some people from as high as 10-12 will use the stairs, descending being less physically arduous than ascending.

In addition, the Anlar School day starts at 9.00am and many parents, particularly of younger students, insist on accompanying their progeny in the lifts and delivering them personally to the school door. School day ends at 4.00pm, resulting in a relatively minor hold-up of lifts at that time.

Employers are becoming increasingly anxious about the stress faced by their employees in arriving for and departing from work. Some workers have taken to coming in early or leaving late to avoid the crush, but the majority are still working their normal day.
As Building Manager, you are doubly concerned by the increasing incidence of “lift-rage”, arguments and the odd scuffle have become an almost daily occurrence as someone tries to skip the queue. It will only be a matter of time before someone is seriously hurt and the police become involved.

This issue has been top of the agenda at recent tenant meetings and your proposed options/solutions are scheduled for delivery to the next meeting.

In the evening and at weekends, the lobby is a haven of peace and tranquillity, with only visitors to the viewing platform and 100th floor restaurant, cafes and bars using the building.

In considering your solutions, there are a number of constraints which may limit your options:
(1) Because of surrounding buildings and public walkways, it will not be possible to add additional lift capacity to the external frame of the building.
(2) Your architect advises that installation of additional lift capacity internally will cause huge disruption over an extended period to existing users of the building and is likely to be prohibitively expensive, in terms of actual construction costs and payment of compensation to existing tenants, both for disruption of their business and the need to buy back a portion of their leasehold interest.
(3) It will also involve taking some of the existing lift capacity out of service, temporarily compounding the problem while that particular solution is pursued.

Proposed solutions to - if you crack this one you’ll possibly have gone some way towards solving Dublin’s traffic problem.

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