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Thinking Analytically: Any port in a storm

John ToczekBy John Toczek

There is significant danger to boats caught out in the open sea during a storm. Ideally, boats will dock before the storm hits and wait it out.

The map shows 20 orange boats out at sea. With a storm approaching, each boat needs to be directed to one of three docks. Docks have a limited number of spaces available for boats (indicated by the rectangular spaces). Altogether, there are 20 boat spaces available. The boats are clustered into three areas, and each area varies in distance to the docks (as indicated by the black arrows). All boats must be assigned to one unique space in a dock.

Minimum distance problem

Twenty boats and 20 docks: Which boat goes where?

Question:
What is the minimum possible total distance traveled by all boats to the docks?

Send your answer to puzzlor@gmail.com by May 15. The winner, chosen randomly from correct answers, will receive a $25 Amazon Gift Card. Past questions and answers can be found at puzzlor.com.


John Toczek earned his BSc. in chemical engineering at Drexel University (1996) and his MSc. in operations research from Virginia Commonwealth University (2005). He is a member of INFORMS.

 

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