Puzzles
February 2017 (Port in a Storm)
December 2016 (Galaxy on Fire)
October 2016 (Shelter in Place)
August 2016 (Matchup)
June 2016 (Elevators)
April 2016 (Cell Towers)
February 2016 (Toy builder)
December 2015 (Crazy Cake)
October 2015 (Racecar design)
August 2015 (Moon Rover)
June 2015 (Campsite)
April 2015 (Desert Island)
February 2015 (Coins)
December 2014 (Electrifying)
October 2014 (Fighters)
August 2014 (Good Burger)
June 2014 (Frog and Fly)
April 2014 (Spy Catcher)
February 2014 (Pizza Delivery)
December 2013 (Golf Queuing)
October 2013 (Chutes and Ladders)
August 2013 (Urban Planning)
June 2013 (Self Driving Cars)
April 2013 (Subs vs. Battleships)
February 2013 (Chandelier Balancing)
December 2012 (Cookie Bake Off)
October 2012 (FarmOR)
August 2012 (Combination Locks)
June 2012 (Lost at Sea)
April 2012 (McEverywhere)
February 2012 (Popsicle Scheduling)
December 2011 (Dice Game)
October 2011 (Movie Stars)
August 2011 (Logical Hospital)
June 2011 (Matchmaker)
April 2011 (Choose Your Crew)
February 2011 (Best Host)
December 2010 (Miniopoly)
October 2010 (Home Improvement)
August 2010 (Relief Mission)
June 2010 (SurvivOR)
April 2010 (Patient 21)
February 2010 (Planet Colonization)
December 2009 (Fish Finder)
October 2009 (Connected & Infected)
August 2009 (Bridges)
June 2009 (Grocery Queuing)
April 2009 (Dance Scheduling)
February 2009 (Supply & Demand)
December 2008 (5x5 Poker)
October 2008 (3DPP)
August 2008 (Markov's Prison)
June 2008 (TSP)
April 2008 (Scheduling)
February 2008 (Decision Trees)
Answers
About the PuzzlOR
Analytics Treasure Hunt 2012
The PuzzlOR
Decision Support Puzzles for Applied Mathematicians
April 2009 - Dance Scheduling













Dance-pair    Student    Teacher    Skill
1    Daniel    Mr. Brown    2
2    Camila    Mr. Davis    4
3    Brianna    Ms. Evans    2
4    Eve    Ms. Clark    3
5    Ava    Ms. Anderson    1
6    Camila    Ms. Clark    5
7    Ava    Mr. Davis    3
8    Eve    Ms. Evans    1
9    Camila    Ms. Anderson    4
10    Brianna    Mr. Davis    3


A popular dance studio in New York City holds ballroom dancing showcases twice a year to provide its students with an environment for socializing, practice, and improvement.  A showcase consists of several heats in which multiple dance-pairs dance at the same time.  Because multiple objectives are desired to maximize the quality of the showcase, scheduling the dance-pairs becomes a complex problem that requires OR techniques to solve.

The objectives, when scheduling a showcase, are to minimize the number of heats (in order to minimize the overall duration of the showcase), group similarly skilled dance-pairs in the same heat, and minimize the number of heats that have only one dance-pair.

Table 1 shows the dance-pairs that must be scheduled for the showcase.  For example, dance-pair 1 shows student Daniel will dance with teacher Mr. Brown.  Their Skill level is an indicator of how well this dance-pair performs together.  Each dance-pair must be assigned to one heat.  You may schedule as many heats as you like in order to fulfill this requirement but you cannot schedule students or teachers twice to the same heat.  For example, you cannot assign dance-pairs 6 and 9 to heat 1 because it would require Camila to dance with both Ms. Clark and Ms. Anderson at the same time.

Scoring:
The quality of the showcase is based on a points system.  A dance-pair arrangement requiring 3 total heats is worth 110 points, 4 heats are worth 100 points, 5 heats are worth 90, 6 heats are worth 80, 7 heats are worth 70, etc.  For every heat with a standard deviation over 1 there is a 25 point penalty.  For every heat with only one dance-pair there is a 10 point penalty.

Question: What is the optimal way to assign the dance-pairs to heats in order to maximize the quality of the showcase?

Tweet
Copyright 2017 - All Rights Reserved