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Knights Exchange Puzzle—Teaching the Efficiency of Modeling

Author

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  • Mehdi Iranpoor

    (Department of Industrial and Systems Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran)

Abstract

Puzzles and games enhance the quality of teaching by creating an enjoyable, interactive, and playful atmosphere. The knight exchange is a famous, very old, and amusing game on the chessboard. This puzzle was used by the author to teach modeling in a mathematical programming course designed for graduate students. The aim was to teach the students the efficiency of the models. Accordingly, first, a binary programming formulation was developed. This formulation was, however, found to be inefficient, and tremendous time (i.e., more than four hours) and a large amount of processing memory were needed to solve the puzzle. The puzzle was subsequently formulated as a minimum cost network flow problem. The latter formulation outperformed the general binary formulation by solving the puzzle in less than a minute. The network formulation could also save the required processing memory. The results could help students to learn the value of modeling combinatorial optimization problems as network flows.

Suggested Citation

  • Mehdi Iranpoor, 2021. "Knights Exchange Puzzle—Teaching the Efficiency of Modeling," INFORMS Transactions on Education, INFORMS, vol. 22(1), pages 108-114, January.
    • Handle: RePEc:inm:orited:v:21:y:2021:i:2:p:108-114
    DOI: 10.1287/ited.2019.0235
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    References listed on IDEAS

    as
    1. Craig Letavec & John Ruggiero, 2002. "The n -Queens Problem," INFORMS Transactions on Education, INFORMS, vol. 2(3), pages 101-103, May.
    2. Sönke Hartmann, 2019. "Puzzle—More Logic Puzzle Apps Solved by Mathematical Programming," INFORMS Transactions on Education, INFORMS, vol. 20(1), pages 49-55, September.
    3. Gail W. DePuy & G. Don Taylor, 2007. "Using Board Puzzles to Teach Operations Research," INFORMS Transactions on Education, INFORMS, vol. 7(2), pages 160-171, January.
    4. Martin J. Chlond & Cath M. Toase, 2002. "IP Modeling of Chessboard Placements and Related Puzzles," INFORMS Transactions on Education, INFORMS, vol. 2(2), pages 1-11, January.
    5. Martin J. Chlond & Robert Bosch, 2006. "The Gunport Problem," INFORMS Transactions on Education, INFORMS, vol. 6(2), pages 37-43, January.
    6. Robin H. Pearce & Michael A. Forbes, 2017. "Puzzle—The Fillomino Puzzle," INFORMS Transactions on Education, INFORMS, vol. 17(2), pages 85-89, January.
    Full references (including those not matched with items on IDEAS)

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