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The Snake Eggs Puzzle: Preparing Students for Benders Decomposition

Author

Listed:
  • Mitchell Harris

    (School of Mathematics and Physics, The University of Queensland, Brisbane, St Lucia, QLD 4072, Australia)

  • Michael Forbes

    (School of Mathematics and Physics, The University of Queensland, Brisbane, St Lucia, QLD 4072, Australia)

Abstract

Logic puzzles are an effective way to introduce students to advanced solution techniques in operations research, such as Lagrangian relaxation, Dantzig-Wolfe decomposition, and Benders decomposition. The Snake Egg puzzle asks the player to draw a one-cell wide path, or “snake,” in a grid. The remaining cells should form a fixed number of separate, connected, discontiguous regions called “eggs.” We propose two solution approaches: a flow-based model and lazy constraints. Instead of providing the complete model at the outset, we will step through the puzzle in a manner suitable to the classroom, emphasizing the skills that are crucial to successfully implementing advanced techniques. The puzzle functions in particular as a prelude to Benders decomposition.

Suggested Citation

  • Mitchell Harris & Michael Forbes, 2023. "The Snake Eggs Puzzle: Preparing Students for Benders Decomposition," INFORMS Transactions on Education, INFORMS, vol. 23(3), pages 210-217, May.
    • Handle: RePEc:inm:orited:v:23:y:2023:i:3:p:210-217
    DOI: 10.1287/ited.2023.0281
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    References listed on IDEAS

    as
    1. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    2. Robin H. Pearce & Michael A. Forbes, 2017. "Puzzle—The Fillomino Puzzle," INFORMS Transactions on Education, INFORMS, vol. 17(2), pages 85-89, January.
    3. SönkeHartmann, 2018. "Puzzle—Solving Smartphone Puzzle Apps by Mathematical Programming," INFORMS Transactions on Education, INFORMS, vol. 18(2), pages 127-141, January.
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