Knights Exchange Puzzle—Teaching the Efficiency of Modeling

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

INFORMS Transactions on Education, 2021, vol. 22, issue 1, 108-114

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.

Keywords: teaching modeling; puzzles; efficient models; network flow optimization (search for similar items in EconPapers)
Date: 2021
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