Research Article Open Access

Layout Optimization in a Fitness Industry: An Application of QAP Formulation and Heuristic Approaches

İbrahim Miraç Eligüzel1, Eren Özceylan1 and Yakup Atasagun2
  • 1 Gaziantep University, Turkey
  • 2 Konya Technical University, Turkey


The Quadratic Assignment Problem (QAP) is the problem of determining a one-to-one and onto assignment between two sets, each consisting of n objects (e.g., n facilities and n locations) so as to minimize the sum of the distance × flow associated with pairs of assignments. In this study, QAP formulation is applied to a fitness center to assign the sports equipment to the related locations on the layout. Facilities are considered as sports equipment and locations are considered the required area for equipment on the layout. A case study with 19 sports equipment is considered. The objective of the study is to allocate the equipment to the 19 available locations to minimize the total walking distance while considering the interactions between sports equipment. An Integer Programming (IP) formulation is applied using GUROBI package program. 2-opt and tabu search algorithms are also applied to find the feasible/optimal solutions in a reasonable time. The results show that the heuristic approaches are more effective than IP in terms of computational time. The optimal result which is obtained by IP, 2-opt and tabu search provides a better layout with 55.47% less distance × flow compared to the current layout.

Journal of Computer Science
Volume 17 No. 4, 2021, 440-450


Submitted On: 28 January 2021 Published On: 3 May 2021

How to Cite: Eligüzel, �. M., Özceylan, E. & Atasagun, Y. (2021). Layout Optimization in a Fitness Industry: An Application of QAP Formulation and Heuristic Approaches. Journal of Computer Science, 17(4), 440-450.

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  • 2-opt
  • Fitness Center
  • Integer Programming
  • Layout Optimization
  • Quadratic Assignment Problem
  • Tabu Search