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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.