GRASP with Path-Relinking for Facility Layout
This paper proposes a mathematical formulation for the facility layout problem (FLP) based on the generalized quadratic assignment problem (GQAP). The GQAP is a generalization of the NP-hard quadratic assignment problem (QAP) that allows multiple facilities to be assigned to a single location as long as the capacity of the location allows. As a case study, we adapt the GRASP with path-relinking (GRASP-PR) heuristic introduced in Mateus et al. (J. Heuristics 17:527–565, 2011) for the hospital layout problem (HLP). In the HLP, we are given a set of areas in a hospital where medical facilities, such as surgery and recovery rooms, can be located and a set of medical facilities, each facility with a required area, that must be located in the hospital. Furthermore, we are given a matrix specifying, for each ordered pair of facilities, the number of patients that transition from the first to the second facility. The objective of the assignment is to minimize the total distance traveled by the patients. We illustrate our algorithm with a numerical example.
KeywordsHospital layout Generalized quadratic assignment problem GRASP Path-relinking Heuristics
The research of R.M.A Silva was partially supported by the Brazilian National Council for Scientific and Technological Development (CNPq), the Foundation for Support of Research of the State of Minas Gerais, Brazil (FAPEMIG), Coordination for the Improvement of Higher Education Personnel, Brazil (CAPES), Foundation for the Support of Development of the Federal University of Pernambuco, Brazil (FADE), the Office for Research and Graduate Studies of the Federal University of Pernambuco (PROPESQ), and the Foundation for Support of Science and Technology of the State of Pernambuco (FACEPE).
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