Delivered by Ingenta to: Rice University IP: 185.14.195.149 On: Sun, 12 Jun 2016 10:26:12 Copyright: American Scientific Publishers RESEARCH ARTICLE Copyright © 2015 American Scientific Publishers All rights reserved Printed in the United States of America Journal of Computational and Theoretical Nanoscience Vol. 12, 3817–3826, 2015 A New Exact Formulation and Simulated Annealing Algorithm for One-Sided Closed Loop Layout Sadegh Niroomand 1 ∗ , Nima Mirzaei 2 , Ramazan ¸ Sahin 3 , and Béla Vizvári 1 1 Industrial Engineering Department, Eastern Mediterranean University, Famagusta, North Cyprus, Mersin 10, Turkey 2 Industrial Engineering Department, Istanbul Aydin University, Florya, Istanbul 34295, Turkey 3 Industrial Engineering Department, Engineering Faculty, Gazi University, Ankara 06500, Turkey A closed loop facility layout problem consists of an arrangement of several rectangular cells around a rectangular closed loop. This paper introduces a mathematical model for cases where the cells are located outside the closed loop. The transportation cost for a closed loop formation is proved to be strictly less than the transportation cost for a single row. A simulated annealing (SA) algorithm is used to solve benchmark problems in the single row facility layout literature. Latin square design is used to design experiments to find the most effective levels of factors for the SA algorithm. Computational results for the benchmark problems are strictly better for a closed loop formation than for single row formation. Keywords: Facility Layout, Close Loop Layout, Single Row Layout, Mixed Integer Linear Programming, Simulated Annealing. 1. INTRODUCTION The facility layout problem (FLP) is used to arrange a limited number of facilities in a given area (bounded or unbounded) based on the interactions between the facilities (e.g., transportation). In FLP, the total cost of interaction between facilities is minimized. FLP has several real-life applications, e.g., the arrangement of departments in the manufacturing and service sectors. A famous type of FLP is known as the Single Row Facility Layout Problem (SRFLP). In SRFLP, a limited number of rectangular cells (facilities) are arranged on one side of a straight line. The objective function minimizes the sum of the transportation costs between all pairs of cells. SRFLP has a wide range of applications: the arrange- ment of departments on one side of a corridor of an office building, a supermarket or a hospital; 1 the assignment of disk cylinders to files; 2 and the arrangement of machines on one side of a line traversed by an automated guided vehicle. 3 4 Because SRFLP is a NP-complete problem, 5 several heuristic methods can produce an accurate feasible solu- tion. Heragu and Kusiak 6 developed a mixed-integer linear programming (MILP) model for SRFLP. The model was ∗ Author to whom correspondence should be addressed. solved using a penalty technique. Heragu and Alfa 7 also developed a simulated annealing algorithm for SRFLP. Kumar et al. 8 introduced a constructive greedy heuristic. A combination of a genetic algorithm and a simulated annealing algorithm was also used by Braglia. 9 Another genetic algorithm was applied by Fickoet. 10 A nonlinear 0–1 formulation of SRFLP was introduced by Solimanpur et al., 4 who used an ant colony algorithm to solve the model. A semi-definite programming relaxation was devel- oped by Anjos et al. 11 to calculate a lower bound on the optimal value. A lower bound also obtained by Amaral. 12 Samarghandi et al. 13 applied a particle swarm optimization method. Another tabu algorithm was used by Samarghandi and Eshghi. 14 These citations show that there is a rich and comprehensive literature on SRFLP. Another type of FLP is known as the Closed Loop Facil- ity Layout Problem (CLFLP). In CLFLP, a limited num- ber of cells are arranged around a rectangular closed loop material handling path. Based on the origin of the CLFLP, one side (outside) or both sides (outside and inside) of the closed loop may be used to arrange the cells. As in all lay- out problems, an objective function in CLFLP minimizes the total transportation cost. CLFLP is an intriguing layout problem but little research has been performed on this type of problem. 29 Chae and Peters 15 proposed a simulated annealing algo- rithm to arrange the cells around a double-sided closed J. Comput. Theor. Nanosci. 2015, Vol. 12, No. 10 1546-1955/2015/12/3817/010 doi:10.1166/jctn.2015.4287 3817