On the unboundedness of facility layout problems
Tóm tắt
Facility layout problems involve the location of facilities in a planar arrangement such that facilities that are strongly connected to one another are close to each other and facilities that are not connected may be far from one another. Pairs of facilities that have a negative connection should be far from one another. Most solution procedures assume that the optimal arrangement is bounded and thus do not incorporate constraints on the location of facilities. However, especially when some of the coefficients are negative, it is possible that the optimal configuration is unbounded. In this paper we investigate whether the solution to the facility layout problem is bounded or not. The main Theorem is a necessary and sufficient condition for boundedness. Sufficient conditions that prove boundedness or unboundedness are also given.
Tài liệu tham khảo
Anjos MF, Vannelli A (2002) An attractor-repeller approach to floor planning. Math Methods Oper Res 56: 3–27
Anjos MF, Vannelli A (2006) A new mathematical programming framework for facility layout design. INFORMS J Comput 18: 111–118
Armour GC, Buffa ES (1963) A heuristic algorithm and simulation approach to relative location of facilities. Manage Sci 9: 294–309
Burkard RE (1990) Locations with spatial interactions: the quadratic assignment problem. In: Mirchandani PB, Francis RL (eds) Discrete location theory. Wiley-Interscience, New York, NY, pp 387–437
Castillo I, Kampas FJ, Pinter JD (2008) Solving circle packing problems by global optimization: numerical results and industrial applications. Eur J Oper Res 191: 786–802
Castillo I, Sim T (2004) A spring-embedding approach for the facility layout problem. J Oper Res Soc 55: 73–81
Cela E (1998) The quadratic assignment problem: theory and algorithms. Kluwer Academic Publishers, Dordrecht
Drezner Z (1980) DISCON—a new method for the layout problem. Oper Res 28: 1375–1384
Drezner Z (1987) A heuristic procedure for the layout of a large number of facilities. Manage Sci 33: 907–915
Drezner Z (2008a) Extensive experiments with hybrid genetic algorithms for the solution of the quadratic assignment problem. Comput Oper Res 35: 717–736
Drezner Z (2008b) Tabu searchand hybrid genetic algorithms for quadratic assignment problems. In: Jaziri W (ed) Tabu search, pp 89–108. In-tech available free on: http://books.itechonline.com
Drezner Z, Hahn PM, Taillard ED (2005) Recent advances for the quadratic assignment problem with special emphasis on instances that are difficult for meta-heuristic methods. Ann Oper Res 139: 65–94
Drezner Z, Wesolowsky GO (1991) The Weber problem on the plane with some negative weights. INFOR 29: 87–99
Grobelny J (1999) Some remarks on scatter plots generation procedures for facility layout. Int J Prod Res 37: 1119–1136
Koopmans TC, Beckmann MJ (1957) Assignment problems and the location of economic activities. Econometrica 25: 53–76
Rendl F (2002) The quadratic assignment problem. In: Drezner Z, Hamacher HW (eds) Facility location: applications and theory. Springer, Berlin, pp 439–457