Location Allocation is one of the most important decision making problems, which attracted many operational researchers during recent decades and many solution procedures are developed so far to cope with this problem. This paper proposes a new graph theory based method to cope with small size capacitated location allocation problems. Additionally, a genetic algorithm is utilized to solve medium and large scale problems. Finally, through some computational experiments, the quality and capability of these algorithms are shown.
Keywords: Location; Capacitated Location Allocation; Graph Theory; Genetic Algorithm
References Ahuja, R. K. A., Magnanti, T. L., &Orlin, J.B. (1993).Network Flows: Theory, Algorithms and Applications. Prentice Hall.
Anand, S., &Knott, K. (1986). Computer assisted models used in the solution of warehouse location-allocation problems. Computers & Industrial Engineering, 11(1-4), 100-104.
Badri, M.A. (1999). Combining the analytic hierarchy process and goal programming for global facility location-allocation problem. International Journal of Production Economics, 62 (3), 237-248.
Barreto, S, Ferreira, C, Paixão, J, &Santos, B.S. (2007).Using clustering analysis in a capacitated location-routing problem.European Journal of Operational Research, 179 (3), 968-977.
Beasley, J.E., &Chu, P.C. (1996).A genetic algorithm for the set covering problem.European Journal of Operational Research, 94, 392-404.
Bischoff, M., &Dächert, K. (2009).Allocation search methods for a generalized class of location–allocation problems.European Journal of Operational Research, 192 (3), 793-807.
Bondy, J.A., &Murty, U.S.R. (2008).Graduate Texts in Mathematics. Graph Theory. London: Springer.
Brimberg, J., Hansen, P., Mladenovic, N., & Taillard, E.D. (2000).Improvements and comparison of heuristics for solving the uncapacitated multisource Weber problem. Operations Research, 48 (3), 444-460.
Charnes, A., Cooper, W. W., &Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.
Cooper, L. (1963). Location-allocation problems.Operations Research, 11, 331-344, 1963.
Ernst, A.T., & Krishnamoorthy, M. (1999). Solution algorithms for the capacitated single allocation hub location problem. Annals of Operations Research, 86, 141-159.
Gen, M., (2000). Genetic Algorithms & Engineering optimization. NewYork: John Wiley.
Krarup, J., &Pruzan, P.M., (1983). The simple facility location problem: Survey and synthesis. European Journal of Operational Research, 12, 36–81.
Lovász, L., & Plummer, M. D. (2009).Matching Theory.AMS Chelsea Publishing.
Logendran, R., & Terrell, M.P. (1988).Uncapacitated plant location-allocation problems with price sensitive stochastic demands. Computers and Operations Research, 15 (2), 189-198.
Love, R. F., & Morris, J. G. (1975).A computation procedure for the exact solution of location–allocation problems with rectangular distances.Naval Research Logistics, 22, 441–53.
Marian, R. M., Luong, L. H. S., & Akararungruangkul, R. (2008).Optimisation of distribution, networks using genetic algorithms. part 1 - problem modelling and automatic generation of solutions. International Journal of Manufacturing Technology and Management, 15(1), 64-83.
Marian, R. M., Luong, L. H. S., & Akararungruangkul, R. (2008).Optimisation of distribution networks using genetic algorithms. part 2 - the genetic algorithm and genetic operators. International Journal of Manufacturing Technology and Management, 15(1), 84-101.
Melo, M.T., Nickel, S. & Saldanha-da-Gama, F. (2009). Facility location and supply chain management – A review. European Journal of Operational Research, 196, 401–412.
Mohammadi, M., Tavakkoli-Moghaddam, R., & Rostami, H. (2011).A multi-objective imperialist competitive algorithm for a capacitated hub covering location problem.International Journal of Industrial Engineering Computations, 2(3), 671-688.
Owen S.H. & Daskin, M. S. (1998). Strategic facility location: a review. European Journal of Operational Research, 111, 423–447.
Yazdian, S. A., & Shahanaghi, K. (2011).A multi-objective possibilistic programming approach for locating distribution centers and allocating customers’ demands in supply chains.International Journal of Industrial Engineering Computations, 2(1), 193-202.
Zhou, G., Min, H., & Gen, M. (2002). The balanced allocation of customers to multiple distribution centers in the supply chain network: a genetic algorithm approach. Computers and Industrial Engineering archive, 43(1-2), 251 – 261.
Zhou, G., Min, H., & Gen M. (2003).A genetic algorithm approach to the bi-criteria allocation of customers to warehouses. International Journal of Production Economics, 86, 35–45.
Zhou, J., & Liu, B. (2007). Modeling capacitated location–allocation problem with fuzzy demands. Computers & Industrial Engineering, 53, 454–468.
® 2010 GrowingScience.Com