Experiment Design for the Location-Allocation Problem


The allocation of facilities and customers is a key problem in the design of supply chains of companies. In this paper, this issue is approached by partitioning the territory in areas where the distribution points are allocated. The demand is modelled through a set of continuous functions based on the population density of the geographic units of the territory. Because the partitioning problem is NP hard, it is necessary to use heuristic methods to obtain reliable solutions in terms of quality and response time. The Neighborhood Variable Search and Simulated Annealing heuristics have been selected for the study because of their proven efficiency in difficult combinatorial optimization problems. The execution time is the variable chosen for a factorial experimental design to determine the best-performing heuristics in the problem. In order to compare the quality of the solutions in the territorial partition, we have chosen the execution time as the common parameter to compare the two heuristics. At this point, we have developed a factorial statistical experimental design to select the best heuristic approaches to this problem. Thus, we generate a territorial partition with the best performing heuristics for this problem and proceed to the application of the location-allocation model, where the demand is modelled by a set of continuous functions based on the population density of the geographical units of the territory.

Share and Cite:

Loranca, M. , Velázquez, R. , Analco, M. , Díaz, M. , Guzman, G. and López, A. (2014) Experiment Design for the Location-Allocation Problem. Applied Mathematics, 5, 2168-2183. doi: 10.4236/am.2014.514210.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Zoltners, A.A. and Sinha, P. (1983) Towards a Unified Territory Alignment: A Review and Model. Management Science, 29, 1237-1256.
[2] Bernábe, M.B., Espinosa, J.E., Ramírez, J. and Osorio, M.A. (2011) A Statistical Comparative Analysis of Simulated Annealing and Variable Neighborhood Search for the Geographical Clustering Problem. Computación y Sistemas, 14, 295-308.
[3] Koskosidis, Y.A. and Powell, W.B. (1992) Clustering Algorithms for Consolidations of Customers Order in to Vehicle Ship Shipment. Transportations Research, 26, 325-379.
[4] Piza, E., Murilo, A. and Trejos, J. (1999) Nuevas Técnicas de Particionamiento en Clasficación Automática. Revista de Matemáticas Teoría y Aplicaciones, 6, 51-66.
[5] Altman, M. (1997) Is Automation the Answer: The Computational Complexity of Automated Redistricting? Rutgers Computer and Law Technology Journal, 23, 81-142.
[6] Kirkpatrick, S., Gelatt, C.D. and Vecchi, M.P. (1983) Optimization by Simulated Annealing. Science, 220, 671-680.
[7] Newling, B.E. (1969) The Spatial Variation of Urban Population Densities. Geographical Review, 59, 242-252.
[8] Zamora, E. (1996) Implementación de un Algoritmo Compacto y Homogéneo para la Clasificación de Zonas Geográficas AGEBs Bajo una Interfaz Gráfica. Thesis, Benemérita Universidad Autónoma de Puebla, México.
[9] Daskin, M.S. (1995) Network and Discrete Location, Models, Algorithms, and Applications. John Willey & Sons Ltd., Hoboken.
[10] Mladenovic, N. and Hansen, P. (1997) Variable Neighborhood Search. Computer Operation Research, 24, 1097-1100.
[11] Hansen, P., Mladenovic, N. and Moreno, P.J. (2010) A Variable Neighborhood Search: Methods and Applications. Annals of Operations Research, 175, 367-407.
[12] Box, G.E. and Wilson, K.G. (1951) On the Experimental Attainment of Optimum Conditions. Journal of the Royal Statistical Society, 13, 1-45.
[13] Cady, F.B and Laird, R.J. (1973) Treatment Design for Fertilizer Use Experimentation. CIMMYT Research Bulletin, 26, 29-30.
[14] Box, G.E. and Draper, NR. (1959) A Basis for the Selection of a Response Surface Design. Journal of the American Statistical Association, 54, 622-654.
[15] Briones, E.F and Martínez, G.A. (2002) Eficiencia de Algunos Diseños Experimentales en la Estimación de una Superficie de Respuesta. Agrociencia, 36, 201-210.
[16] Montgomery, D. (1991) Design and Analisis of Experiments. 2nd Edition, Wiley, Hoboken.
[17] Church, R.L. (2003) COBRA: A New Formulation of the Classic P-median Location Problem. Annals of Operations Research, 122, 103-120.
[18] Bennett, C.D. and Mirakhor, A. (1974) Optimal Facility Location with Respect to Several Regions. Journal of Regional Science, 14, 131-136.
[19] Murat, A., Verter, V. and Laporte, G. (2010). A Continuous Analysis Framework for the Solution of Location—Allocation Problem with Dense Demand. Compute rs& Operations Research, 37, 123-136.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.