Diseño de cadenas de distribución con demanda bajo incertidumbre: una aproximación de programación lineal difusa

Design of distribution networks under uncertainty demand: A fuzzy linear programming approach

  • Eduyn López Santana Universidad Distrital Francisco José de Caldas
  • Germán Andrés Méndez Giraldo Universidad Distrital Francisco José de Caldas
  • Carlos Franco Universidad Distrital Francisco José de Caldas
Keywords: distribution networks, fuzzy linear programming, uncertainty demand. (en_US)
Keywords: redes de distribución, programación lineal difusa, demanda bajo incertidumbre. (es_ES)

Abstract (es_ES)

Este artículo presenta un modelo para el diseño de una red de distribución considerando la demanda bajo incertidumbre en un ambiente de múltiples productos y múltiples periodos. El modelo propuesto integra un problema de localización de instalaciones y un problema de distribución con restricciones difusas en el cumplimiento de la demanda, el cual se resuelve utilizando el método de restricciones suaves propuesto por Zimmermann considerando parámetros difusos en el lado derecho de las restricciones de un problema de programación lineal entera mixta y funciones de pertenecía lineales. Los resultados encontrados muestran como la localización de las plantas y almacenes se puede conservar para en el modelo flexible, mientras se realiza un balance entre el inventario generado y el costo incurrido.

Abstract (en_US)

This paper presents a model for designing a distribution network considering the demand under uncertainty, in a multi-products and multiperiods environment. The proposal model integrates a Facility Location Problem and a Distribution Problem with fuzzy constraints in demands satisfying which is solved using the soft constraints method proposed by Zimmermman, which considers fuzzy parameters in the right hand side of a Mixed Integer Linear Programming problem and linear membership functions. The obtained results show how the localization of the plants and distribution centers can be conserved for different membership degrees, while there is a balance between the inventory and the cost.


Download data is not yet available.


N. C. Nam, T. H. L. An, and P. D. Tao, “A Branch and Bound Algorithm Based on DC Programming and DCA for Strategic Ca-pacity Planning in Supply Chain Design for a New Market Opportunity,” in Operations Research Proceedings 2006, P. D. K.-H. Waldmann and D.-W.-I. U. M. Stocker, Eds. Springer Berlin Heidelberg, 2007, pp. 515–520.

Y. Yin, I. Kaku, J. Tang, and J. Zhu, “Supply Chain Design Using Decision Analysis,” in Data Mining, Springer London, 2011, pp. 121–132.

R. Velásquez, M. T. Melo, and S. Nickel, “An LP-based Heuristic Approach for Strategic Supply Chain Design,” in Operations Research Proceedings 2005, P. D. H.-D. Haasis, P. D.-I. H. Kopfer, and D. J. Schönberger, Eds. Springer Berlin Heidelberg, 2006, pp. 167–172.

T. Seidel, “Rapid Supply Chain Design by Integrating Modelling Methods,” in Build To Order, G. Parry and A. Graves, Eds. Springer London, 2008, pp. 277–295.

S.-H. Liao and C.-L. Hsieh, “Integrated Location-Inventory Retail Supply Chain Design: A Multi-objective Evolutionary Ap-proach,” in Simulated Evolution and Learning, K. Deb, A. Bhattacharya, N. Chakraborti, P. Chakroborty, S. Das, J. Dutta, S. K. Gupta, A. Jain, V. Aggarwal, J. Branke, S. J. Louis, and K. C. Tan, Eds. Springer Berlin Heidelberg, 2010, pp. 533–542.

Z.-J. M. Shen and M. S. Daskin, “Trade-offs Between Customer Service and Cost in Integrated Supply Chain Design,” MSOM, vol. 7, no. 3, pp. 188–207, Jun. 2005.

H. Yan, Z. Yu, and T. C. Edwin Cheng, “A strategic model for supply chain design with logical constraints: formulation and so-lution,” Computers & Operations Research, vol. 30, no. 14, pp. 2135–2155, Dec. 2003.

R. Hammami, Y. Frein, and A. B. Hadj-Alouane, “A strategic-tactical model for the supply chain design in the delocalization context: Mathematical formulation and a case study,” International Journal of Production Economics, vol. 122, no. 1, pp. 351–365, Nov. 2009.

S. Talluri and R. C. Baker, “A multi-phase mathematical programming approach for effective supply chain design,” European Journal of Operational Research, vol. 141, no. 3, pp. 544–558, Sep. 2002.

B. M. Beamon, “Supply chain design and analysis:,” International Journal of Production Economics, vol. 55, no. 3, pp. 281–294, Aug. 1998.

V. Jayaraman and A. Ross, “A simulated annealing methodology to distribution network design and management,” European Journal of Operational Research, vol. 144, no. 3, pp. 629–645, Feb. 2003.

N. V. Sahinidis, “Optimization under uncertainty: state-of-the-art and opportunities,” Computers & Chemical Engineering, vol. 28, no. 6–7, pp. 971–983, Jun. 2004.

A. R. Singh, R. Jain, and P. K. Mishra, “Capacities-based supply chain network design considering demand uncertainty using two-stage stochastic programming,” Int J Adv Manuf Technol, pp. 1–8.

H. Selim and I. Ozkarahan, “A supply chain distribution network design model: An interactive fuzzy goal programming-based solution approach,” Int J Adv Manuf Technol, vol. 36, no. 3–4, pp. 401–418, Mar. 2008.

K. N. Rao, K. V. Subbaiah, and G. V. P. Singh, “Design of supply chain in fuzzy environment,” J Ind Eng Int, vol. 9, no. 1, pp. 1–11, Dec. 2013.

S. Ahmed and N. V. Sahinidis, “An Approximation Scheme for Stochastic Integer Programs Arising in Capacity Expansion,” Operations Research, vol. 51, no. 3, pp. 461–471, May 2003.

M. C. Georgiadis, P. Tsiakis, P. Longinidis, and M. K. Sofioglou, “Optimal design of supply chain networks under uncertain transient demand variations,” Omega, vol. 39, no. 3, pp. 254–272, Jun. 2011.

F. Pan and R. Nagi, “Robust supply chain design under uncertain demand in agile manufacturing,” Computers & Operations Research, vol. 37, no. 4, pp. 668–683, Apr. 2010.

H.-J. Zimmermann, “Fuzzy programming and linear programming with several objective functions,” Fuzzy Sets and Systems, vol. 1, no. 1, pp. 45–55, Jan. 1978.

J. C. Figueroa-García, C. A. Lopez-Bello, and D. Kalenatic, “An iterative algorithm for fuzzy mixed production planning based on the cumulative membership function,” Ingeniería, vol. 16, no. 2, pp. 6–17, 2011.

J. C. Figueroa-García, D. Kalenatic, and C. A. Lopez-Bello, “Multi-period Mixed Production Planning with uncertain de-mands: Fuzzy and interval fuzzy sets approach,” Fuzzy Sets and Systems, vol. 206, pp. 21–38, Nov. 2012.

How to Cite
Santana, E. L., Giraldo, G. A. M., & Franco, C. (2013). Design of distribution networks under uncertainty demand: A fuzzy linear programming approach. Ingeniería, 18(2). https://doi.org/10.14483/udistrital.jour.reving.2013.2.a05
Published: 2013-12-06
Sección Especial: Mejores Trabajos “VI Simposio en Optimización”