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Journal of applied research and technology

versión On-line ISSN 2448-6736versión impresa ISSN 1665-6423

J. appl. res. technol vol.12 no.4 Ciudad de México ago. 2014

 

Efficient Frontier for Multi-Objective Stochastic Transportation Networks in International Market of Perishable Goods

 

A. Bustos*1, L. Herrera2 and E. Jiménez1

 

1 Coordinación de Integración del Transporte. Instituto Mexicano del Transporte, Querétaro, México.

2 Escuela de Ingeniería Industrial y de Sistemas. ITESM Campus Estado de México, Atizapán, Estado de México Saltillo, Coahuila, México. * abustos@imt.mx

 

ABSTRACT

Effective planning of a transportation network influences tactical and operational activities and has a great impact on business. Planning typically considers multiple aspects such as variable transportation costs, various levels of customer service offered, security of goods, and traveling time. These aspects often vary with time. Although the minimum cost flow problem is a widely seen approach to configure a transportation network, there is no much work considering variations on arcs; even more, the problem with varying nodes has hardly been addressed. In this work is developed a mathematical model for the multi-objective minimum cost flow problem, applied in networks with varying attributes on arcs. The model finds the set of non-dominated solutions for a multi-objective stochastic network having variations in attributes of its arcs and nodes, such as cost or transportation time. A modified version of the two-stage method was used to address the stochastic nature of the problem combined with the epsilon-constraint method, which is used for building the set of non-dominated solutions.

This paper presents the main features of the model, the theoretical bases and a computational implementation. Experiments were applied in a transport network for the exportation market of ornamental flowers as perishable goods from Mexico to the United States, which considered variations in border crossing times.

Keywords: Multi-objective optimization; Minimum cost flow; stochastic network; perishable goods.

 

RESUMEN

Una planeación eficaz de una red de transporte tiene un gran impacto en las empresas, al considerar múltiples aspectos como costos de transporte, seguridad de las mercancías, tiempo de viaje y demás niveles de servicio ofrecidos. Atributos que frecuentemente varían con el tiempo. Aunque el problema de flujo a costo mínimo (MCF) ha sido ampliamente visto para configurar redes de transporte, no hay muchos trabajos que consideren variaciones en los arcos. En este trabajo se desarrolla un modelo matemático para el problema MCF multi-objetivo, aplicado en redes con atributos variantes en los arcos. El modelo encuentra la Frontera Pareto para una red estocástica con variaciones en los atributos de costo o tiempo de transporte. Para enfrentar la naturaleza estocástica del problema se utiliza Descomposición de Benders para el problema estocástico de dos etapas, posteriormente se conjunta con el método £-restricción, que es utilizado para la construcción del conjunto de soluciones no dominadas.

Este artículo presenta las principales características del modelo, las bases teóricas y una implementación computacional. Los experimentos fueron aplicados en una red de transporte para el mercado de exportación de flores ornamentales como productos perecederos desde México a Estados Unidos, considerando las variaciones en los tiempos de cruce de fronteras.

 

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References

[1] Portal del Observatorio Estratégico Tecnológico, https://oet.itesm.mx/portal/page/portal/OET/Publica7p_iPortal=3. Oct/10/2011.         [ Links ]

[2] C. Martner et al., "Export logistics chains in Mexico". Cadenas logísticas de exportación en México. Publicación técnica 276. Instituto Mexicano del Transporte. 2005.         [ Links ]

[3] C. Morales, and M. de la Torre, M. "Characteristics of refrigerated transport in Mexico". Características del transporte refrigerado en México. Publicación técnica 297. Instituto Mexicano del Transporte. 2006.         [ Links ]

[4] H. Hamacher et al., Multiple objective minimum cost flow problems: A review. European Journal of Operational Research...;176. Vol. 176, Issue: 3. pp. 1404-1422. 2007.         [ Links ]

[5] S. Opasanon, and E. Miller-Hooks. Multicriteria adaptive paths in stochastic, time-varying networks. European Journal of Operational Research., 173: pp. 7291. 2006.         [ Links ]

[6] M. Fonseca, et al., Solving scalarized multi-objective network flow problems with an interior point method. International Transactions in Operational Research 17(5): pp. 607-636. 2009.         [ Links ]

[7] A. Eusebio, and J. Figueira. Finding non-dominated solutions in bi-objective integer network flow problems. Computers & Operations Research 36: pp. 2554-2564. 2009.         [ Links ]

[8] A. Raith and M. Ehrgott. A two-phase algorithm for the bi-objective integer minimum cost flow problem. Computers & Operations Research 36: pp. 1945-1954. 2009.         [ Links ]

[9] A. Przybylski et al., The biobjective integer minimum cost flow problem-incorrectness of Sedeño-Noda and Gonzalez Martin's algorithm. Computers & Operations Research; 33(5): pp. 1459-1463. 2006.         [ Links ]

[10] A. Bustos, and L. Herrera. Building an efficient frontier for multi-objective stochastic transportation networks. in: IERC Annual Conference and Expo 2011. Reno, Nevada. 2011.         [ Links ]

[11] R. Ahuja et al. Network Flows, Theory, algorithms and applications. Prentice Hall. 1997.         [ Links ]

[12] L. Kantorovich. Mathematical Methods in the Organization and Planning of Production. Management Science 6: pp. 336-422. 1939.         [ Links ]

[13] F. Hitchcock. The Distribution of a Product from Several Sources to Numerous Localities. Journal of Maths Physics, 20: pp. 224-230. 1941.         [ Links ]

[14] L. Ford and D. Fulkerson. Flows in Networks. Princeton University Press. 1962        [ Links ]

[15] A. Weintraub. A Primal Algorithm to Solve Network Flow Problems with Convex Costs. Management Science, 21: pp. 87-97. 1974.         [ Links ]

[16] R. Helgason and J. Kennington. An Efficient Procedure for Implementing a Dual Simplex Network Flow Algorithm. AIEE Transactions. 9: pp. 63-68. 1977.         [ Links ]

[17] D. Kelly et al., The Minimum Cost Flow Problem and The Network Simplex Solution Method. National University of Ireland. 1991.         [ Links ]

[18] C. Coello et al., Evolutionary algorithms for solving multi-objective problems. 2nd edition. Genetic and evolutionary computation series. Springer. 2007.         [ Links ]

[19] B. Bernábe et al., A Multiobjective Approach for the Heuristic Optimization of Compactness and Homogeneity in the Optimal Zoning. Journal of Applied Research and Technology. Vol 10 No. 3. pp. 447-457. 2012.         [ Links ]

[20] R. Marler and J. Arora. Survey of multi-objective optimization methods for engineering. Review article. Struct Multidisc Optim, 26: pp. 369-395. 2004.         [ Links ]

[21] G. Rangaiah. Multi-Objective Optimization, Techniques and Applications in Chemical Engineering. National University of Singapore. 2008.         [ Links ]

[22] E. Talbi. Metaheuristics: From Design to Implementation. Canada: John Wiley & sons inc. 2009.         [ Links ]

[23] K. Deb and A. Kumar. Interactive Evolutionary Multi-Objective Optimization and Decision-Making using Reference Direction Method. 2007. GECCO'07, July 711, London, England, United Kingdom. 2007.         [ Links ]

[24] E. Rincón et al., Multiobjective Algorithm for Redistricting. Journal of Applied Research and Technology. Vol 11 No. 3. pp. 324-330. 2013.         [ Links ]

[25] V. Chankong and Y. Haimes. Multi-objective Decision Making: Theory and Methodology. Elsevier-North Holland. 1983.         [ Links ]

[26] Y. Haimes et al., Multi-objective Optimization in Water Resources Systems: The Surrogate Worth Trade-off Method. Elsevier Scientific Publishing Company. 1975.         [ Links ]

[27] G. Mavrotas. Generation of efficient solutions in Multi-objective Mathematical Programming problems using GAMS. Effective implementation of the £-constraint method. School of Chemical Engineering. National Technical University of Athens. 2007.         [ Links ]

[28] A. Madansky. Inequalities for Stochastic Linear Programming Problems. Management Science, 6(2): pp.197-204. 1960.         [ Links ]

[29] A. Shapiro et al., Lectures on stochastic programming, modeling and theory. Society for industrial and applied mathematics and the Mathematical programming society. Philadelphia. 2009.         [ Links ]

[30] G. Dantzig. Linear programming under uncertainty. Management Science, Vol. 1, (pp. 197-206). 1955.         [ Links ]

[31] T. Santoso et al., A stochastic programming approach for supply chain network design under uncertainty. School of Industrial & Systems Engineering, Georgia Institute of Technology. 2003.         [ Links ]

[32] E. Kalvelagen. Two stage stochastic linear programming with GAMS. Amsterdam Optimization Modeling Group LLC, Washington DC. 2003.         [ Links ]

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