Mathematical Model of Multi-Product P-hub Median Problem by Considering Methods of Finance and Environmental Approach Using Meta-Heuristic Algorithms: “A Case Study in Iran's Transportation Network”

Document Type : Scientific - Research

Authors

1 School of Industrial Engineering, Alborz Campus, University of Tehran, Tehran, Iran

2 School of Industrial Engineering, University of Tehran, Tehran, Iran

Abstract

Transportation systems are among the most important sectors in each country. With population growth, demand increases for transport of goods. In such situations importance of the proper design of transportation networks is undeniable. Inter-city transport is completely essential for distributing goods around the country. The proper design of an efficient public transport system is crucial. Using Hub networks become popular in such situations. Therefore, with respect to important applications in public transport, in this paper we investigate the multi-product multi-objective p-hub median location problem. Also, considering the importance of environmental issues and pollution of transport networks in this study a multi-objective model is intended to minimize greenhouse gas emissions. Due to the scarcity of financial resources in the economy, methods of Finance in the proposed model are also included. Data from the statistics of country road transport in 1392 is obtained. To solve the problem, the Gams 24.1.3 optimization software and meta-heuristic algorithms, i.e. Simulated Annealing (SA) and Imperialist Competitive Algorithm (ICA) are applied. The results show that ICA overcomes SA.

Keywords

References

- چراغی، اسماعیل، حیدری، جعفر و رزمی، جعفر.(1393) مدل سازی مساله مکان یابی هاب چند محصوله با در نظر گرفتن روش های تامین مالی ، چشم انداز مدیریت صنعتی، شماره 16، صفحات 55-74
- Alumur, S., Kara, B. and Karasan O. E. (2009) “The design of single allocation incomplete hub networks”, Transportation Research Part B: Methodological, Vol. 43, No. 10, pp. 936-951.
- Aykin T. (1994) “Lagrangean relaxation based approaches to capacitated hub-and-spoke network design problem”, European Journal of Operational Research Vol. 79, No. 3, pp. 501–523.
- Aykin, T. (1995a) “Networking policies for hub-and-spoke systems with application to the air transportation system”, Transportation Science, Vol. 29, No. 3, pp. 201–221.
- Aykin, T. (1995b) “The hub location and routing problem”, European Journal of Operational Research, Vol. 83, pp.200–219.
- Camargoa, R. S., Miranda, G. and Ferreira, R.. (2011) “A hybrid Outer-Approximation/Benders Decomposition algorithm for the single allocation hub location problem under congestion”. Operations Research Letters, Vol. 39, pp. 329–337.
- Campbell, J. F. (1991) “Hub location problems and the p-hub median problem”, Center for Business and Industrial Studies, University of Missouri – St. Louis, St. Louis, MO.
-  Campbell, J. F. (1992) “Location and allocation for distribution systems with transshipments and transportation economies of scale”, Annals of Operations Research, Vol. 40, pp. 77–99.
- Campbell, J. F. (1994) “A survey of network hub location”, Studies in Locational Analysis, Vol. 6, pp. 31–49.
- Campbell, J. F., Ernst A. T. and Krishnamoorthy M. (2002) “Hub location problems”, Drezner Z., Hamacher H., eds. “Facility Location: Applications and Theory (Springer, Berlin)”, pp. 373–407.
- Campbell, J. F. and O’Kelly, M. E. (2012) “Twenty-five years of hub location research”. Transportation Science, Vol. 46, No. 2, pp. 153–169.
- Correia, I, Nickel, S. and, Saldanha-da-Gama, F. (2010) “The capacitated single-allocation hub location problem revisited: A note on a classical formulation”, European Journal of Operational Research Vol. 207, pp. 92–96.
- Correia, I, Nickel, S. and Saldanha-da-Gama, F. (2011) “Hub and spoke network design with single-assignment, capacity decisions and balancing requirements”, Applied Mathematical Modelling, Vol. 35, pp. 4841–4851.
- Correia, I., Nickel, S. and Saldanha-da-Gama, F. (2010) “Single-assignment hub location problems with multiple capacity levels”. Transportation Research Part B, Vol. 44, pp. 1047–1066.
- Estrada-Romeua, M. and Robustéb, F. (2015) “Stopover and hub-and-spoke shipment strategies in less-than-truckload carriers”, Transportation Research Part E: Logistics and Transportation Review, Vol. 76, pp. 108-121.
- Farahani, R.,Z., Hekmatfar, M., Arabani, A.,B. and  Nikbakhsh, E. (2013) “Hub location problems: A review of models, classification, solution techniques, and applications”,  Computers and Industrial Engineering, Vol. 64, pp. 1096–1109.
- Gelareh, S.  and Nickel,  S. (2011)  “Hub  location  problems  in transportation  networks”,  Transport at ion  Research  Part  E: Logistics  and  Transportation  Review, Vol. 47, No. 6, pp. 1092-1111.
- Goldman,  A.J. (1969) “Optimal location for centers in a network”, Transportation Science, Vol. 3, pp. 352–360.
- Guu, S. M. and Wu, Y. K. (1999) “Two phase approach for solving the fuzzy linear programming problems”. Fuzzy Sets and Systems, Vol. 107, pp. 191–195.
-Hakimi, S. L. (1964) “Optimum location of switching centers and the absolute centers and medians of a graph”, Operations Research, Vol. 12, No. 3, pp. 450–459.
-Hwang, C. L. and Masud, A. (1979) “Multiple objective decision making. Methods and applications: A state of the art survey”, Lecture notes in economics and mathematical systems, Vol. 164, Berlin: Springer-Verlag.
-Karimi, H. and Setak, M. (2014) “Proprietor and customer costs in the incomplete hub location-routing network topology”, Applied Mathematical Modelling, Vol. 38, No. 3, pp. 1011–1023.
-Khosravi, Sh, Akbari Jokar, M. R. (2014) “Hub location problem considering an elastic demand”, CIE44 and IMSS’14 Proceedings, 14-16, Istanbul / Turkey, pp. 581-588.
-Klincewicz, J. G. (1991) “Heuristics for the p-hub location problem”, European Journal of Operational Research, Vol. 53, pp. 25–37.
-Klincewicz, J. G. (1992) “Avoiding local optima in the p-hub location problem using Tabu search and grasp”, Annals of Operational Research, Vol.40, pp. 283–302.
-Klincewicz, J. G. (1998) “Hub location in backbone tributary network design: A review”, Location Science, Vol. 6, pp. 307–335.
-Lai, Y. J. and Hwang, C. L. (1992) “A new approach to some possibilistic linear programming problems”, Fuzzy Sets and Systems, Vol. 49, pp. 121–133.
-Mohammadi, M., Jolai, F. and Rostami, H. (2011) “An M/M/c queue model for hub covering location problem”. Mathematical and Computer Modelling. Vol. 54, pp. 2623–2638.
-Mohammadi, M., Jolai, J. and  Tavakkoli-Moghaddam, R. (2013) “Solving a new stochastic multi-modep-hub covering location problem considering risk by a novel multi-objective algorithm”, Applied Mathematical Modelling, Vol. 37, pp. 10053–10073.
-Mohammadi, M., Tavakkoli-Moghaddam, R., Siadat., A. and Rahimi, Y. (2016) “A game-based meta-heuristic for a fuzzy bi-objective reliable hub location problem”,  Engineering Applications of Artificial Intelligence, Vol. 50, pp.1–19.
-Mohammadi, M., Torabi, S.A. and Tavakkoli-Moghaddam., R. (2014) “Sustainable hub location under mixed uncertainty”, Transportation Research Part E, Vol. 62, pp. 89–115.
-O’Kelly, M. E. (1986a) “The location of interacting hub facilities”, Transportation Sci. Vol. 20, No. 2, pp. 92–106.
-O’Kelly, M. E. (1986b) “Activity levels at hub facilities in interacting networks”, Geographical Anal. Vol. 18, No. 4, pp. 343–356.
-O’Kelly, M. E. (1987) “A quadratic integer program for the location of interacting hub facilities”, European Journal of Operational Research, Vol. 32, pp. 393–404.
-O’Kelly M. E. (1992) “Hub facility location with fixed costs”,  Papers in Regional Science, Vol. 71, No. 3, pp. 293–306.
-O’Kelly,  M. E. and Miller, H. (1994) “The hub network design problem: A review and synthesis”, Journal of Transport Geography, Vol. 2, No. 1, pp. 31–40.
-Rahimi, Y., Tavakkoli-Moghaddam, R., Mohammadi, M. and Sadeghi, M. (2015) “Multi-objective hub network design under uncertainty considering congestion: An M/M/c/K queue system”, Applied Mathematical Modelling, Vol. 40, pp.4179–4198.
-Sadeghi, M., Jolai, F., Tavakkoli-Moghaddam, R. and Rahimi, Y. (2015) “A new stochastic approach for a reliable p-hub covering location problem”, Computers and Industrial Engineering, Vol. 90, pp. 371–380.
-Sakawa, M., Yano, H. and Yumine, T. (1987) “An interactive fuzzy satisfying method for multi objective linear-programming problems and its application”, IEEE Transactions on Systems, Man and Cybernetics SMC, Vol. 17, pp. 654–661.
-Sedehzadeh, S. and Tavakkoli-Moghaddam, R. (2014) “Using a fuzzy approach for a new bi-objective model for a multi-modal tree p-hub median location problem”, Int. J. Fuzzy Computation and Modelling, Vol. 1, No. 2, pp. 194-211.
-Toh, R. S., Higgins, R. C. (1985) “The impact of hub and spoke network centralization and route monopoly on domestic airline profitability”, Transportation Journal, Vol. 24, pp. 16–27.
-Torabi, S. A. and Hassini, E. (2008) “An interactive possibilistic programming approach for multiple objective supply chain master planning”, Fuzzy Sets and Systems, Vol. 159, No. 2, pp. 193-214.
-Wang, J. and  Shu, Y. F. (2007) “A possibilistic decision model for new product supply chain design”, European Journal of Operational Research, Vol. 177, pp. 1044–1061.
Quarterly Journal of Transportation Engineering
Volume 8, Issue 2 - Serial Number 2
January 2017
Pages 195-213

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History

  • Receive Date: 01 September 2015
  • Revise Date: 12 November 2015
  • Accept Date: 14 March 2016

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