Location-Routing Problems: A Review of Concepts, Models, Methods and Research Gaps

Document Type : Research Paper

Authors

1 Faculty of Industrial Engineering, Payame Noor University, Tehran, Iran

2 Faculty of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

3 Faculty of Engineering, University of Tehran, Iran

Abstract

A location-routing problem is a kind of location problem with the routing aspects. Although the basic idea of simultaneously solving the two problems started on 1961, and it has been done a lot of researches on this issue, but a comprehensive review of the problem literature in this paper, has identified research gaps, which indicates the potentiality of this problem in new studies. This paper surveys 303 related published researches. in which the large number of survey focuses on the location-routing problem in different periods, in this research, based on a comprehensive review of the problem definition, it is studied the different aspects and indexes, type of LRPs, type of objectives, categories of LRPs and solution methods with the authors’ proposed reforms. Finally, research gaps and recommendations for future studies are explained.

Keywords

Main Subjects

References

1-     Weber, A. (1962). Theory of the Location of Industries. C. J. Friedrich (Ed.). Chicago, Ill, USA: University of Chicago Press.
2-     Lin, C., Choy, K.L., Ho, G.T.S., Chung, S.H. and Lam, H. Y. (2014). “Survey of Green Vehicle Routing Problem: Past and future trends”, Expert System with Application, Vol. 41, No. 4, PP. 1118–1138.
3-     Montoya-Torres, J.R., Franco, J.L., Isaza, S. N., Jiménez, H.F. and Herazo-Padilla, N., (2015). “A literature review on the vehicle routing problem with multiple depots”, Computers & Industrial Engineering, Vol. 79, No. 1, PP. 115–129.
4-     Lahyani, R., Khemakhem, M., Semet, F., (2015). “Rich vehicle routing problems: From a taxonomy to a definition” European Journal of Operational Research, Vol. 241, No. 1, PP. 1–14.
5-     Drexl, M., Schneider, M. (2013). A survey of location-routing problems, Technical Report LM-2013-03, Chair of Logistics Management, Gutenberg School of Management & Economics, Johannes Gutenberg Uni., Mainz.
6-     Prodhon, C., Prins, C., (2014). “A survey of recent Research on location-routing problems”, European Journal of Operational Research, Vol. 238, No. 1, PP. 1–17.
7-     Min, H., Jayaraman, V., Srivastava, R., (1998). “Combined location-routing problems: a synthesis”, future Research Dir. European Journal of Operational Research, Vol. 108, No. 1, PP. 1–15.
8-     Nagy, G., Salhi, S. (2007). “Location-routing: Issues, models and methods”, European Journal of Operational Research, Vol. 177, No.12, PP. 649–672.
9-     Lopes, R.B., Ferreira, C., Santos, B.S., Barreto, S., (2013), “A taxonomical analysis, current methods and objectives on location-routing problems”, International Transactions in Operational Research, Vol. 20, No. 6, PP. 795–822.
10-  Boventer, V., (1961). “The relationship between Transportation costs and location rent in Transportation problems”, Journal of Regional Science, Vol. 2, PP. 27-40.
11-  Lawrence, R.M., Pengilly, P.J., (1969). “The number, location of depots required for handling products for distribution to retail stores in south-east England”, Operational Research Quarterly, Vol. 20, No. 1, PP. 23–32.
12-  Tapiero, C.S., (1971). “Transaction-location-allocation problems over time”, Journal of Regional Science, Vol. 2, No. 3, PP. 377-384.
13-  Chan, A.W., Francis, R.L. (1976). “A round-trip location problem on a tree graph”, Transportation Science, Vol. 10, No. 1, PP. 35–51.
14-  Burness, R.C., White, J.A., (1976). “The traveling salesman location problem”, Transportation Science, Vol. 10, No. 4, PP. 348–360.
15-   Jacobsen, S.K., Madsen, O.B.G., (1978). “On the location of transfer points in a two-level newspaper delivery system-A case study”, The International Symposium on Locational Decisions, Ban, Alberta, Canada.
16-  Jacobsen, S.K., Madsen, O.B.G, (1980). “A comparative study of heuristics for a two-level routing-location problem”, European Journal of Operational Research, Vol. 5, No. 6, PP. 378–387.
17-  Laporte, G., Nobert, Y. (1981). “An exact algorithm for minimizing routing and operating costs in depot location”, European Journal of Operational Research, Vol. 6, No. 2, PP. 224–226.
18-  Perl, J., Daskin, M. (1984). “A unified warehouse location-routing methodology”, Journal of Business Logistics, Vol. 5, No. 1, PP. 92–111.
19-  Drezner, Z., Steiner, G., Wesolowsky, G.O., (1985). “One-facility location with rectilinear tour distances”, Naval Research Logistics Quarterly., Vol. 32, No. 3, PP. 391–405.
20-  Maze, T.H., Khasnabis, S., (1985). “Bus garage location planning with dynamic vehicle assignments: A methodology”, Transportation Research B, Vol. 19, No. 1, PP. 1–13.
21-  Labbe, M., Laporte, G., (1986). “Maximizing user convenience, postal service efficiency in post box location”. Belgian Journal of Operational Research, Statistics, Computer Science, Vol. 26, No. 2, PP. 21–35.
22-  Laporte, G. (1988). “Location-routing problems”, in B. Golden and A. Assad (Eds.), Vehicle routing: Methods and studies, North-Holland, Amsterdam, PP. 163–198.
23-  Levy, L., Bodin, L., (1989). “The arc oriented location routing problem”, INFOR27, Vol. 1, No. 1, PP. 74–94.
24-  Nambiar, J.M., Gelders, L.F., Van Wassenhove, L.N., (1989). “Plant location, vehicle routing in the Malaysian rubber smallholder sector: a case study”, European Journal of Operational Research, Vol. 38, No. 1, PP. 14–26.
25-  Zografos, K.G., Samara, S., (1989). “A combined location-routing model for hazardous waste Transportation and disposal”, Transportation Research Record,Vol. 1245, No. 1, PP. 52–59.
26-  Nagy, G., (1996). “Heuristic Methods for the Many-to-Many Location-Routing Problem”, PhD dissertation, University of Birmingham.
27-  Ghiani, G., Laporte, G., (1999). “Eulerian location problems”, Networks., Vol. 34, No. 4, PP. 291–302.
28-  Liu, S., Lee, S., (2003). “A two-phase heuristic method for the multi-depot location routing problem taking inventory control decisions into consideration”, International Journal of Advanced Manufacturing Technology, Vol. 22, No. 11–12, PP. 941–950.
29-  Wasner, M., Zapfel, G., (2004). “An integrated multi-depot hub-location vehicle routing model for network planning of parcel service”, International Journal of Production Economics, Vol. 90, No. 3, PP. 403–419.
30-  Ambrosino, D., Scutella, M.G., (2005). “Distribution network design: new problems”, related models. European Journal of Operational Research, Vol. 165, No. 3, PP. 610–624.
31-  Schwardt, M., Dethloff, J., (2005). “Solving a continuous location-routing problem by use of a self-organising map”, International Journal of Physical Distribution & Logistics Management, Vol. 35, No. 6, PP. 390–408.
32-  Glicksman, H., Penn, M. (2008). “Approximation algorithms for group prize-collecting and location-routing problems”, Discrete Applied Mathematics, Vol. 156, No. 17, PP. 3238–3247.
33-  Prodhon, C., (2008). “A metaheuristic for the periodic location-routing problem”, In J. Kalcsics, S. Nickel, Operational Research Proceedings 2007, 159–164. Springer.
34-  Mirzaei, Sh., Krishnan, K., (2012), “Location Routing Problem with Time Dependent Travel Times”, Journal of Supply Chain and Operational Management, Vol. 10, No. 1, PP. 87-106.
35-  Karaoglan, I., Altiparmak, F., Kara, I., Dengiz, B. (2011). “A branch and cut algorithm for the location-routing problem with simultaneous pickup and delivery”, European Journal of Operational Research, Vol. 211, No. 2, PP. 318–332.
36-  Zarandi, M.H.F., Hemmati, A., Davari, S. (2011). “The multi-depot capacitated location-routing problem with fuzzy travel times”, Expert System with Application, Vol. 38, No. 8, PP. 10075–10084.
37-  Xuefeng, W., 2012, “An location-routing problem with simultaneous pickup and delivery in urban-rural dual-directions logistics network”, Proceedings of the 2012 2nd ICCIA 2012, PP. 1645-1649.
38-  Harks, T., Konig, F.G., Matuschke, J. (2013). “Approximation algorithms for capacitated location routing”, Transportation Science, Vol. 47, No. 1, PP. 3–22.
39-  Ahmadi-Javid, A., Seddighi, A. (2013). “A location-routing problem with disruption risk”, Transportation Research Part E: Logistics and Transportation Review, Vol. 53, No. 1, PP. 63–82.
40-  Ahmad, H., Hamzah, P., Yasin, Z. A. Md, Radiah, S. S., (2014). “Location Routing Inventory Problem with Transshipment (LRIP-T)”, Proceedings of the 2014 International Conference on Industrial Engineering and Operational Management, Bali, Indonesia, January 7- 9, PP. 1595-1605.
41-  Yu, V.F., Lin, S.Y., (2015), “A simulated annealing heuristic for the open location-routing problem”, Computer  & Operational Research, Vol. 62, No. ???, PP. 184–196.
42-  Karaoglan, I., Altiparmak, F., (2015). “A memetic algorithm for the capacitated location-routing Problem with mixed backhauls”, Computer  & Operational Research, Vol. 55, No. 2, PP. 200–216.
43-  Huang, S. H. (2015). “Solving the multi-compartment capacitated location routing problem with pickup–delivery routes and stochastic demands”, Computers & Industrial Engineering, Vol. 87, No. 1, PP. 104-113.
44-  Moshref-Javadi, M., Lee, S. (2016). “The Latency Location-Routing Problem”, European Journal of Operational Research, Vol. 255, No. 2, PP. 604-619.
45-  Toro, E.M., Franco, J.F., Echeverri, M.G., Guimarães, F.G., Rendón, R.A.G., (2017). “Green open location-routing problem considering economic and environmental costs”, International Journal of Industrial Engineering Computers, Vol. 8, No. 2, PP. 203–216.
46-  Drexl, M., Schneider, M. (2015). “A survey of variants and extensions of the location-routing problem”, European Journal of Operational Research, Vol. 241, No. 2, PP. 283-308.
47-  Drexl, M., Schneider, M. (2014). “A survey of the standard location-routing problem”, Working paper, Logistics Planning and Information Systems, TU Darmstadt, Germany.
48-  Liu, T., Jiang, Z., Chen, F., Liu, R., Liu, S., (2008). “Combined Location-Arc Routing Problems: Asurvey and Suggestions for Future Research”, Service Operational and Logistics, and Informatics, 2008.
49-  Srivastava, R., (1986). “Algorithms for Solving the Location Routing Problem”, PhD dissertation, Ohio State University.
50-  Balakrishnan, A., Ward, J., Wong, R. (1987). “Integrated facility location and vehicle routing models: Recent work and future prospects”, American Journal of Mathematics and Management Science, Vol. 7, No. (1-2), PP. 35–61.
51-  Namazian, A., (2009). “Models and methods for routing location.” Ms thesis, University ghom.
52-  Jalili Bolhasani, S., Karimi, H., Satac, M., (2012). “Evaluate and compare different methods for solve the location routing problem”, 2th National Conference on Industrial Engineering & system, Islamic Azad University of Najafabad, Iran.
53-  Delavari, M., (2015), A mathematical model for multi-objective location routing problem for Landfill and recovery of hospital waste under environmental considerations and uncertainty, University of Tehran.
54-  Salhi, S., Nagy, G., (1999). “Consistency and robustness in location-routing”, Studies in Locational Analysis, Vol. 13, No. 1, PP. 3–19.
55-  Jouzdani, J., Fathian, M., (2014). “A linear MmTSP formulation of robust location-routing problem: a dairy products supply chain case study”, International JJournal Applied Decision Science, Vol. 7, No. 3, PP. 327-342.
56-  Stowers, C.L., Palekar, U.S., (1993a). “Location models with routing considerations for a single obnoxious facility”, Transportation Science, Vol. 27, No. 4, PP. 350–362.
57-  Boffey, B., Karkazis, J., (1995). “Location, routing and the environment”, In: Drezner, Z. (Ed.), Facility Location: A Survey of Applications and Methods. Springer, New York, PP. 453–466.
58-  Berger, R., (1997). “Location-routing models for distribution system design”, PhD dissertation, Northwestern University.
59-  Perl, J., (1983). “A unified warehouse location-routing analysis”, Ph.D. Dissertation, Department of Civil Engineering, Northwestern University, Evanston, Illinois.
60-  Salhi, S., (1987). “The Integration of Routing into the Location Allocation and Vehicle Fleet Composition Problems”, PhD dissertation, Lancaster University.
61-  Laporte, G., Nobert, Y., Taillefer, S., (1988). “Solving a family of multi-depot vehicle routing, location-routing problems”, Transportation Science, Vol. 22, No. 3, PP. 161–172.
62-  Murty, K.G., Djang, P.A., (1999). “The U.S. army National Guard’s mobile training simulators location, routing problem”, Operational Research, Vol. 47, No. 2, PP. 175–182.
63-  Lin, C.K.Y, Chow, C.K., Chen, A., (2002). “A location-routing-loading problem for bill delivery services”, Computer  & Industrial Engineering, Vol. 43, No. 1–2, PP. 5–25.
64-  Barreto, S. (2004). “Analysis and modelling of location-routing problems”, Ph.D. thesis, University of Aveiro, Aveiro, Portugal. (In Portuguese)
65-  Tham, W.C., (2005). “Depot location-routing models based on a real supply chain network”, PhD dissertation, Lancaster University.
66-  Prodhon, C., (2006). “Le Problème de Localisation-Routage (The location-routing problem)”, Ph.D. thesis, Troyes University of Technology, France. (In French)
67-  Berger, R. T., Coullard, C. R., Daskin, M. S. (2007). “Location-routing problems with distance constraints”, Transportation Science, Vol. 41, No. 1, PP. 29–43.
68-  Özyurt, Z., Aksen, D., (2007). “Solving the multi-depot location-routing problem with Lagrangian relaxation”, in E. Baker et.al., Extending the Horizons: Advances in Computing, Optimization, and Decision Technologies, of Operational Research/Computer  Science Interfaces, Springer., Vol. 37, No. 1, PP. 125–144.
69-  Sterle, C. (2010). “Location-routing models and methods for freight distribution and infomobility in city logistics”, Technical report CIRRELT-2010-38, CIRRELT, Canada.
70-  Carnes, T., Shmoys, D.B. (2011). “Primal-dual schema and Lagrangian relaxation for the k-location-routing problem”, In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (pp. 99-110). Springer Berlin Heidelberg.
71-  Catanzaro, D., Gourdin, E., Labbe, M., Ozsoy, F.A., (2011). “A branch-and-cut algorithm for the partitioning-hub location routing problem”, Computer  & Operational Research, Vol. 38, No. 2, PP. 539–549.
72-  Hua-Li, S., Xun-Qing, W., Yao-Feng, X. (2012). “A bi-level programming model for a multi-facility location-routing problem in urban emergency system”, Engineering Education and Management, Vol. 111 of the series Lecture Notes in Electrical Engineering, 75-80.
73-  Boudahri, F., Aggoune-Mtalaa, W., Bennekrouf, M., Sari, Z. (2013). “Application of a clustering based location-routing model to a real agri-food supply chain redesign”, In N.T. Nguyen et.al., Advanced methods for computational collective intelligence, Springer, PP. 323–331.
74-  Ceselli, A., Righini, G., Tresoldi, E., (2014). “Combined location and routing problems for drug distribution”, Discrete Applied Mathematics, Vol. 165, No. 1, PP. 130–145.
75-  Yıldız, B., Arslan, O., Karaşan, O. E., (2016). “A branch and price approach for routing and refueling station location model”, European Journal of Operational Research, Vol. 248, No. 3, PP. 815–826.
76-  Alinaghian, M., Behrozi, M., (2006). “A mathematical programming models for locating warehouses in vehicle routing a production unit with solving method”, 2th National Conference on Logistics & Supply Chain, Iran Logistics Society, Tehran, Iran.
77-  Tavakoli-Moghaddam, R., Haidar, M., Mousavi, S.A., (2008) A model of location routing problems with allocation of a product. 6th International Conference on Industrial Engineering, Iran Institute of Industrial Engineering.
78-  Setak, M., Azizi, V., Karimi, H., (2013), “Location routing problem with simultaneous pickup and delivery and split Loads with soft time window”, 10th International Conference on Industrial Engineering, Iran Institute of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran.
79-  Mazahery, S., Homayouni, S.M., (2014). Modeling location-routing problem for Cross- warehouses in waste collection network. 2th National Conference on Industrial Engineering & Sustainable Management (IESM’14), 15-16 Oct, Islamic Azad University, Isfahan, Iran.
80-  Maranzana, F. (1964). “On the location of supply points to minimize transport costs”, Operational Research Quarterly, Vol. 15, No. 1, PP. 261–270.
81-  Watson-Gandy, C.D.T., Dohrn, P.J., (1973). “Depot location with van salesmen–a practical approach”, Omega, Vol. 1, No. 3, PP. 321–329.
82-  Or, I., Pierskalla, W.P., (1979). “A Transportation location-allocation model for regional blood banking”, AIIE Transportation, Vol. 11, No. 2, PP. 86–95.
83-  Nambiar, J.M., Gelders, L.F., Van Wassenhove, L.N., (1981). “A large scale location-allocation problem in the natural rubber industry”, European Journal of Operational Research, Vol. 6, No. 2, PP. 183–189.
84-  Srivastava, R., Benton, W.C., (1990). “The location-routing problem: considerations in physical distribution system design”, Computer  & Operational Research, Vol. 17, No. 5, PP. 427–435.
85-  Min, H., (1996). “Consolidation terminal location-allocation, consolidated routing problems”, Journal of Business Logistics, Vol. 17, No. 2, PP. 235–263.
86-  Nagy, G., Salhi, S., (1996a). “Nested heuristic methods for the location-routeing problem”, Journal of the Operational Research Society, Vol. 47, No. 9, PP. 1166–1174.
87-  Nagy, G., Salhi, S., (1996b). “A nested location-routing heuristic using route length estimation”, Studies in Locational Analysis, Vol. 10, No. ???, PP. 109–127.
88-  Salhi, S., Fraser, M., (1996). “An integrated heuristic approach for the combined location vehicle fleet mix problem”, Studies in Locational Analysis, Vol. 8, No. 1, PP. 3–21.
89-  Albareda-Sambola, M., (2003). “Models and Algorithms for Location-Routing and Related Problems”, PhD dissertation, Catalonia Polytechnic University.
90-  Albareda-Sambola, M., Díaz, J. A., Fernández, E. (2005). “A compact model and tight bounds for a combined location-routing problem”, Computer  & Operational Research, Vol. 32, No. 3, PP. 407–428.
91-  Singh, N., Shah, J., 2004. “Managing tendu patta leaf logistics: an integrated approach”, International Transportation in Operational Research, Vol. 11, No. 6, PP. 683–699.
92-  Chan, Y, Baker, S. (2005). “The multiple depots, multiple traveling salesmen facility-location problem: Vehicle range, service frequency, and heuristic implementations”, Mathematics & Computer  Modelling, Vol. 41, No. 8-9, PP. 1035–1053.
93-  Melechovsky, J., Prins, C., Wolfler Calvo, R., (2005). “A metaheuristic to solve a location-routing problem with non-linear costs”, Journal of Heuristics, Vol. 11, No. 5, PP. 375–391.
94-  Wang, X., Sun, X., Fang, Y., (2005). “A two-phase hybrid heuristic search approach to the location-routing problem”, IEEE International Conference on Systems, Man and Cybernetics, Vol. 4, No. 1, PP. 3338–3343.
95-  Lashine, S.H., Fattouh, M., Issa, A., (2006). “Location/allocation, routing decisions in supply chain network design”, Journal of Modelling in Management, Vol. 1, No. 2, PP. 173–183.
96-  Chen, C., Ting, C. (2007). “A hybrid Lagrangian heuristic/simulated annealing algorithm for the multi-depot location routing problem”, Proceedings of the Eastern Asia Society for Transportation Studies, Vol. 6, No. 1, PP. 137–150.
97-  Aksen, D., Altinkemer, K. (2008). “A location-routing problem for the conversion to the click-and-mortar retailing: the static case”, European Journal of Operational Research, Vol. 186, No. 2, PP. 554–575.
98-  Ambrosino, D., Sciomachen, A., Scutellà, M.G. (2009). “A heuristic based on multiexchange techniques for a regional fleet assignment location-routing problem”, Computer  Operational Research, Vol. 36, No. 2, PP. 442–460.
99-  Prodhon, C., (2009a). “An ELS×path relinking hybrid for the periodic location-routing problem”, In M. Blesa et. al..6th International workshop of lecture notes in Computer  Science, Hybrid metaheuristics 5818: 15–29. Springer.
100-   Schittekat, P., Sorensen, K., (2009). “Supporting 3PL decisions in the automotive industry by generating diverse solutions to a large-scale location-routing problem”, Operational Research, Vol. 57, No. 5, PP. 1058–1067.
101-   Derbel, H., Jarboui, B., Hanafi, S., Chabchoub, H. (2010). “An iterated local search for solving a location-routing problem”, Electronic Notes in Discrete Mathematics, Vol. 36, No. 1, PP. 875–882.
102-   Pirkwieser, S., Raidl, G. R. (2010). “Variable neighborhood search coupled with ILPbased very large neighborhood searches for the (periodic) location-routing problem”, Hybrid Metaheuristics, series Lecture Notes in Computer  Science 6373, PP. 174-189.
103-   Prodhon, C. (2011). “A hybrid evolutionary algorithm for the periodic location-routing problem”, European Journal of Operational Research, Vol. 210, No. 2, PP. 204–212.
104-   Rath, S., Gutjahr, W.J., (2011). “A math-heuristic for the warehouse location–routing problem in disaster relief”, Computer  and Operational Research, Vol. 42, No. ???, PP. 25–39
105-   Ahn, J., de Weck, O., Geng, Y., Klabjan, D. (2012). “Column generation based heuristics for a generalized location routing problem with profits arising in space exploration”, European Journal of Operational Research, Vol. 223, No. 1, PP. 47–59.
106-   Albareda-Sambola, M., Fernandez, E., Nickel, S. (2012). “Multi-period location-routing with decoupled time scales”, European Journal of Operational Research, Vol. 217, No. 1, PP. 248–258.
107-   Xu, Z., Xu, D., Zhu, W., (2012). “Approximation results for a min–max location-routing problem”, Discrete Applied Mathematics, Vol. 160, No. 3, PP. 306–320.
108-   Alvim, A., Taillard, E. (2013). “POPMUSIC for the world location-routing problem”, Eur J. on Transportation and Logistics, Vol. 2, No. 3, PP. 231–254.
109-   Hemmelmayr, V.C. (2015). “Sequential and parallel large neighborhood search algorithms for the periodic location routing problem”, European Journal of Operational Research, Vol. 243, No. 1, PP. 52-60.
110-   Koç, Ç., Bektaş, T., Jabalib, O., Laporte, G., (2016). “The fleet size and mix location-routing problem with time windows: Formulations and a heuristic algorithm”, European Journal of Operational Research, Vol. 248, No. 1, PP. 33–51.
111-   Badiozaman, M.M., salmasi, N., (2008), “An approximate solution for a distribution network model of location-routing problem”, 6th International Conference on Industrial Engineering, Tehran, Iran.
112-   Prodhon, C., Prins, C., (2008). “A memetic algorithm with population management (MAPM) for the periodic location-routing problem”, In Blesa et al. (Vol. Eds.). 5th International workshop, lecture notes in Computer  Science, Hybrid metaheuristics, 5296, 43–57. Springer.
113-   Prodhon, C., (2009b). “An evolutionary algorithm for the periodic location-routing problem”, In Odysseus 2009- Fourth International Workshop on Freight Transportation and Logistics.
114-   Derbel, H., Jarboui, B., Hanafi, S., Chabchoub, H., (2012). “Genetic algorithm with iterated local search for solving a location-routing problem”, Expert Systems with Application, Vol. 39, No. 3, PP. 2865–2871.
115-   Stenger, A., Schneider, M., Schwind, M., Vigo, D. (2012). “Location routing for small package shippers with subcontracting options”, International Journal of Production Economics, Vol. 140, No. 2, PP. 702–712.
116-   Linfati, R., Escobar, J.W., Gatica, G., (2014). “A metaheuristic algorithm for the location routing problem with heterogeneous fleet”, IngIneering CIENC., Vol. 10, No. 19, PP. 55–76, enero-junio.
117-   Meiyi, W., Lean, Y., Xiang, L., (2014). “Credibilistic Location-Routing Model for Hazardous Materials Transaction”, International Journal of Intelligent System, Vol. 00, No. 1, PP. 1–17.
118-   Razavi, M., Sokakhyan, M., Ziaraty, K., (2012). “Ant Colony Algorithm for location routing problem with multiple warehouses and assumption of allocation multiple paths to each vehicle”, Journal of Industrial Management, Vol. 3, No. 6, PP. 17-38
119-   Azizi, V., (2013). “Model of location routing problem simultaneous and cut pickup and delivery”, MS thesis, K. N. Toosi University of Technology.
120-   Lin, C.K.Y., Kwok, R.C.W., (2006). “Multi-objective metaheuristics for a location-routing problem with multiple use of vehicles on real data, simulated data”, European Journal of Operational Research, Vol.175, No. 3, PP. 1833–1849.
121-   Mahmoudabadi, A., Seyedhosseini, S. M., (2013), “Developing a Bi-level Objective Model of Risk-Cost Trade-off for Solving Locating-Routing Problem in Transaction of Hazardous Material”, International Journal of Transportation Engineering, Vol. 1, No. 3, PP. 173-182.
122-   Johnson, M.P., Gorr, W.L., Roehrig, S.F., (2002). “Location/allocation/routing for home-delivered meals provision”, International Journal of Industrial Engineering, Vol. 9, No. 1, PP. 45–56.
123-   Caballero, R., Gonzalez, M., Guerrero, F.M., Molina, J., Paralera, C. (2007). “Solving a multiobjective location routing problem with a metaheuristic based on tabu search. Application to a real case in Andalusia”, European Journal of Operational Research, Vol. 177, No. 3, PP. 1751–1763.
124-   Tavakkoli-Moghaddam, R., Makui, A., Mazloomi, Z. (2010). “A new integrated Mathematics model for a bi-objective multi-depot location-routing problem solved by a multi-objective scatter search algorithm”, Journal of Manufacturing System, Vol. 29, No. 2-3, PP. 111–119.
125-   Lopes, R.B., Barreto, S., Ferreira, C., Santos, B.S., (2008). “A decision-support tool for a capacitated location-routing problem”, Decision Support System, Vol. 46, No. 1, PP. 366–375.
126-   Laporte, G., Nobert, Y., Arpin, D. (1984). Capacitated location-routing problems. Paper presented at The Third International Symposium on Locational Decisions, Boston, Massachusetts.
127-   Laporte, G., Nobert, Y., Arpin, D., (1986). “An exact algorithm for solving a capacitated location-routing problem”, Annals of Operational Research, Vol. 6, No. 9, PP. 293–310.
128-   Chien, T.W., (1993). “Heuristic procedures for practical-sized uncapacitated location-capacitated routing problems”, Decision Science, Vol. 24, No. 5, PP. 995–1021.
129-   Prins, C., Prodhon, C., Wolfler Calvo, R. (2004). “Nouveaux algorithmes pour le problème de localisation et routage sous contraintes de capacité”, In A. Dolgui and S. Dauzère-Pérèz (eds), MOSIM’ 04, 2, PP. 1115–1122.
130-   Akca, Z., Berger, R.T., Ralphs, T.K. (2009). “A branch-and-price algorithm for combined location and routing problems under capacity restrictions”, InOperations research and cyber-infrastructure (pp. 309-330). Springer US.
131-   Baldacci, R., Mingozzi, A., Wolfler-C., R. (2011). “An exact method for the capacitated location-routing problem”, Operational Research, Vol. 59, No. 5, PP. 1284–1296.
132-   Belenguer, J.M., Benavent, E., Prins, C., Prodhon, C., Wolfler Calvo, R. (2011). “A branch-and-cut method for the capacitated location-routing problem”, Computer  Operational Research, Vol. 38, No. 6, PP. 931–941.
133-   Contardo, C., Cordeau, J.F., Gendron, B. (2013a). “A computational comparison of flow formulations for the capacitated location-routing problem”, Discrete Optimization, Vol. 10, No. 4, PP. 263-295.
134-   Contardo, C., Cordeau, J.F, Gendron, B. (2013b). “An exact algorithm based on cut-and-column generation for the capacitated location-routing problem”, INFORMS J. on Computing.
135-   Contardo, C., Cordeau, J.F., Gendron,B. (2013c). “A branch-and-cut-and-price algorithm for the capacitated location-routing problem”, CIRRELT.
136-   Irannezhad, S., Jalili Bolhasani, S., Rezazadeh, H., (2012). “The multi product locating-routing problem with constraints on capacity and maximum time of vehicle availability vehicle”, Journal of Supply Chain Management, Vol. 38, No. 1, PP. 26-31.
137-   Perl, J., Daskin, M.S. (1985). “A warehouse location-routing problem”, Transportation Research B, Vol. 19B, No. 5, PP. 381-396.
138-   Srisvastava. R., (1993). “Alternate solution procedures for the location-routing problem”, Omega, Vol. 21, No.4, PP. 497-506.
139-   Hansen, P., Hegedahl, B., Hjortkjr, S., Obel, B. (1994). “A heuristic solution to the warehouse location-routing problem”, European Journal of Operational Research, Vol. 76, No. 1, PP. 111–127.
140-   Su, C.T., (1998). “Locations, vehicle routing designs of physical distribution systems”, Production Planning & Control, Vol. 9, No. 7, PP. 650–659.
141-   Wu, T.H., Low, C., Bai, J.W. (2002). “Heuristic solutions to multi-depot location-routing problems”, Computer  & Operational Research, Vol. 29, No. 10, PP. 1393–1415.
142-   Barreto, S., Ferreira, C., Paixao, J., Santos, B. (2007). “Using clustering analysis in a capacitated location-routing problem”, European Journal of Operational Research, Vol. 179, No. 3, PP. 968-977.
143-   Guerra, L., Murino, T., Romano, E., (2007). “A heuristic algorithm for the constrained location–routing problem”, International Journal of System Application Engineering & Development, Vol. 1, No. 4, PP. 146–154.
144-   Duhamel, C., Lacomme, P., Prins, C., Prodhon, C. (2008). “A memetic approach for the capacitated location routing problem”, International Workshop on Metaheuristics for Logistics and Vehicle Routing (EU/MEeting 2008).
145-   Lam, M., Mittenthal, J., Gray, B., (2009). “The impact of stopping rules on hierarchical capacitated clustering in location routing problems”, Academy of Information and Management Science Journal, Vol. 12, No. 1, PP. 13-28.
146-   Sahraeian, R., Nadizadeh, A. (2009). “Using greedy clustering method to solve capacitated location-routing problem”, Direccion y Organ., Vol. 39, No. 17, PP. 79–85.
147-   Derbel, H., Jarboui, B., Chabchoub, B., Hanafi, S., Mladenovic, N. (2011). “A variable neighborhood search for the capacitated location-routing problem”, LOGISTIQUA, 4th International Conference on logistics, PP. 514-519.
148-   Jabal-Ameli, M., Aryanezhad, M., Ghaffari-Nasab, N. (2011). “A variable neighborhood descent based heuristic to solve the capacitated location routing problem”, International Journal of Industrial Engineering Comput., Vol. 2, No. 1, PP. 141–154.
149-   Jokar, A., Sahraeian, R. (2011). “An iterative two phase search based heuristic to solve the capacitated location-routing problem”, Australian Journal of Basic and Applied Science, Vol. 5, No. 12, PP. 1613–1621.
150-   Nadizadeh, A., Sahraeian, R., Zadeh, A.Homayouni, S. (2011). “Using greedy clustering method to solve capacitated location-routing problem”, African Journal of Business Management, Vol. 5, No. 21, PP. 8470–8477.
151-   Jokar, A., Sahraeian, R. (2012). “A heuristic based approach to solve a capacitated location-routing problem”, Journal of Management and Sustainability, Vol. 2, No. 2, PP. 219–226.
152- Contardo, C., Cordeau, J.F., Gendron, B. (2013d). “A GRASP +ILP-based metaheuristic for the capacitated location-routing problem”, Journal of Heuristics, Vol. 20, No. 1, PP. 1-38.
153-   Escobar, J.W., Linfati, R., Toth, P., (2013). “A two-phase hybrid heuristic algorithm for the capacitated location-routing problem”, Computer  & Operational Research, Vol. 40, No. 1, PP. 70–79.
154-   Lam, M., Mittenthal, J. (2013). “Capacitated hierarchical clustering heuristic for multi depot location routing problems”, International Journal of Logistics Research and Applications 16(5), PP. 433–444.
155-   Zare Mehrjerdi, Y., Nadizadeh, A. (2013). “Using greedy clustering method to solve capacitated location-routing problem with fuzzy demands”, European Journal of Operational Research, Vol. 229, No. 1, PP. 75–84.
156-   Irannezhad, S., Ahmady, A., (2012). “Heuristic algorithm based on clustering for solving capacity location-routing problem using neural network of self organization map”, 10th International Conference on Industrial Engineering, Tehran, Iran.
157-   Tuzun, D., Burke, L.I., (1999). “A two-phase tabu search approach to the location routing problem”, European Journal of Operational Research, Vol. 116, No. 1, PP. 87–99.
158-   Bouhafs, L., Hajjam, A., Koukam, A. (2006). “A combination of simulated annealing and ant colony system for the capacitated location-routing problem”, In Gabrys et. al., Knowledge-Based Intelligent Information and Engineering Systems, Vol. 4251 of Lecture Notes in Computer  Science, Springer, PP. 409–416.
159-   Prins, C., Prodhon, C., Wolfler Calvo, R., (2006a). “Solving the capacitated location-routing problem by a GRASP complemented by a learning process, a path relinking”, 4OR4: A Quarterly Journal of Operations Research, Vol. 4, No. 3,  221–238.
160-   Prins, C., Prodhon, C., Wolfler Calvo, R. (2006b). “A memetic algorithm with population management (MAPM) for the capacitated location-routing problem”, 16 Conference: Evolutionary Computation in Combinatorial Optimization”, 6th European Conference, EvoCOP 2006, Budapest, Hungary, April.
161-   Prins, C., Prodhon, C., Ruiz, A., Soriano, P., Wolfler Calvo, R. (2007). “Solving the capacitated location-routing problem by a cooperative Lagrangean relaxation-granular tabu search heuristic”, Transportation Science, Vol. 41, No. 4, PP. 470–483.
162-   Marinakis, Y., Marinaki, M. (2008a). “A bilevel genetic algorithm for a real life location routing problem”, International Journal of Logistics Research & Applications, Vol. 11, No. 1, PP. 49–65.
163-   Marinakis, Y., Marinaki, M. (2008b). “A particle swarm optimization algorithm with path relinking for the location routing problem”, Journal of Mathematics Modelling and Algorithm, Vol. 7, No. 1, PP. 59–78.
164-   Duhamel, C., Lacomme, P., Prins, C., Prodhon, C. (2010). “A GRASP+ELS approach for the capacitated location-routing problem”, Computer  & Operational Research, Vol. 37, No. 11, PP. 1912–1923.
165-   Yu, V.F., Lin, S.W., Lee, W., Ting, C.J., (2010). “A simulated annealing heuristic for the capacitated location routing problem”, Computer  & Industrial Engineering, Vol. 58, No. 2, PP. 288–299.
166-   Stenger, A., Schneider, M., Enz, S. (2011). “A hybrid GRASP×VNS algorithm with effective depot reduction mechanism for the capacitated location routing problem”, Technical report 01/2011, IT-based Logistics, Goethe University Frankfurt.
167-   Golozari, F., Jafari, A., Amiri, M. (2013). “Application of a hybrid simulated annealing-mutation operator to solve fuzzy capacitated location-routing problem”, International Journal of Advanced Manufacturing Technology, Vol. 67, No. 5-8, PP. 1791–1807.
168-   Jarboui, B., Derbel, H., Hanafi, S., Mladenovic, N., (2013). “Variable neighborhood search for location routing”, Computer  & Operational Research, Vol. 40, No. 1, PP. 47–57.
169-   Ting, C.J., Chen, C.H. (2013). “A multiple ant colony optimization algorithm for the capacitated location routing problem”, International Journal of Production Economics, Vol. 141, No. 1, PP. 34–44.
170-   Zhang, Y., Qi, M., Lin, W.H., Miao, L., (2015). “A metaheuristic approach to the reliable location routing problem under disruptions”, Transportation Research Part E, Vol. 83, No. 1, PP. 90–110.
171-   Mohammadi-Shad, A., Fattahi, P., (2011). “A hybrid heuristic algorithm for solving capacity locating-routing problem”, 2th International Conference & 4th National Conference of Supply Chain, Tehran, Iran.
172-   Mohammadi-Shad, A., Fattahi, P., (2012). “A hybrid meta-heuristic method for capacity locating routing problem with hard time windows”, Journal of Industrial Engineering, Vol. 46, No. 2, PP. 219-223.
173-   Ebadati, M., (2012). “Presented an algorithm for integrated location routing problem (compared with other iterative methods and hierarchical)”, MS thesis, Bu-Ali Sina University.
174-   Setak, M., Azizi, V., Karimi, H., (2015), “Multi depots Capacitated Location-Routing Problem with Simultaneous Pickup and delivery and Split Loads: Formulation and heuristic methods”, Journal of Industrial Engineering Research in Production System, Vol. 2. No.4. PP. 67-81.
175-   Ghaffari-Nasab, N., Jabalameli, M. S., Aryanezhad, M. B., Makui, A. (2012). “Modeling and solving the bi-objective capacitated location-routing problem with probabilistic travel times”, International Journal of Advanced Manufacturing Technology, Vol. 67, No. 9, PP.2007-2019.
176-   Samaei, F., (2011). “Capacity location - routing problem with time window”, MS thesis, Shahed University.
177-   Azizi, M., Javanshir, H., Proud, A.h., (1392). “A new mathematical model for Multi-Objective location routing problem and solving with efficient meta-heuristic algorithm”, 10th International Conference on Industrial Engineering, Tehran, Iran.
178-   Cooper, L., (1972). “The Transaction-location problem”, Operational Research, Vol. 20, No. 1, PP. 94–108.
179-   Cooper, L., (1978). “The stochastic Transaction-location problem”, Computer  & Mathematics with Application, Vol. 4, No. 3, PP. 265–275.
180-   Franca, P.M., Luna, H.P.L., (1982). “Solving stochastic Transaction-location problems by generalized Benders decomposition”, Transportation Science, Vol. 16, No. 2, PP. 113-126.
181-   Hindi, K.S., Basta, T., (1994). “Computationally efficient solution of a multiproduct, two-stage distribution-location problem”, Journal of the Operational Research, Society, Vol. 45, No. 11, PP. 1316–1323.
182-   Nema, A.K., Gupta, S.K., (1999). “Optimization of regional hazardous waste management systems: an improved formulation”, Waste Management, Vol. 19, No. 7–8, PP. 441–451.
183-   Cappanera, P., Gallo, G., Maffioli, F., (2004). “Discrete facility location, routing of obnoxious activities”, Discrete Applied Mathematics, Vol. 133, No. 1–3, PP. 3–28.
184-   Antunes, A.P., Teixeira, J.C., Coutinho, M.S., (2008). “Managing solid waste through discrete location analysis: a case study in central Portugal”, Journal of the Operational Research Society, Vol. 59, No. 8, PP. 1038–1046.
185-   Klibi, W., Lasalle, F., Martel, A., Ichoua, S. (2010). “The stochastic multiperiod location Transaction problem”, Transportation Science, Vol. 44, No. 2, PP. 221–237.
186-   Samanlioglu, F., (2013). “A multi-objective mathematic model for the industrial hazardous waste location-routing problem”, European Journal of Operational Research, Vol. 226, No. 2, PP. 332–340.
187-   Cooper, L., (1976). “An efficient heuristic algorithm for the Transportation-location problem”, Journal of Regional Science, Vol.16, No. 3, PP. 309–315.
188-   LeBlanc, L.J., (1977). “A heuristic approach for large scale discrete stochastic Transportation-location problems”, Computer  & Mathematics with Application, Vol. 3, No. 2, PP. 87–94.
189-   Lee, C. Y., (1993). “A heuristic approach for a stochastic Transportation-location problem with cross decomposition”, Information & Management Science, Vol. 4, No. 2, PP. 47-65.
190-   Aykin, T., 1995. “The hub location-routing problem”, European Journal of Operational Research, Vol. 83, No. 1, PP. 200–219.
191-   Averbakh, I., Berman, O., (2002). “Minmaxp-traveling salesmen location problems on a tree”, Annals of Operational Research, Vol. 110, No. 1, PP. 55–62.
192-   Lee, Y., Kim, S.I., Lee, S., Kang, K., (2003). “A location-routing problem in designing optical internet access with WDM systems”, Photonic Network Commu., Vol. 6, No. 2, PP. 151–160.
193-   Ogryczak, W., Studzinski, K., Zorychta, K., (1989). “A solver for the multi-objective transshipment problem with facility location”, European Journal of Operational Research, Vol. 43, No. 1, PP. 53–64.
194-   List, G.F., Mirchandani, P.B., (1991). “An integrated network/planar multiobjective model for routing, siting for hazardous materials wastes”, Transportation Science, Vol. 25, No. 2, PP. 146–156.
195-   ReVelle, C., Cohon, J., Shobrys, D., (1991). “Simultaneous siting, routing in the disposal of hazardous wastes”, Transportation Science, Vol. 25, No. 2, PP. 138–145.
196-   Ogryczak, W., Studzinski, K., Zorychta, K., (1992). “DINAS: a Computer-assisted analysis system for multiobjective transshipment problems with facility location”, Computer  & Operational Research, Vol. 19, No. 7, PP. 637–647.
197-   Boffey, B., Karkazis, J., (1993). “Models and methods for location and routing decision relating to hazardous materials”, Studies in Locational Analysis, Vol. 5, No. ???, PP. 149–166.
198-   Stowers. C.L., Palekar. U.S., (1993b). “Location models with routing”, Computer  & Operational Research, Vol. 6, No. ???, PP. 427-435.
199-   Jacobs, T.L., Warmerdam, J.M., (1994). “Simultaneous routing, siting for hazardous-waste”, Operational Journal of Urban Planning, Development, Vol. 120, No. 3, PP. 115–131.
200-   Current, J., Ratick, S., 1995. “A model to assess risk, equity, efficiency in facility location, Transaction of hazardous materials”, Location Science, Vol. 3, No. 3, PP. 187–201.
201-   Wyman, M.M., Kuby, M., (1995). “Proactive optimization of toxic waste Transaction, location”, Technology Location Science, Vol. 3, No. 3, PP. 167–185.
202-   Kulcar, T., (1996). “Optimizing solid waste collection in Brussels”, European Journal of Operational Research, Vol. 90, No. 1, PP. 71–77.
203-   Giannikos, I., (1998). “A multi objective programming model for locating treatment sites, routing hazardous wastes”, European Journal of Operational Research, 104, No. 2, PP. 333–342.
204-   Alumur, S., Kara, B. Y. (2007). “A new model for the hazardous waste location routing problem”, Computer  & Operational Research, Vol. 34, No. 5, PP. 1406–1423.
205-   Coutinho-Rodrigues, J., Tralhao, L., Alc¸ ada-Almeida, L., (2012). “Solving a location-routing problem with a multi-objective approach: the design of urban evacuation plans”, Journal of Transportation Geo., Vol. 22, No. ???, PP. 206–218.
206-   Xie, Y., Lu, W., Wang, W., Quadrifoglio, L., (2012). “A multimodal location, routing model for hazardous materials Transaction”, Journal of Hazardous Mater., Vol. 227, No. ???, PP. 135–141.
207-   Ehrgott, M., Verma, R., (2001). “A note on solving multi criteria Transportation-location problems by fuzzy programming”, Asia-Pacific Journal of Operational Research, Vol. 18, No. 2, PP. 149–164.
208-   Boffey, T. et. al. (2008). “Locating a low-level waste disposal site”, Computer  & Operational Research, Vol. 35, No. 3, PP. 701–716.
209-   Martínez-Salazar, I.A., Molina, J., Ángel-Bello, F., Gómez, T., Caballero, R., (2015). “Solving a bi-objective Transportation location routing problem by metaheuristic algorithms”, European Journal of Operational Research, Vol. 234, No. 1, PP. 25–36.
210-   Gonzalez, F.,J., (2009). “The multi-echelon location-routing problem: Concepts and methods for tactical and operation planning”, Technical Report, Transport Economics Laboratory, Lyon, France.
211-   Gendron, B., Semet, F. (2009). “Formulations and relaxations for a multi-echelon capacitated location–distribution problem”, Computer  and Operational Research, Vol. 36, No. 5, PP. 1335–1355.
212-   Boccia, M., Crainic, T., Sforza, A., Sterle, C. (2011). “Location-routing models for designing a two-echelon freight distribution system”, Technology Rep., CIRRELT-2011-06, Université de Montréal.
213-   Contardo, C., Hemmelmayr, V., Crainic, T. G. (2012). “Lower and upper bounds for the two-echelon capacitated location-routing problem”, Computer  and Operational Research, Vol. 39, No. 12, PP. 3185–3199.
214-   Hamidi, M., Farahmand, K., Sajjadi, S.R. (2012). “Modeling a four-layer location-routing problem”, International Journal of Industrial Engineering Computers, Vol. 3, No. ???, PP. 43–52.
215-   Madsen, O., (1983). “Methods for solving combined two level location-routing problems of realistic dimensions”, European Journal of Operational Research, Vol. 12, No. 3, PP. 295–301.
216-   Burks, R., (2006). “An adaptive tabu search heuristic for the location routing pickup and delivery problem with time windows with a theater distribution application”, PhD thesis, Graduate School of Engineering and Management, Air Force Institute of Technology, Ohio.
217-   Lin, J.R., Lei, H.C., (2009). “Distribution systems design with two-level routing considerations”, Annals of Operational Research, Vol. 172, No. 1, PP. 329–347.
218-   Boccia, M., Crainic, T., Sforza, A., Sterle, C. (2010). “A metaheuristic for a two echelon location-routing problem”, In P. Festa, Symposium on experimental algorithms (SEA 2010). Lecture notes in Computer  Science (6049, 288–301). Berlin: Springer-Verlag.
219-   Nguyen, V.P., Prins, C., Prodhon, C. (2010). “A multi-start evolutionary local search for the two-echelon location routing problem”, in Blesa, et. al., Hybrid Metaheuristics, Vol. 6373 of Lecture Notes in Computer  Science, Springer, p. 88–102.
220-   Nikbakhsh, E., Zegordi, S. (2010). “A heuristic algorithm and a lower bound for the two-echelon location-routing problem with soft time window constraints”, Scientia Iranica Transaction E: Industrial Engineering, Vol. 17, No. ???, PP. 36–47.
221-   Crainic, T. G., Sforza, A., Sterle, C. (2011a). “Tabu search heuristic for a two-echelon location-routing problem”, Technical Report 2011-07, CIRRELT, Canada.
222-   Hamidi, M., Farahmand, K., Sajjadi, S.R., Nygard, K. (2012). “A hybrid GRASP tabu search metaheuristic for a four-layer location-routing problem”, International Journal of Logistics System and Management, Vol. 12, No. ???, PP. 267–287.
223-   Nguyen, V.P., Prins, C., Prodhon, C., (2012a). “A multi-start iterated local search with tabu list, path relinking for the two-echelon location-routing problem”, Engineering Application of Artificial Intell., Vol. 25, No. 1, PP. 56–71.
224-   Nguyen, V.P., Prins, C., Prodhon, C. (2012b). “Solving the two-echelon location routing problem by a GRASP reinforced by a learning process, path relinking”, European Journal of Operational Research, Vol. 216, No. 1, PP. 113–126.
225-   Toyoglu, H., Karasan, O.E., Kara, B.Y., (2012). “A new formulation approach for location-routing problems”, Networks, Spatial Economics, Vol. 12, No. 4, PP. 635–659.
226-   Hamidi, M., Farahmand, K., Sajjadi, S.R., Nygard, K. (2014). “A heuristic algorithm for a multi-product four-layer capacitated location-routing problem”, International Journal of Industrial Engineering Comput., Vol. 5, No. 1, PP. 87–100.
227-   Rahmani, Y. et. al. (2015). “The two-echelon multi products location-routing problem with pickup and delivery: formulation and heuristic approaches”, International Journal of Production Research, Vol. 54, No. 4, PP. 999-1019.
228-   Jowkar, A., Sahraeian, R., (2011). “Solving multi-level location-routing problem due to limitations in storage capacity and restrictions on the path using heuristic methods”, MS thesis, University Shahed.
229-   Crainic, T. G., Sforza, A., Sterle, C. (2011b). “Location-routing models for two-echelon freight distribution system design”, Technical report 2011-40, CIRRELT, Canada. Transportation, Amsterdam: Elsevier, PP. 467–537.
230-   Hamidi, M., (2011). “Modeling And Solving Multi-Product Multi-Layer Location-routing Problems”, PhD dissertation, University of North Dakota State.
231-   Schwengerer, M., Pirkwieser, S., Raidl, G.R., (2012). “A variable neighborhood search approach for the two-echelon location-routing problem”, In J. K. Hao & M. Middendorf (Eds.), Evolutionary computation in combinatorial optimization. Lecture notes in Computer  Science (Vol. 7245, PP. 13–24). Berlin Heidelberg: Springer.
232-   Dalfard, V.M., Kaveh, M., Nosratian, N.E., (2013). “Two meta-heuristic algorithms for two echelon location-routing problem with vehicle fleet capacity and maximum route length constraints”, Neural Comput. Appl., Vol. 23, No. ???, PP. 2341–2349.
233-   Govindan, K., Jafarian, A., Khodaverdi, R., Devika, K. (2014). “Two-echelon multiple vehicle LRP with time windows for optimization of sustainable supply chain network of perishable food”, International Journal of Production Economics, Vol. 152, No. ???, PP. 9–28.
234-   Zegordy, S.H.A., nikbakhsh, A., (2009). “Solutions lower bound and innovative for the two-level location routing problem”, International Journal of Industrial Engineering & Production Management, Vol. 20, No. 1, PP. 1-14.
235-   Jiahong, Z., Vedat, V., (2015). “A bi-objective model for the used oil location-routing problem”, Computer  and Operational Research, Vol. 62, No. ???, PP. 157–168.
236-   Jin, L., Zhu, Y., Shen, H., Ku, T. (2010). “Research on two-layer location-routing problem and optimization algorithm”, International Journal of Advancment in Computers Technology, Vol. 2, No. ???, PP. 102–108.
237-   Barzinpour, F., Saffarian, M., Teymoori, E., (2015a). “Metahuristic algorithm for solving model of multi-objective location programming and three-level allocation in relief logistics”, Journal of Operational Research in Its Application, Vol. 2, No. 41, PP. 27-50.
238-   Berman, O., Simchi-Levi, D., (1986). “Minisum location of a traveling salesman”, Networks, Vol. 16, No. 3, PP. 239–254.
239-   Berman, O., Simchi-Levi, D., (1988a). “Minisum location of a travelling salesman on simple networks”, European Journal of Operational Research, Vol. 36, No. 2, PP. 241–250.
240-   Berman, O., Simchi-Levi, D., (1988b). “Finding the optimal a priori tour, location of a traveling salesman with nonhomogeneous customers”, Transportation Science, Vol. 22, No. 2, PP. 148–154.
241-   Berman, O., Simchi-Levi, D., Tamir, A., (1988). “The minimax multistop location problem on a tree”, Networks, Vol. 18, No. 1, PP. 39–49.
242-   Berman, O., Simchi-Levi, D., (1989). “The traveling salesman location problem on stochastic networks”, Transportation Science, Vol. 23, No. 1, PP. 54–57.
243-   Bertsimas, D.J., (1989). “Traveling salesman facility location problems”, Transportation Science, Vol. 23, No. 3, PP. 184–191.
244-   Bertsimas, D.J., Jaillet, P., Odoni, A.R., (1990). “A priori optimization”, Operational Research, Vol. 38, No. 6, PP. 1019–1033.
245-   McDiarmid, C, (1992). “Probability modelling, optimal location of a travelling salesman”, Journal of the Operational Research Society., Vol. 43, No. 5, PP. 533–538.
246-   Averbakh, I., Berman, O., Simchi-Levi, D., (1994). “Probabilistic a priori routing-location problems”, Naval Research Logistics, Vol. 41, No. 7, PP. 973–989.
247-   Averbakh, I., Berman, O., (1995). “Probabilistic sales-delivery man, sales-delivery facility location problems on a tree”, S Transportation Science, Vol. 29, No. 2, PP. 184–197.
248-   Simchi-Levi, D., Berman, O., (1987). “Heuristics and bounds for the travelling salesman location problem on the plane”, Operational Research Letters, Vol. 6, No. 5, PP. 243–248.
249-   Simchi-Levi, D., Berman, O., (1988). “A heuristic algorithm for the traveling salesman location problem on networks”, European Journal of Operational Research, Vol. 36, No. ???, PP. 478-484.
250-   Simchi-Levi, D., (1991). “The capacitated traveling salesman location problem”, Transportation Science, Vol. 25, No. 1, PP. 9–18.
251-   Mosheiov, G., 1995. “The pickup delivery location problem on networks”, Networks, Vol. 26, No. 4, PP. 243–251.
252-   Laporte, G., Louveaux, F., Mercure, H., (1989). “Models, exact solutions for a class of stochastic location-routing problems”, European Journal of Operational Research, Vol. 39, No. 1, PP. 71–78.
253-   Chan, Y., Carter, W.B., Burnes, M.D., (2001). “A multiple-depot, multiple-vehicle, location-routing problem with stochastically processed demands”, Computer  & Operational Research, Vol. 28, No. 8, PP. 803–826.
254-   Liu, S., Lin, C., (2005). “A heuristic method for the combined location routing and inventory problem”, International Journal of Advanced Manufacturing Technology, Vol. 26, No. 4, PP. 372–381.
255-   Albareda-Sambola, M., Fernandez, E., Laporte, G., (2007). “Heuristic, lower bound for a stochastic location-routing problem”, European Journal of Operational Research, Vol. 179, No. 3, PP. 940–955.
256-   Shen, Z., Qi, L. (2007). “Incorporating inventory and routing costs in strategic location models”, European Journal of Operational Research, Vol. 179, No. 2, PP. 372–389.
257-   Zarandi, M.H.F., Hemmati, A., Davari, S., Turksen, I.B., (2013). “Capacitated location-routing problem with time windows under uncertainty”, Knowledge-Based System, Vol. 37, No. ???, PP. 480–489.
258-   Sajjadi, R.S., Cheraghi, H.S. (2011). “Multi-products location-routing problem integrated with inventory under stochastic demand”, International Journal of Industrial and Systems Engineering, Vol. 7, No. 4, PP. 454–476.
259-   Hassan-Pour, H.A., Mosadegh-Khah, M., Zareei, M., (2014). “An Efficient Algorithm for Solving a Stochastic Location-Routing Problem”, Journal of Mathematics and Computer  Science, Vol. 12, PP. 27–38.
260-   Hassanpour, H., Mosaddegh-khah, M., Tavakkoli-Moghaddam, R., (2007). Developing two mathematical models for stocastice location-routing problem, 5th InternationalIndustrialEngineering Con., Tehran, Iran.
261-   Hassan-Pour, H., et. al. (2009). “Solving a multi-objective multi-depot stochastic location-routing problem by a hybrid simulated annealing algorithm”, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacturing, Vol. 223, No. 8, PP. 1045-1054.
262-   Nadizadeh, A., Hosseini Nasab, H. (2014). “Solving the dynamic capacitated location routing problem with fuzzy demands by hybrid heuristic algorithm”, European Journal of Operational Research, Vol. 238, No. ???, PP. 458–470.
263-   Nadizadeh, A., Hosseini Nasab, H., Sadeghieh, A., Fakhrzad, M.B., (2014). “A location-routing problem model with multiple periods and fuzzy demands”, Journal of Data Envelopment Analysis & Decision Science, PP. 1-24.
264-   Ghaffari-Nasab, N., Ghazanfar Ahari, S., Ghazanfari, M., (2013), “A hybrid simulated annealing based heuristic for solving the location-routing problem with fuzzy demands”, Scientia Iranica, Vol. 20, No. 3, PP. 919–930.
265-   Shouying, L., Huijuan, Z., (2014). “Optimization model of fuzzy location-routing problem of victim search in flood disaster”, Journal of Chemical and Pharmaceutical Research, Vol. 6, No. 6, PP. 2080-2085.
266-   Teimoori, S., Khademi-Zare, H., Fallah-Nezhad, M.S., (2014). “Location-routing problem with fuzzy time windows and traffic time”, International Journal of Supply & Operational Management, Vol. 1, No. 1, PP. 38-53.
267-   Torfi, F., Farahani, R.Z., Mahdavi, I., (2015). “Fuzzy MCDM for weight of object’s phrase in Location Routing Problem”, Applied Mathematics Modeling, Vol. 40, No. 1, PP. 526–541.
268-   S., Li, H., Zhou, Y., Li, (2016). “Research on Fuzzy Dynamic Location-Routing Problem of Victim Search in Flood Disaster”, International Journal of u- and e- Service, Science & Technology, Vol. 9, No. 7, PP. 61-70.
269-   Golozari, F., (2008). “Using simulated annealing algorithm mutation operator combined for location-routing problem fuzzy with limited capacities”, MS thesis, University of Science and Art.
270-   Teymoori, SH., (2013). “Developed a mathematical model and algorithm for location routing problem with fuzzy time windows”, MS thesis, University of Science and Art.
271-   Barzinpour, F., Saffarian, M., Maku, A., Teymoori, E., (2015b). “Model of multi-objective Location Routing Problem in the relief chain management with multi period approach”, Journal of Operational Research in Its Application, Vol. 3, No. 42, PP. 71-91.
272-   Mahdizadeh,E., Keshavarzi, S., (2015). “Multi-objective model for location routing problem with fuzzy time travel and delivery”, Journal of Supply Chain Management, Vol. 17, No. 47, PP. 42-61.
273-   Chan, A.W., Hearn, D.W., (1977). “A rectilinear distance round-trip location problem”, Transportation Science, Vol. 11, No. 2, PP. 107–123.
274-   Ghosh, J.K., Sinha, S.B., Acharya, D., (1981). “A generalized reduced gradient based approach to round-trip location problem”, in: Jaiswal, N.K. (Ed.), Scientific Management of Transport Systems, Amsterdam, Holland, 209- 213.
275-   Drezner, Z., (1982). “Fast algorithms for the round trip location problem”, IEE Transactions, Vol. 14, No. 4, PP. 243–248.
276-   Drezner, Z., Wesolowsky, G.O., (1982). “A trajectory approach for the round-trip location problem”, Transportation Science, Vol. 16, No. 1, PP. 56–66.
277-   Drezner, Z., (1985). “O(N log N) algorithm for the rectilinear round-trip location problem”, Transportation Science, Vol. 19, No. 1, PP. 91–100.
278-   Kolen, A., (1985). “The round-trip p-center, covering problem on a tree”, Transportation Science, Vol. 19, No. 3, PP. 222–234.
279-   Bruns, A.D., (1998). “Zweistufige Standort planung unter Berucksichtigung von Touren planungsaspekten – Primale Heuristiken und Lokale Suchverfahren”, PhD Dissertation, Sankt Gallen University.
280-   De Camargo, R., de Miranda, G., Lkketangen, A. (2013). “A new formulation and an exact approach for the many-to-many hub location-routing problem”, Applied Mathematics Modelling, Vol. 37, No. 12, PP. 7465–7480.
281-   Nagy, G., Salhi, S., (1998). “The many-to-many location-routing problem”, TOP, Vol. 6, No. 2, PP. 261–275.
282-   Karaoglan, I., Altiparmak, F., Kara, I., Dengiz, B. (2012). “The location-routing problem with simultaneous pickup and delivery: Formulations and a heuristic approach”, Omega, Vol. 40, No. 4, PP. 465–477.
283-   Rieck, J., Ehrenberg, C., Zimmermann, J. (2014). “Many-to-many location-routing with inter-hub transport and multi-commodity pickup-and-delivery”, European Journal of Operational Research,Vol. 236, No. 3, PP.863–878.
284-   Ahmadi-Javid, A., Seddighi, A. (2012). “A location-routing-inventory model for designing multisource distribution networks”, Engineering Optimization, Vol. 44, No. 6, PP. 637–656.
285-   Taei, A., (2011). “The locating - Routing - inventory problem with deteriorating ware”, MS Thesis, K. N. Toosi University of Technology.
286-   Safari, S., Pasandideh, S.H.R., (2014), “Stocastic models location-routing-inventory supply chain with heterogeneous transport fleet”, National Conference on Research of Industrial Engineering, 27 Sep 2014, Hamedan, Iran.
287-   Riquelme-Rodríguez, J.P., Gamache, M., Langevin, A. (2016). “Location arc routing problem with inventory constraints”, Computers & Operational Research, Vol. 76, No. 1, PP. 84-94.
288-   Ahmadi, A., Azad,N., (2010). “Incorporating location, routing, inventory decisions in supply chain network design”, Transportation Research Part E, Vol. 46, No. 5, PP. 582–597.
289-   Belenguer, J.M., Benavent, E., Lacomme, P., Prins, C. (2006). “Lower and upper bounds for the mixed capacitated arc routing problem”, Computer  Operational Research, Vol. 33, No. 12, PP. 3363–3383.
290-   Ghiani, G., Laporte, G. (2001).“Location-arc routing problems.” Opsearch, Vol. 38, No. 2, 151–159.
291-   Hashemi Doulabi, S. H., Seifi, A. (2013). “Lower and upper bounds for location-arc routing problems with vehicle capacity constraints”, European Journal of Operational Research, Vol. 224, No. 1, PP. 189–208.
292-   Lopes, R.B., Plastria, F., Ferreira, C., Santos, B.S. (2014). “Location-arc routing problem: Heuristic approaches and test instances”, Computer  & Operational Research, Vol. 43, No. 1, PP. 309–317.
293-   Salhi, S., Nagy, G., (2009). “Local improvement in planar facility location using vehicle routing”, Annals of Operational Research, Vol. 167, No. 1, PP. 287–296.
294-   Schwardt, M., Fischer, K., (2009). “Combined location-routing problems – a neural network approach”, Annals of Operational Research, Vol. 167, No. 1, PP. 253–269.
295-   Manzour-al-Ajdad, S., Torabi, S., Salhi, S. (2012). “A hierarchical algorithm for the planar single-facility location routing problem”, Computer  and Operational Research, Vol. 39, No. 2, PP. 461–470.
296-   Beasley, J.E., Nascimento, E.M., (1996). “The vehicle routing-allocation problem: A unifying framework”, TOP., Vol. 4, No. 1, PP. 65–86.
297-   Labbe, M., Laporte, G., Martin, I.R., Salazar Gonzalez, J.J., (2005). “Locating median cycles in networks”, European Journal of Operational Research, Vol. 160, No. 2, PP. 457–470.
298-   Gunnarsson, H., Ronnqvist, M., Carlsson, D., (2006). “A combined terminal location, ship routing problem”, Journal of the Operational Research Society, Vol. 57, No. 8, PP. 928–938.
299-   Sadeghi, A., (2011), “Solving split delivery open location routing problem using simulated annealing algorithm”, MS Thesis, University of Science & Culture.
300-   Jafari, A., Sadeghi Sarvestani, A., (2014). “Modeling the split delivery open location routing problem and solving it by simulated annealing”, Journal of Industrial Engineering Research in Production System, Vol. 2. No. 3. PP. 47-61.
301-   Labbe, M., Rodriguez Martin, I. and Salazar Gonzalez, J. J. (2004). “A branch-and-cut algorithm for the plant-cycle location problem”, Journal of the Operational Research Society, Vol. 55, No. 5, PP. 513–520.
302-   Billionnet, A., Elloumi, S. and Grouz-Djerbi, L. (2005). “Designing radio-mobile access networks based on synchronous digital hierarchy rings”, Computer  & Operational Research, Vol. 32, No. 2, PP. 379–394.
303-   Laporte, G. AND Dejax, P. J. (1989). “Dynamic location-routeing problems”, Journal of the Operational Research Society, Vol. 40, No. 5, PP. 471–482.
Advances in Industrial Engineering
Volume 51, Issue 2
July 2017
Pages 223-250

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