A Lagrangian-Based Branch-and-Bound Algorithm for the Two-Level Uncapacitated Facility Location Problem with Single-Assignment Constraints

References

• Aardal K, Labbé M, Leung JMY, Queyranne M (1996) On the two-level uncapacitated facility location problem. INFORMS J. Comput. 8(3):289–301.Link, Google Scholar
• Achterberg T, Koch T, Martin A (2005) Branching rules revisited. Oper. Res. Lett. 33(1):42–54.Crossref, Google Scholar
• Applegate D, Bixby RE, Chvátal V, Cook W (1995) Finding cuts in the TSP. DIMACS Technical report 95-05, Rutgers University, Piscataway, NJ.Google Scholar
• Barahona F, Chudak F (2005) Near-optimal solutions to large-scale facility location problems. Discrete Optim. 2(1):35–50.Crossref, Google Scholar
• Barros AI (1995) Discrete and fractional programming techniques for location models. Unpublished doctoral thesis, Erasmus University Rotterdam, Rotterdam, Netherlands.Google Scholar
• Barros AI, Labbé M (1994) A general model for the uncapacitated facility and depot location problem. Location Sci. 2(3):173–191.Google Scholar
• Barros AI, Dekker R, Scholten V (1998) A two-level network for recycling sand: A case study. Eur. J. Oper. Res. 110(2):199–214.Crossref, Google Scholar
• Beltran-Royo C, Vial J-P, Alonso-Ayuso A (2012) Semi-Lagrangian relaxation applied to the uncapacitated facility location problem. Comput. Optim. Appl. 51(1):387–409.Crossref, Google Scholar
• Benichou M, Gauthier JM, Girodet P, Hentges G, Ribiere G, Vincent O (1971) Experiments in mixed-integer linear programming. Math. Programming 1(1):76–94.Crossref, Google Scholar
• Bloemhof-Ruwaard JM, Salomon M, Van Wassenhove LN (1994) On the coordination of product and by-product flows in two-level distribution networks: model formulations and solution procedures. Eur. J. Oper. Res. 79(2):325–339.Crossref, Google Scholar
• Bloemhof-Ruwaard JM, Salomon M, Van Wassenhove LN (1996) The capacitated distribution and waste disposal problem. Eur. J. Oper. Res. 88(3):490–503.Crossref, Google Scholar
• Bumb A (2001) An approximation algorithm for the maximization version of the two level uncapacitated facility location problem. Oper. Res. Lett. 29(4):155–161.Crossref, Google Scholar
• Chardaire P, Lutton JL, Sutter A (1999) Upper and lower bounds for the two-level simple plant location problem. Ann. Oper. Res. 86:117–140.Crossref, Google Scholar
• Cornuéjols G, Nemhauser GL, Wolsey LA (1991) The uncapacitated facility location problem. Michandani PB, Francis RL, eds. Discrete Location Theory (John Wiley and Sons, New York), 119–171.Google Scholar
• Farahani R, Hekmatfar M, Fahiminia B, Kazemzadeh N (2014) Hierarchical facility location problem: Models, classifications, techniques, and applications. Comput. Indust. Engrg. 68(1):104–117.Crossref, Google Scholar
• Frangioni A (1996) Solving semidefinite quadratic problems within nonsmooth optimization algorithms. Comput. Oper. Res. 23(11):1099–1118.Crossref, Google Scholar
• Frangioni A (2005) About Lagrangian methods in integer optimization. Ann. Oper. Res. 139(1):163–193.Crossref, Google Scholar
• Gabor AF, van Ommeren J-KCW (2010) A new approximation algorithm for the multilevel facility location problem. Discrete Appl. Math. 158(5):453–460.Crossref, Google Scholar
• Gao LL, Robinson EP Jr (1992) A dual-based optimization procedure for the two-echelon uncapacitated facility location problem. Naval Res. Logist. 39(2):191–212.Crossref, Google Scholar
• Gendron B, Semet F (2009) Formulations and relaxations for a multi-echelon capacitated location-distribution problem. Comput. Oper. Res. 36(5):1335–1355.Crossref, Google Scholar
• Gendron B, Khuong PV, Semet F (2015) Multilayer variable neighborhood search for two-level uncapcaitated facility location problems with single assignment. Networks 66(3):214–234.Crossref, Google Scholar
• Hansen P, Brimberg J, Urosevic D, Mladenovic N (2007) Primal-dual variable neighborhood search for the simple plant-location problem. INFORMS J. Comput. 19(4):552–564.Link, Google Scholar
• Ignacio AAV, Filho VJMF, Galvão RD (2008) Lower and upper bounds for a two-level hierarchical location problem in computer networks. Comput. Oper. Res. 35(6):1982–1998.Crossref, Google Scholar
• Kaufman L, Eede MV, Hansen P (1977) A plant and warehouse location problem. Oper. Res. Quart. 28(3):547–554.Crossref, Google Scholar
• Klose A, Drexl A (2005) Facility location models for distribution system design. Eur. J. Oper. Res. 162(1):4–29.Crossref, Google Scholar
• Kochetov Y, Ivanenko D (2005) Computationally difficult instances for the uncapacitated facility location problem. Ibaraki T, Nonobe K, Yagiura M, eds. Metaheuristics: Progress as Real Problem Solvers, Oper. Res./Comput. Sci. Interfaces Series, Vol. 32 (Springer Science+Business Media, New York), 351–367.Crossref, Google Scholar
• Körkel M (1989) On the exact solution of large-scale simple plant location problems. Eur. J. Oper. Res. 39(2):157–173.Crossref, Google Scholar
• Krarup J, Pruzan PM (1983) The simple plant location problem: Survey and synthesis. Eur. J. Oper. Res. 12(1):36–81.Crossref, Google Scholar
• Landete M, Marín A (2009) New facets for the two-stage uncapacitated facility location polytope. Comput. Optim. Appl. 44(3):487–519.Crossref, Google Scholar
• Letchford AN, Miller SJ (2012) Fast bounding procedures for large instances of the simple plant location problem. Comput. Oper. Res. 39(5):985–990.Crossref, Google Scholar
• Letchford AN, Miller SJ (2014) Fast bounding procedures for large instances of the simple plant location problem. Eur. J. Oper. Res. 234(3):674–682.Crossref, Google Scholar
• Maric M (2010) An efficient genetic algorithm for solving the multi-level uncapacitated facility location problem. Comput. Informatics 29(2):183–201.Google Scholar
• Marín A (2006) Lower bounds for the two-stage uncapacitated facility location problem. Eur. J. Oper. Res. 179(3):1126–1142.Crossref, Google Scholar
• Marín A, Pelegrin B (1999) Applying Lagrangian relaxation to the resolution of two-stage location problems. Ann. Oper. Res. 86:179–198.Crossref, Google Scholar
• Melo MT, Nickel S, Saldanha da Gama F (2009) Facility location and supply chain management—A review. Eur. J. Oper. Res. 196(2):401–412.Crossref, Google Scholar
• Mitropoulos P, Giannikos I, Mitropoulos I (2009) Exact and heuristic approaches for the locational planning of an integrated solid waste management system. Eur. J. Oper. Res. 9(3):329–347.Google Scholar
• Narula SC, Ogbu UI (1979) An hierarchical location—Allocation problem. Omega 7(2):137–143.Crossref, Google Scholar
• Pirkul H, Jayaraman V (1996) Production, transportation and distribution planning in a multi-commodity tri-echelon system. Transportation Sci. 30(4):291–302.Link, Google Scholar
• Pirkul H, Jayaraman V (1998) A multi-commodity multi-plant capacitated facility location problem: Formulation and efficient heuristic solution. Comput. Oper. Res. 25(10):869–878.Crossref, Google Scholar
• Posta M, Ferland JA, Michelon P (2014) An exact cooperative method for the simple plant location problem. Math. Programming Comput. 6(3):199–231.Crossref, Google Scholar
• Ro HB, Tcha DW (1984) A branch and bound algorithm for the two-level uncapacitated facility location problem with some side constraints. Eur. J. Oper. Res. 18(3):349–358.Crossref, Google Scholar
• Sahin G, Süral H (2007) A review of hierarchical facility location models. Comput. Oper. Res. 34(8):2310–2331.Crossref, Google Scholar
• Zhang J (2006) Approximating the two-level facility location problem via a quasi-greedy approach. Math. Programming A 108(1):159–176.Crossref, Google Scholar