, Volume 27, Issue 1, pp 125–145 | Cite as

Facility location problems with user cooperation

  • Mercedes LandeteEmail author
  • Gilbert Laporte
Original Paper


This paper introduces the concept of cooperative users in facility location problems with a median or a covering objective. Cooperative users can act as intermediate facilities which are more accessible than primary facilities to excentric users. Four versions of location problems with cooperative users are modeled, for all four combinations of median and covering objectives. Several families of valid inequalities are then presented. This is followed by the development of a non-linear model to assess the fair price of cooperation. The results of computational experiments on randomly generated and benchmark instances demonstrate the positive effect of having cooperative users on the solution structure and cost, as well the impact of the valid inequalities on the LP relaxation value and on the CPU time.


Location problems Cooperative users Median objective Covering objective Price of cooperation 



This work was partially funded by the Canadian Natural Sciences and Engineering Research Council under grant 2015-06189 and by Spanish Ministerio de Economía y Competividad (MINECO/FEDER) project MTM-2015-68097(P). This support is gratefully acknowledged. We want to express our deep appreciation to the reviewers for their valuable comments, some of which have lead to significant improvements


  1. Aardal K, Labbé M, Leung J, Queyranne M (1996) On the two-level uncapacitated facility location problem. INFORMS J Comput 8(3):289–301CrossRefGoogle Scholar
  2. Archetti C, Savelsbergh MWP, Speranza MG (2016) The vehicle routing problem with occasional drivers. Eur J Oper Res 254(2):472–480CrossRefGoogle Scholar
  3. Buldeo R, Verlinde H, Merckx J, Macharis C (2017) Crowd logistics: an opportunity for more sustainable urban freight transport? Eur Transp Res Rev 9:39CrossRefGoogle Scholar
  4. Cuda R, Guastaroba G, Speranza MG (2015) A survey on two-echelon routing problems. Comput Oper Res 55:185–199CrossRefGoogle Scholar
  5. Daskin MS, Maass KL (2015) The \(p\)-median problem. In: Laporte G, Nickel S, Saldanha da Gama F (eds) Location science. Springer, BerlinGoogle Scholar
  6. Espejo I, Marín A, Rodríguez-Chía AM (2012) Closest assignment constraints in discrete location problems. Eur J Oper Res 219(1):49–58CrossRefGoogle Scholar
  7. Fernández E, Landete M (2015) Fixed-charge facility location problems. In: Laporte G, Nickel S, Saldanha da Gama F (eds) Location science. Springer, BerlinGoogle Scholar
  8. Fiestras-Janeiro MG, García-Jurado I, Meca A, Mosquera MA (2015) Cooperation on capacitated inventory situations with fixed holding costs. Eur J Oper Res 241:719–726CrossRefGoogle Scholar
  9. García S, Marín A (2015) The covering location problem. In: Laporte G, Nickel S, Saldanha da Gama F (eds) Location science. Springer, BerlinGoogle Scholar
  10. García S, Labbé M, Marín A (2011) Solving large \(p\)-median problems with a radius formulation. INFORMS J Comput 23(4):546–556CrossRefGoogle Scholar
  11. Gendron B, Semet F (2009) Formulations and relaxations for a multi-echelon capacitated location-distribution problem. Comput Oper Res 36:1335–1355CrossRefGoogle Scholar
  12. Gendron B, Khuong P-V, Semet F (2016) A Lagrangian-based branch-and-bound algorithm for the two-level uncapacitated facility location problem with single-assignment constraints. Transp Sci 50(4):1286–1299CrossRefGoogle Scholar
  13. Gendron B, Khuong P-V, Semet F (2017) Comparison of formulations for the two-level uncapacitated facility location problem with single assignment constraints. Comput Oper Res 86:86–93CrossRefGoogle Scholar
  14. Grötschel M, Lovász L, Schrijver A (1988) Geometric algorithms and combinatorial optimization. Springer, BerlinCrossRefGoogle Scholar
  15. Hagtvedt R, Ferguson M, Giffin P, Jones GT, Keskinocak P (2009) Cooperative strategies to reduce ambulance diversion. In: Proceedings of the 2009 Winter Simulation Conference, pp 1861–1874Google Scholar
  16. Kolen A, Tamir A (1990) Covering problems. In: Mirchandani PB, Francis RL (eds) Discrete location theory. Wiley, New YorkGoogle Scholar
  17. Krajewska MA, Kopfer H, Laporte G, Røpke S, Zaccour G (2008) Horizontal cooperation among freight carriers: request allocation and profit sharing. J Oper Res Soc 59:1483–1491CrossRefGoogle Scholar
  18. Marín A (2007) Lower bounds for the two-stage uncapacitated facility location problem. Eur J Oper Res 179:1126–1142CrossRefGoogle Scholar
  19. Marín A, Pelegrín B (1999) Applying Lagrangian relaxation to the resolution of two-stage location problems. Ann Oper Res 86:179–198CrossRefGoogle Scholar
  20. Mercer A, Tao X (1996) Alternative inventory and distribution policies of a food manufacturer. J Oper Res Soc 47(6):755–765CrossRefGoogle Scholar
  21. Ortiz-Astorquiza C, Contreras I, Laporte G (2018) Multi-level facility location problems. Eur J Oper Res 267:791–805CrossRefGoogle Scholar
  22. Paterson C, Kiesmüller G, Teunter R, Glazebrook K (2011) Inventory models with lateral transshipments: a review. Eur J Oper Res 210(2):125–136CrossRefGoogle Scholar
  23. Rancourt M-È, Cordeau J-F, Laporte G, Watkins B (2015) Tactical network planning for food aid distribution in Kenya. Comput Oper Res 56:68–83CrossRefGoogle Scholar
  24. Savelsbergh MWP, Van Woensel T (2016) City logistics: challenges and opportunities. Transp. Sci. 50(2):579–590CrossRefGoogle Scholar
  25. Wagner JL, Falkson LM (1975) The optimal nodal location of public facilities with price-sensitive demand. Geogr Anal 7:69–83CrossRefGoogle Scholar
  26. Walker WE, Chaiken JM, Ignall EJ (eds) (1979) Fire department deployment analysis: a public policy analysis case study. North-Holland, AmsterdamGoogle Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2019

Authors and Affiliations

  1. 1.Departamento de Estadística, Matemáticas e InformáticaInstituto Universitario Centro de Investigación Operativa, Universidad Miguel Hernández de ElcheElcheSpain
  2. 2.HEC MontréalMontréalCanada

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