Location Allocation Problem

  • Zeinab Azarmand
  • Ensiyeh Neishabouri
Part of the Contributions to Management Science book series (MANAGEMENT SC.)


Location-allocation (LA) problem is to locate a set of new facilities such that the transportation cost from facilities to customers is minimized and an optimal number of facilities have to be placed in an area of interest in order to satisfy the customer demand.

This problem occursin many practical settings where facilities provide homogeneous services such as the determination and location of warehouses, distribution centers, communication centers and production facilities.

Since LA problem was proposed by Cooper (1963) and spread to a weighted network by Hakimi (1964), network LA problem and many models were presented by Badri (1999).

For solving these models, numerous algorithms have been designed, involving branch-and-bound algorithms (Kuenne and Soland 1972), simulated annealing (Murray and Church 1996) and Tabu search (Brimberg and Mladenovic 1996; Ohlemüller 1997) and P-Median plus Weber (Hansen et al. 1998). Some hybrid algorithms have been also suggested, such as the one based on simulated annealing and random descent method (Ernst and Krishnamoorthy 1999) and the one utilizing the Lagrange relaxation method and genetic algorithm (Gong et al. 1997). Brimberg et al. (2000) improved present algorithms and proposed variable neighborhood search, which is proved to obtain the best results when the number of facilities to locate is large.


Variable Neighborhood Search Perturbation Scheme Organ Procurement Organization Transplant System Lagrange Relaxation Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Badri MA (1999) Combining the analytic hierarchy process and goal programming for global facility location-allocation problem. Int J Prod Econ 62:237–248CrossRefGoogle Scholar
  2. Brimberg J, Mladenovic N (1996) Solving the continuous Location-Allocation problem with tabu search. Stud Locational Ann 8:23–32Google Scholar
  3. Brimberg J, Hansen P, Mladenovic N, Taillard ED (2000) Improvements and comparison of heuristics for solving the uncapacitated multi source Weber problem. Oper Res 48:444–460CrossRefGoogle Scholar
  4. Bruni M, Conforti D, Sicilia N, Trotta S (2006) A new organ transplantation Location-Allocation policy: A case study of Italy. Health Care Manage Sci 9:125–142CrossRefGoogle Scholar
  5. Cooper L (1963) Location-Allocation problems. Oper Res 11(3):331–343CrossRefGoogle Scholar
  6. Cooper L (1964) Heuristic methods for location-allocation problems. SIAM Rev 6(1):37–53CrossRefGoogle Scholar
  7. Eilon S, Watson-Gandy CDT, Christofides N (1971) Distribution Management. New York, HafnerGoogle Scholar
  8. Ernst AT, Krishnamoorthy M (1999) Solution algorithms for the capacitated single allocation hub location problem. Ann Oper Res 86:141–159CrossRefGoogle Scholar
  9. Gong D, Gen M, Yamazaki G, Xu W (1997) Hybrid evolutionary method for capacitated location-allocation problem. Comput Ind Eng 33:577–580CrossRefGoogle Scholar
  10. Hakimi S (1964) Optimum distribution of switching centers in a communication network and some related graph theoretic problems. Oper Res 13:462–475CrossRefGoogle Scholar
  11. Hansen P, Jaumard B, Taillard E (1998) Heuristic solution of the multi source Weber problem as a p-median problem. Oper Res Lett 22:55–62CrossRefGoogle Scholar
  12. Henrik J, Robert FL (1982) Properties and solution methods for large location-allocation problems. J Oper Res Soc 33(5):443–452Google Scholar
  13. Kuenne RE, Soland RM (1972) Exact and approximate solutions to the multi source Weber problem. Math Program 3:193–209CrossRefGoogle Scholar
  14. Louwers D, Kip BJ, Peters E, Souren F, Flapper SDP (1999) A facility location-allocation model for reusing carpet materials. Comput Ind Eng 36:855–869CrossRefGoogle Scholar
  15. Murray AT, Church RL (1996) Applying simulated annealing to location-planning models. J Heuristics 2:31–53CrossRefGoogle Scholar
  16. Ohlemüller M (1997) Tabu search for large location-allocation problems. J Oper Res Soc 48(7):745–750Google Scholar
  17. Scaparra MP, Scutellà MG (2001) Facilities, locations, customers: Building blocks of location models: A survey. Technical report TR-01–18, Computer Science Department, University of Pisa, ItalyGoogle Scholar
  18. Salhi S, Gamal MDH (2003) A Genetic algorithm based approach for the uncapacitated continuous location–allocation problem. Ann Oper Res 123:203–222CrossRefGoogle Scholar
  19. Zhou J, Liu B (2003) New stochastic models for capacitated location-allocation problem. Comput Ind Eng 45:111–125CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Industrial EngineeringAmirkabir University of TechnologyTehranIran

Personalised recommendations