A Capacitated Facility Allocation Approach Based on Residue for Constrained Regions

  • Monika ManglaEmail author
  • Deepak Garg
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1059)


Allocation of services has observed widespread applications in real life. Therefore, it has gained comprehensive interest of researchers in location modeling. In this paper, the authors aim to allocate \( p \) capacitated facilities to \( n \) demand nodes in constrained demand plane. The allocation is aimed to minimize the total transportation cost. The authors consider continuous demand plane, which is constrained by the presence of barriers. Here, the authors present a residue-based capacitated facilities allocation (RBCFA) approach for allocation of capacitated facilities. Finally, an illustration of RBCFA is presented in order to demonstrate its execution. Authors also perform tests to validate the solution, and the tests yield that suggested approach outperforms traditional approach of allocation. It is observed that although the achievement by RBCFA is not significant for few resources, achievement is significant as the number of resources rises.


Facility location Barriers Visibility graph Constrained demand plane Convex hull 


  1. 1.
    Rohaninejad M, Navidi H, Nouri BV, Kamranrad R (2017) A new approach to cooperative competition in facility location problems: mathematical formulations and an approximation algorithm. Comput Oper Res 83:45–53MathSciNetCrossRefGoogle Scholar
  2. 2.
    Toro EM, Franco JF, Echeverri MG, Guimarães FG (2017) A multi-objective model for the green capacitated location-routing problem considering environmental impact. Comput Ind Eng 110:114–125CrossRefGoogle Scholar
  3. 3.
    Hajipour V, Fattahi P, Tavana M, Di Caprio D (2016) Multi-objective multi-layer congested facility location-allocation problem optimization with Pareto-based meta-heuristics. Appl Math Model 40(7–8):4948–4969MathSciNetCrossRefGoogle Scholar
  4. 4.
    Davoodi M, Mohades A, Rezaei J (2011) Solving the constrained p-center problem using heuristic algorithms. Appl Soft Comput 11(4):3321–3328CrossRefGoogle Scholar
  5. 5.
    Aneja YP, Parlar M (1994) Algorithms for Weber facility location in the presence of forbidden regions and/or barriers to travel. Transp. Sci. 28(1):70–76CrossRefGoogle Scholar
  6. 6.
    Butt SE, Cavalier TM (1996) An efficient algorithm for facility location in the presence of forbidden regions. Eur J Oper Res 90(1):56–70CrossRefGoogle Scholar
  7. 7.
    Pfeiffer B, Klamroth K (2008) A unified model for Weber problems with continuous and network distances. Comput Oper Res 35(2):312–326MathSciNetCrossRefGoogle Scholar
  8. 8.
    Oncan T (2013) Heuristics for the single source capacitated multi-facility Weber problem. Comput Ind Eng 64(4):959–971MathSciNetCrossRefGoogle Scholar
  9. 9.
    Quevedo-Orozco, DR, Ríos-Mercado RZ (2015) Improving the quality of heuristic solutions for the capacitated vertex p-center problem through iterated greedy local search with variable neighborhood descent. Comput Oper Res 62:133–144MathSciNetCrossRefGoogle Scholar
  10. 10.
    Canbolat MS, Wesolowsky GO (2012) A planar single facility location and border crossing problem. Comput Oper Res 39(12):3156–3165MathSciNetCrossRefGoogle Scholar
  11. 11.
    Sarkar A, Batta R, Nagi R (2007) Placing a finite size facility with a center objective on a rectangular plane with barriers. Eur J Oper Res 179(3):1160–1176CrossRefGoogle Scholar
  12. 12.
    McGarvey RG, Cavalier TM (2003) A global optimal approach to facility location in the presence of forbidden regions. Comput Ind Eng 45(1):1–15CrossRefGoogle Scholar
  13. 13.
    Katz IN, Cooper L (1981) Facility location in the presence of forbidden regions, I: Formulation and the case of Euclidean distance with one forbidden circle. Eur J Oper Res 6(2):166–173MathSciNetCrossRefGoogle Scholar
  14. 14.
    Larson RC, Sadiq G (1983) Facility locations with the Manhattan metric in the presence of barriers to travel. Oper Res 31(4):652–669MathSciNetCrossRefGoogle Scholar
  15. 15.
    Batta R, Ghose A, Palekar US (1989) Locating facilities on the Manhattan metric with arbitrarily shaped barriers and convex forbidden regions. Transp. Sci. 23(1):26–36MathSciNetCrossRefGoogle Scholar
  16. 16.
    Mirzapour SA, Wong KY, Govindan K (2013) A capacitated location-allocation model for flood disaster service operations with border crossing passages and probabilistic demand locations. Math Probl Eng 2013Google Scholar
  17. 17.
    Klamroth K (2001) Planar Weber location problems with line barriers. Optimization 49(5–6):517–527MathSciNetCrossRefGoogle Scholar
  18. 18.
    Shiripour S, Amiri-Aref M, Mahdavi I (2011) The capacitated location-allocation problem in the presence of k connections. Appl. Math. 2(8):947MathSciNetCrossRefGoogle Scholar
  19. 19.
    Shiripour S, Mahdavi I, Amiri-Aref M, Mohammadnia-Otaghsara M, Mahdavi-Amiri N (2012) Multi-facility location problems in the presence of a probabilistic line barrier: a mixed integer quadratic programming model. Int J Prod Res 50(15):3988–4008CrossRefGoogle Scholar
  20. 20.
    Akyüz MH (2017) The capacitated multi-facility weber problem with polyhedral barriers: efficient heuristic methods. Comput Ind Eng 113:221–240CrossRefGoogle Scholar
  21. 21.
    Canbolat MS, Wesolowsky GO (2012) On the use of the Varignon frame for single facility Weber problems in the presence of convex barriers. Eur J Oper Res 217(2):241–247MathSciNetCrossRefGoogle Scholar
  22. 22.
    Hamacher HW, Klamroth K (2000) Planar Weber location problems with barriers and block norms. Ann Oper Res 96:191–208MathSciNetCrossRefGoogle Scholar
  23. 23.
    Butt SE (1995) Facility location in the presence of forbidden regions and congested regionsGoogle Scholar
  24. 24.
    Klamroth K (2002) Planar Weber location problems with line barriers. Optimization 49(5–6):517–527MathSciNetzbMATHGoogle Scholar
  25. 25.
    Hamacher HW Klamroth K (1999) Planar location problems with barriers under polyhedral gaugesGoogle Scholar
  26. 26.
    Ghosh S, Mount D (1991) An output-sensitive algorithm for computing visibility graphs. SIAM J Comput 20(5):888–910MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.CSEDThapar UniversityPatialaIndia
  2. 2.Faculty of CSEDLTCoENavi MumbaiIndia
  3. 3.CSEDBennett UniversityGreater NoidaIndia

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