Skip to main content
Log in

Location of a distribution center for a perishable product

  • Original Article
  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

A model that combines an inventory and location decision is presented, analyzed and solved. In particular, we consider a single distribution center location that serves a finite number of sales outlets for a perishable product. The total cost to be minimized, consists of the transportation costs from the distribution center to the sales outlets as well as the inventory related costs at the sales outlets. The location of the distribution center affects the inventory policy. Very efficient solution approaches for the location problem in a planar environment are developed. Computational experiments demonstrate the efficiency of the proposed solution approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Notes

  1. We thank Arie Tamir for turning our attention to this proof.

  2. We thank Atsuo Suzuki for his Fortran program that finds the triangulation based on Sugihara and Iri (1994) subroutines first developed in Ohya et al. (1984).

References

  • Al-Khayyal F, Tuy H, Zhou F (2002) Large-scale single facility continuous location by D.C. optimization. Optimization 51:271–292

    Article  MathSciNet  MATH  Google Scholar 

  • Ballou RH (2003) Business logistics management, 5th edn. Prentice Hall Inc., New Jersey

    Google Scholar 

  • Carrizosa E (2001) An optimal bound for D.C. programs with convex constraints. Math Methods Oper Res 54:47–51

    Article  MathSciNet  MATH  Google Scholar 

  • Cooper L (1963) Location-allocation problems. Oper Res 11:331–343

    Article  MATH  Google Scholar 

  • Cooper L (1964) Heuristic methods for location-allocation problems. SIAM Rev 6:37–53

    Article  MathSciNet  MATH  Google Scholar 

  • Daskin MS, Coullard C, Shen Z-JM (2002) An inventory-location model: formulation, solution algorithm and computational results. Ann Oper Res 110:83–106

    Article  MathSciNet  MATH  Google Scholar 

  • Drezner T, Drezner Z (2007) Equity models in planar location. Comput Manag Sci 4:1–16

    Article  MathSciNet  MATH  Google Scholar 

  • Drezner T, Drezner Z, Guyse J (2009) Equitable service by a facility: minimizing the Gini coefficient. Comput Oper Res 36:3240–3246

    Article  MATH  Google Scholar 

  • Drezner Z (2007) A general global optimization approach for solving location problems in the plane. J Glob Optim 37:305–319

    Article  MathSciNet  MATH  Google Scholar 

  • Drezner Z (2009) On the convergence of the generalized Weiszfeld algorithm. Ann Oper Res 167:327–336

    Article  MathSciNet  Google Scholar 

  • Drezner Z, Drezner T (1998) Applied location theory models. In: Marcoulides GA (ed) Modern methods for business research. Lawrence Erlbaum Associates, Mahwah, NJ, pp 79–120

    Google Scholar 

  • Drezner Z, Suzuki A (2004) The big triangle small triangle method for the solution of non-convex facility location problems. Oper Res 52:128–135

    Article  MATH  Google Scholar 

  • Drezner Z, Scott CH, Song J-S (2003) The central warehouse location problem revisited. IMA J Manag Math 14:321–336

    Article  MathSciNet  MATH  Google Scholar 

  • Horst R, Thoai NV (1999) DC programming: overview. J Optim Theory Appl 103:1–43

    Article  MathSciNet  Google Scholar 

  • Lee DT, Schachter BJ (1980) Two algorithms for constructing a Delaunay triangulation. Int J Parallel Program 9(3):219–242

    MathSciNet  MATH  Google Scholar 

  • Maranas CD, Floudas CA (1993) A global optimization method for Weber’s problem with attraction and repulsion. In: Hager WW, Hearn DW, Pardalos PM (eds) Large scale optimization: state of the art. Kluwer, Dordrecht, pp 259–293

    Google Scholar 

  • Nahmias S (2008) Production and operations management, 6th edn. McGraw Hill/Irwin, Chicago

    Google Scholar 

  • Ohya T, Iri M, Murota K (1984) Improvements of the incremental method of the Voronoi diagram with computational comparison of various algorithms. J Oper Res Soc Jpn 27:306–337

    MathSciNet  MATH  Google Scholar 

  • Scott CH, Song J-S (1996) On the location of a central warehouse. Stud Locat Anal 9:123–126 (ISOLDE VII Proceedings)

    Google Scholar 

  • Scwartz LB (1981) Physical distribution: the analysis of inventory and location. AIIE Trans 13:138–151

    Article  Google Scholar 

  • Shen Z-JM, Coullard C, Daskin MS (2003) A joint location-inventory model. Transp Sci 37:40–55

    Article  Google Scholar 

  • Sugihara K, Iri M (1994) A robust topology-oriented incremental algorithm for Voronoi diagram. Int J Comput Geom Appl 4:179–228

    Article  MathSciNet  MATH  Google Scholar 

  • Tuy H, Al-Khayyal F, Zhou F (1995) A D.C. optimization method for single facility location problems. J Glob Optim 7:209–227

    Article  MathSciNet  MATH  Google Scholar 

  • Weiszfeld E (1936) Sur le point pour lequel la somme des distances de n points donnes est minimum. Tohoku Math J 43:355–386

    Google Scholar 

  • Weiszfeld E, Plastria F (2009) On the point for which the sum of the distances to n given points is minimum. Ann Oper Res 167:7–41 (English Translation of Weiszfeld (1936))

    Article  MathSciNet  Google Scholar 

  • Wendell RE, Hurter AP (1973) Location theory, dominance and convexity. Oper Res 21:314–320

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zvi Drezner.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Drezner, Z., Scott, C.H. Location of a distribution center for a perishable product. Math Meth Oper Res 78, 301–314 (2013). https://doi.org/10.1007/s00186-013-0445-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00186-013-0445-6

Keywords

Navigation