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N. Christofides and J. E. Beasley, “Extensions to a Lagrangean Relaxation Approach for the Capacitated Warehouse Location Problem,” European Journal of Operational Research, Vol. 12, No. 1, 1983, pp. 19-28. doi:10.1016/0377-2217(83)90179-0

has been cited by the following article:

• TITLE: Vertical Decomposition Approach to Solve Single Stage Capacitated Warehouse Location Problem (SSCWLP)

  AUTHORS: Priyanka Verma, R. R. K. Sharma

  KEYWORDS: Single Stage Capacitated Warehouse Location Problem, Linear Programming Relaxation, Lagrangian Relaxation, Vertical Decomposition

  JOURNAL NAME: American Journal of Operations Research, Vol.1 No.3, September 30, 2011

  ABSTRACT: Single Stage Capacitated Warehouse Location Problem (SSCWLP) has been attempted by few researchers in the past. These are Geoffrion and Graves [1], Sharma [2], Sharma [3] and Sharma and Berry [4]. In this paper we give a “vertical decomposition” approach to solve SSCWLP that uses Lagrangian relaxation. This way SSCWLP is broken into two versions of capacitated plant location problem (the CPLP_L and CPLP_R) by relaxing the flow balance constraints. For CPLP_R, we use well known Lagrangian relaxations given in literature (Christofides and Beasley [5] and Nauss [6]); and adopt them suitably for solving CPLP_L. We show theoretically in this paper that SSCWLP can be more efficiently solved by techniques of vertical decomposition developed in this paper than the method available in literature (Sharma and Berry [4]). Encouraging computational study is reported in this paper.