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A Polyhedral Study of Triplet Formulation for Single Row Facility Layout Problem

Sujeevraja Sanjeevi (sujeevraja***at***neo.tamu.edu)
Kiavash Kianfar (kianfar***at***tamu.edu)

Abstract: The Single Row Facility Layout Problem (SRFLP) is the problem of arranging n departments with given lengths on a straight line so as to minimize the total weighted distance between all department pairs. We present a polyhedral study of the triplet formulation of the SRFLP introduced by Amaral [Discrete Applied Mathematics 157(1)(2009)183-190]. For any number of departments n, we prove that the dimension of the triplet polytope is n(n-1)(n-2)/3 (this is also true for the projections of this polytope presented by Amaral). We then prove that several valid inequalities presented by Amaral for this polytope are facet-defining. These results provide theoretical support for the fact that the linear program solved over these valid inequalities gives the optimal solution for all instances studied by Amaral.

Keywords: single row facility layout problem, linear arrangement, polyhedron, valid inequality, facet

Category 1: Integer Programming

Citation: Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX USA 77843-3131, February 2010

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Entry Submitted: 04/01/2010
Entry Accepted: 04/06/2010
Entry Last Modified: 03/13/2011

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