A polyhedral study of triplet formulation for single row facility layout problem |
| |
Authors: | Sujeevraja Sanjeevi Kiavash Kianfar |
| |
Affiliation: | Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX 77843-3131, USA |
| |
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 [A.R.S. Amaral, A new lower bound for the single row facility layout problem, 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 |
本文献已被 ScienceDirect 等数据库收录! |