Machine layout problem in flexible manufacturing systems
Operations Research
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
An ant algorithm for the single row layout problem in flexible manufacturing systems
Computers and Operations Research
A new lower bound for the single row facility layout problem
Discrete Applied Mathematics
An Exact Approach to the One-Dimensional Facility Layout Problem
Operations Research
Provably near-optimal solutions for very large single-row facility layout problems
Optimization Methods & Software - GLOBAL OPTIMIZATION
A computational study and survey of methods for the single-row facility layout problem
Computational Optimization and Applications
A scatter search algorithm for the single row facility layout problem
Journal of Heuristics
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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.