On the partial order polytope of a digraph
Mathematical Programming: Series A and B
An ε-accurate model for optimal unequal-area block layout design
Computers and Operations Research
An ant algorithm for the single row layout problem in flexible manufacturing systems
Computers and Operations Research
Computers and Operations Research
Computers and Industrial Engineering
Optimal solution for the two-dimensional facility layout problem using a branch-and-bound algorithm
Computers and Industrial Engineering
A new optimization model to support a bottom-up approach to facility design
Computers and Operations Research
Expert Systems with Applications: An International Journal
Parameter setting for clonal selection algorithm in facility layout problems
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
A dual-system variable-grain cooperative coevolutionary algorithm: satellite-module layout design
IEEE Transactions on Evolutionary Computation
Applying the sequence-pair representation to optimal facility layout designs
Operations Research Letters
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The facility layout problem (FLP) is a fundamental optimization problem encountered in many manufacturing and service organizations. Montreuil introduced a mixed integer programming (MIP) model for FLP that has been used as the basis for several rounding heuristics. However, no further attempt has been made to solve this MIP optimally. In fact, though this MIP only has 2n(n-1) 0-1 variables, it is very difficult to solve even for instances with n~5 departments. In this paper we reformulate Montreuil's model by redefining his binary variables and tightening the department area constraints. Based on the acyclic subgraph structure underlying our model, we propose some general classes of valid inequalities. Using these inequalities in a branch-and-bound algorithm, we have been able to moderately increase the range of solvable problems. We are, however, still unable to solve problems large enough to be of practical interest. The disjunctive constraint structure underlying our FLP model is common to several other ordering/arrangement problems; e.g., circuit layout design, multi-dimensional orthogonal packing and multiple resource constrained scheduling problems. Thus, a better understanding of the polyhedral structure of this difficult class of MIPs would be valuable for a number of applications.