Mathematical Optimization Approach for Facility Layout on Several Rows

Miguel F Anjos, Manuel V.c. Vieira

Research output: Contribution to journalArticlepeer-review


The facility layout problem is concerned with nding an arrangement
of non-overlapping indivisible departments within a facility so as to minimize
the total expected ow cost. In this paper we consider the special case
of multi-row layout in which all the departments are to be placed in three or
more rows, and our focus is on, for the rst time, solutions for large instances.
We rst propose a new mixed integer linear programming formulation that
uses continuous variables to represent the departments' location in both x
and y coordinates, where x represents the position of a department within a
row and y represents the row assigned to the department. We prove that this
formulation always achieves an optimal solution with integer values of y, but
it is limited to solving instances with up to 13 departments. This limitation
motivates the application of a two-stage optimization algorithm that combines
two mathematical optimization models by taking the output of the rst-stage
model as the input of the second-stage model. This algorithm is, to the best of
our knowledge, the rst one in the literature reporting solutions for instances
with up to 100 departments.
Original languageEnglish
Number of pages15
JournalOptimization letters
Early online date24 Jul 2020
Publication statusE-pub ahead of print - 24 Jul 2020


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