(with Tony Vannelli, Univ. of Waterloo)
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Title: A New Mathematical Programming Framework for Facility Layout Design

We present a new framework for efficiently finding competitive solutions
for the facility layout problem. This framework is based on the
combination of two new mathematical programming models. The first model is
a convex relaxation of the layout problem and is intended to find good
starting points for the iterative algorithm used to solve the second
model. The second model is an exact formulation of the facility layout
problem as a non-convex mathematical program with equilibrium constraints
(MPEC). Aspect ratio constraints, which are frequently used in facility
layout methods to restrict the occurrence of overly long and narrow
departments in the computed layouts, are easily incorporated into this new
framework. We present computational results showing that both models,
and hence the complete framework, can be solved efficiently using widely
available optimization software. This important feature of the new
framework implies that it can be used to find competitive layouts with
relatively little computational effort. This is advantageous for a user
who wishes to consider several competitive layouts rather than simply
using the mathematically optimal layout.

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