An ϵ-accurate model for optimal unequal-area block layout design

This paper proposes a mixed-integer linear programming model for the block layout design problem with unequal areas that satisfies the area requirements with a given accuracy. The basic aspect of the model consists of an ϵ-accurate representation of the underlying nonconvex and hyperbolic area restrictions using cutting planes. The use of such a representation of the area restrictions allow us to solve several challenging test problems to optimality with a guarantee that the final area of each department is within an ϵ% error of the required area. Numerical results indicate that the proposed model seriously challenges other optimization approaches on this important class of hard, fundamental problems.