Optimization of block layout design problems with unequal areas: A comparison of MILP and MINLP optimization methods

The block layout design problem with unequal areas, which was originally formulated by Armour and Buffa in the early 1960s, is a fundamental optimization problem encountered in many manufacturing and service organizations. In this paper, we present a new modelling framework for effectively finding global optimal solutions for the block layout design problem with unequal areas. The most fundamental aspect of the framework consists of an exact representation of the underlying area restrictions. Our computational results consistently yield optimal solutions on several well-known test problems from the published literature. Furthermore, different mixed-integer linear and mixed-integer nonlinear optimization methods are compared. Our study indicates that the new modeling framework together with simple constraints to avoid symmetric layout solutions can be successfully used to find optimal layout solutions; therefore, seriously challenging other optimization methods on this important class of hard, fundamental problems. The new modeling framework may easily be applied in the context of the process plant layout and piping design problems.