CMA member Manuel V. C. Vieira wrote a book published by Springer, “Facility Layout“.

Abstract:

A facility, in the general sense, is a building where people come together for a specific purpose. Activities taking place in a facility normally also  require the presence and use of various items of equipment (furniture, machines, materials, etc.). A well-managed facility is a means to achieve higher productivity. This motivates interest in identifying and implementing optimal decisions for locating, designing, and building facilities.  

This book is concerned with mathematical optimization approaches for facility layout, which is one of the fundamental aspects of facility design. The typical objective is to minimize the total distance travelled by people and materials between departments, in order to maximize the efficiency of the operations in the facility. This distance can be calculated using information about the range and frequency of the activities  that will be carried out: from a functional point of view, it is possible to determine an optimal layout based solely on the walking distances and traffic densities. The purpose of a facility layout algorithm is to compute such an optimal layout for a given instance of the problem or, alternatively, to provide a competitive layout, ideally with a guarantee that it is close to optimality.

In this book we limit our attention to approaches based on mathematical optimization. We consider both exact methods and heuristics (sometimes called matheuristics) that make use of mathematical optimization approximations and/or relaxations. Specifically, we consider models based on integer linear programming, mixed-integer linear programming, semidefinite programming and nonlinear programming. We also include a variety of examples, often with real data, to illustrate the range of applications of facility layout.