Hierarchical and Nesting Approaches for the Facility Layout Problem

Abstract

The Facility Layout Problem (FLP) seeks to determine the dimensions, coordinates and arrangement of rectangular departments within a given facility. The goal is to minimize the cost of inter-department flow. It has several real-world applications, including the design of manufacturing and warehousing facilities and electronic chips. Despite being studied for several decades, the FLP is still very difficult to solve for facilities with thirty or more departments. Thus, many heuristic approaches have been developed to solve the problem in a reasonable time. One such approach tackles the problem in two stages. In the first, some decision, usually the relative positioning of the departments, is fixed. In the second, an easier restricted problem is solved.

This thesis explores hierarchical and nesting approaches for the FLP in an attempt to leverage the fact that smaller instances of the FLP can be solved to optimality relatively quickly. The goal is to find ways in which the FLP can be decomposed into several smaller problems and recombined to form a high-quality solution to the original problem.

Hierarchical approaches use clustering or related methods to generate a tree where the leaves are the original departments and the root is the facility. The intermediate nodes are super-departments within an overall layout. A new hierarchical approach for the FLP is presented which performs layouts down this tree in a manner that controls dead-space and generates high-quality solutions. The approach provides solutions competitive with the best-known solutions on benchmark instances from the literature, with up to 8% improvement.

The success of the hierarchical approach provided the motivation for a new formulation that nests departments within super-departments. The resulting formulation is even more difficult to solve directly than the original FLP; however, it is suitable for a two-stage solution approach. The first stage determines the assignment of departments to super-departments and the relative positioning of the super-departments. In the second stage, the remainder of the formulation is solved. The approach is found to provide better solutions than the hierarchical approach. Solutions are found with up to 14% improvement over the best-known solutions from the literature.