Conversational optimization and facility-layout planning

Facility-layout problems are well-known members of the class of wicked problems. Not only are these problems computationally intractable, they defy precise formulation which underscores their 'wickedness'. A conversational optimization methodology is developed for solving the facility-layout planning problem, which utilizes a Lagrangean relaxation process to transform the original problem into a simpler combinatorial optimization problem. The original problem is a set-packing problem, whereas the transformed problem is a relaxed assignment problem. Along with the conversational optimization methodology an APL (a programming language) implementation of the process, a detailed example, and additional examples demonstrating the range and flexibility of the conversational models are presented.