Decomposition Solution Algorithms for the Multi-floor Facility Layout Problem with Elevators

In this paper, several alternative formulations for the multi-floor facility layout problem are presented. Elevators handle the material transport between different floors. Elevators are allowed to service either all floors or a contiguous set of floors. In this formulation, elevators can be located anywhere within the floors provided they do not overlap with departments. The departments and floors are modeled as rectangular shapes and the floor projections on the ground floor are nested starting from the ground floor to the top floor. The formulations yield large mixed-integer programming problems. We will report on the results of the numerical experiment to solve these problems with a MIP solver. We compare the performance of the monolithic and a hierarchical decomposition algorithm. In the hierarchical algorithm, the first phase assigns department to floors. The second phase determines the locations of elevators, the floors serviced by each elevator, and the location of departments in the floors.