Layout algorithms for single and multiple floor facilities

In this dissertation, the layout problem is considered for both single and multiple floor facilities. Facility layout is an optimization problem concerned with determining an efficient arrangement of unequal-area departments with unspecified shapes, subject to building and departmental area constraints. The efficiency of a layout is generally measured by the cost of moving material between departments which may be located on the same floor or on different floors. In the latter case, the flow is assumed to travel through a lift. Two types of approaches are presented for the facility layout problem: an improvement approach and a construction approach. For the first approach, two algorithms are developed with different search strategies. The first attempts to improve the layout through pairwise department exchanges in a steepest-descent search. The second generates candidate layouts with a generalized exchange routine and employs a simulated-annealing based search. Both algorithms represent the layout of a floor as a one-dimensional sequence of departments, which is mapped into two dimensions via spacefilling curves. The spacefilling curve representation enables the improvement algorithms to consider any area-feasible sequence of departments. In addition, we define a simple measure that limits irregularly-shaped departments. The construction-type algorithm assigns departments to floors optimally with a mathematical program and then determines the layout of each floor concurrently while considering multiple lift locations. The mathematical program is transformed from a quadratic integer-program to a mixed-integer linear program by exploiting the structure of the inter-floor distance function. The above three layout algorithms produce near-optimal solutions for small test problems and lower-cost solutions than those produced by algorithms presented previously in the literature. For multi-floor problems, after the layout of each floor is determined, the lift location-allocation problem is solved with a simulated annealing algorithm which considers the throughput capacity of the lifts. This algorithm produced optimal solutions to all lift location-allocation test problems generated. Furthermore, final solutions determined with the two-stage approach of layout problem followed by lift problem, were very close to optimal solutions which consider both problems simultaneously.