The multidimensional facility layout problem: A hierarchical model and solution method

The facility layout problem deals with the determination of the optimal locations of departments (stations, items, activities, etc.) within a facility, optimizing a given objective that depends on the relative position of the departments. The facility can be a single-floor building, a multi-story one, or it can comprise of a number of single or multi-story buildings within a given complex. The solution procedures have evolved from using iconic models and subjective rules of thumb to complex mathematical programming models. Most of the existing procedures can only solve for the placement of departments in a single-floor facility. The problem of locating departments in a multi-story building is more complex and requires study and a new approach for its solution.; In this dissertation, we provide a hierarchical framework for the solution of the multidimensional layout problem. Assuming that departments that interact heavily should be located on one floor, the problem is decomposed into smaller subproblems by finding groups of departments that should be located on each floor. A dynamic programming based network-partitioning procedure is presented which partitions the original problem into k subproblems (where k is the number of groups desired) such that the resulting total interaction cost between departments of different groups is minimized.; We next develop a heuristic which provides a number of solutions to the planar layout problem, which are "almost equally good" in terms of interaction costs, to place departments in a partitioned group. Most of the existing heuristics attempt to find one good solution based on a quantifiable objective function. In practice, there may be several subjective and non-quantifiable objectives that may have to be considered before a final layout is developed. Therefore, it may be important to provide the layout designer several good solutions with regard to the given objective function.; Multidimensional layout design also involves the placement of connecting points (e.g., elevators, stairwells) if their locations are not already known. We may also need to allocate departments which interact with departments in other groups to the located connecting points. Based on the number and knowledge of the location of the connecting points, we develop a number of procedures for this location/allocation problem.; Finally, using the various heuristics and procedures for the relevant subproblems, we present an overall solution framework for the multidimensional layout problem. We provide extensive empirical evaluation of this framework and our heuristics by comparing how these perform with how existing methods (for planar problem) may perform. The empirical evaluations show that the proposed procedures do perform well and can provide a number of different layouts that are quite "good".