Discretized cell modeling for optimal facility layout plans of unequal and irregular facilities

Facility layout design is an essential planning task to resolve potential spatial conflicts and overlapping during practical operations. A discretized cell optimization model is developed to optimize site space usages. Site areas and facilities are represented by small unit cells to effectively model irregularities, and the availability of unit cells for use in a facility setup is modeled by binary-type variables. With size and shape requirements through linear constraints, the site layout design can be formulated as a binary mixed integer-linear programming (BMILP) problem to allocate different facilities onto different site available areas in optimal shapes and locations. Total material transportation costs across facilities are optimized subject to various design constraints ensuring safety, homogenous facility setups, physical size, and orientation requirements. The proposed cell model is verified by comparing optimization results with results obtained by conventional point notation methods. A standard branch-and-bound algorithm is applied to solve a global optimal solution, and the numerical example is optimized for illustrating the very different optimized layout plan in terms of facility locations, positions of entry and exit points, shapes, and orientations of different facilities.