Facility placement with sub-aisle design in an existing layout

In this paper, we consider the integration of facility placement in an existing layout and the configuration of one or two connecting sub-aisles. This is relevant, for example, when placing a new machine/department on a shop floor with existing machines/departments and an existing aisle structure. Our work is motivated by the work of Savas et al. [Savas, S., Batta, R., Nagi, R., 2002. Finite-size facility placement in the presence of barriers to rectilinear travel. Operations Research 50 (6), 1018-1031], that considered the optimal planar placement of a finite-size facility in the presence of existing facilities. Our work differs from theirs in that we consider material handling to be restricted to the aisle structure. We do not allow the newly placed facility to overlap with existing facilities or with the aisle structure. Facilities are rectangular and travel is limited to new or existing aisles. We show that there are a finite number of candidate placements for the new facility. Algorithms are developed to find the optimal placement and the corresponding configurations for the sub-aisles. Complexity of the solution method is analyzed. Also, a numerical example is provided to explore the impact of the number of sub-aisles added.