Placement of two finite-size facilities in an existing layout with the rectilinear distance metric
Date, Ketan Hemant
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This work considers the problem of optimal placement of two finite-size rectangular facilities with known dimensions in presence of existing rectangular facilities. We consider three types of facility interactions: first, interaction between the new facilities and existing facilities; second, interaction between pairs of existing facilities; and third, interaction between the two new facilities. All interactions are serviced through a finite number of input/output points located strictly on the boundary of each facility. We assume that all travel occurs according to the rectilinear (or Manhattan) metric and travel through the facilities is not permitted. The objective is to find the placement of the new facilities such that the sum of weighted distances between the interacting facilities is minimized. The simultaneous placement of two new facilities introduces new challenges because the placement of a new facility could change the distances between the existing facilities, the distances between the other new facility and existing facilities, and the distance between the new facilities. To arrive at a solution, we first divide the feasible region into sub-regions in which the objective function is concave and then we prove that the candidates for the optimal placement of the two new facilities can be drawn from the corners of these sub-regions, which are finite in number. Finally, we discuss the solution complexity of our procedure and some additional considerations for its generalization.