Rectangular Layout Problems with Worst-Case Distance Measures

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Abstract
This paper considers two related problems involving the design of rectangular layouts of m activities. In each of the problems, costs are incurred which are nondecreasing in distance between activities. The distance between two activities is either the worst-case rectilinear distance, or the worst-case Tchebyshev distance. Minisum and minimax layout problems are then considered and solution techniques are provided. The solution techniques demonstrate that both the area (e.g., number of square feet) taken up by the facilities, as well as the relative use of the facilities, must be considered in order to solve the layout problems of interest.