Engineering Optimization

41Case Study 6: Area Coverage

41.1 Description and Analysis

Consider a square parking lot. Where should one place overhead street lamps to provide light to best cover the area? Or overhead cameras to best monitor the area. If there are five devices, the location pattern could be a pentagon, or that of the five patterns on a die.

The objective could be to cover the area for customer visibility. But it could alternately be to observe the perimeter for security.

The intensity of the lamplight to the surface drops as the square of distance to the surface. From a pole h distance high, with a light directed vertically down in a right circular cone, the distance from the lamp to any point on the ground at radius r from the pole is , and a simple model of light intensity at any point on the ground from the ith pole is . Here, the radial distance from the ith pole to any position (x, y) is , making . This supposes that all poles are of equal height and all lamps of equal intensity, shining the same amount of light in downward directions. To calculate coverage at any particular location on the ...