North Carolina’s Certificate of Need legislation is intended to limit unnecessary growth in the number of acute-care beds throughout the state. In contrast to the current method of computing bed needs based on existing administrative units (counties), we estimate the service area of each acute-care facility using Voronoi diagrams such that the maximum distance from any point in the region to the nearest acute-care facility is minimized. The population in the service area is then used to determine the appropriate bed capacity for the hospital serving that region. The approach is applied to the problem of determining the appropriate number of acute-care beds for each hospital in the state. The discrepancies between the existing hospital sizes and the needed acute-care beds indicate areas where geographical inequities may need attention.