The role of compactness distribution on the development of regionalized waste management systems

Abstract

This study develops and investigates new optimization metrics and the resulting compactness of waste management regions developed for Saskatchewan, Canada. Centroidal Voronoi Tessellation is used to develop waste management regions, and two new optimization metrics are proposed, accounting for the percent spread of landfills, populated places, and roads, as well as the sub-region areas. Federal electoral districts optimized efficiently, requiring only 3 iterations. The optimized percent standard deviation (SD) ranged between 2.64 and 3.17. Constituencies realized a larger reduction in percent SD, but took a maximum of 15 iterations. When accounting for the area of each sub-region constituencies appeared to optimize more efficiently. As a result, the average, median, and distribution of the isoperimetric quotient were used to further evaluate the resulting tessellations. The SD of the isoperimetric quotient was reduced by 56.5% and 55.9% for federal electoral districts and constituencies, respectively. This reduction is similar for both input tessellations even though 7.3 times more iterations were required from optimization of constituencies. However, constituencies had, on average, a higher maximum compactness (0.8344) compared to federal electoral districts (0.7640). The results suggest that the number of sub-regions and area are important factors in spatial optimization of waste management regions.