Abstract
Unequal distribution of contraceptive supplies (Alokon) relative to the target population remains a persistent challenge in family planning programs, particularly in regions with high demographic heterogeneity. Evaluation based on absolute distribution values generates proportional bias, as larger-population areas automatically receive higher volumes without accounting for the proportional needs of the Reproductive Age Couples (PUS) population. This study proposes a ratio-based approach — dividing total Alokon distributed by the number of PUS — as the primary clustering variable to enable proportional comparison and reduce population-scale bias across 33 districts and cities in North Sumatra Province. Two algorithms, K-Means and K-Medoids based on Partitioning Around Medoids (PAM), were comparatively evaluated using Silhouette Score as the evaluation metric. The optimal number of clusters (K = 3) was determined through a combination of the Elbow Method — which identified a 75.12% WCSS reduction from K = 2 to K = 3 — and Silhouette Score validation. Results show that both algorithms produced identical cluster compositions: 16 districts in the low-distribution group (48.5%; = 0.1687), 13 districts in the moderate group (39.4%; = 0.3117), and 4 districts in the high group (12.1%; = 0.6077), with equal average Silhouette Scores of = 0.6998 (reasonable structure). Densely populated areas such as Medan City and Deli Serdang — despite receiving the highest absolute distribution volumes — were classified in the low group when measured proportionally, demonstrating the superiority of the ratio-based approach. To the best of the authors' knowledge, this study is the first to apply comparative clustering on Alokon distribution using a proportional ratio framework in North Sumatra Province, providing empirical evidence on algorithm performance in normalized health service distribution data.
