Location Optimization of Urban Drone Delivery Cabinets Considering Three-Level Gradient Noise Penalty

Abstract

This study puts forward a two-stage site selection method for courier cabinets integrated with a three-tier gradient noise penalty, aiming to resolve weak noise-sensitivity constraints and the unbalanced spatial layout of distribution facilities in suburban “drone delivery + self-pickup” systems. In the first stage, researchers use the K-means clustering method to merge massive delivery demand points into weighted demand nodes, and candidate facility locations are generated by gridding the study area. In the second stage, we construct a 0-1 integer programming model whose objective is to maximize weighted coverage after noise penalty adjustment. The established model adopts a three-tier gradient noise penalty function with threshold boundaries of 200 m and 500 m. It also enforces a minimum spacing requirement of 1800 m between any two distribution sites. A greedy algorithm equipped with an exchange operator considering noise penalties is adopted to solve this model. For empirical verification, we select 81,955 valid SF Express orders collected from Fengnan District, Tangshan City as the research case. Raw demand data are simplified into 200 weighted demand nodes, and 177 noise-sensitive points are added into the case analysis. The results indicate that the three schemes attain weighted coverage rates of 75.71%, 80.97%, and 83.55%, respectively. The marginal benefit brought by newly added distribution sites shows a declining trend. Besides, none of the three schemes arrange facilities inside the 200 m high-penalty zone; approximately 77% of selected sites fall within the 500 m non-affected region, and the overlap rate of service coverage circles stays below 15%. In general, the service-oriented scheme with nine distribution sites obtains the best overall performance in terms of coverage, construction cost and noise environmental suitability.