A planar graph cluster‐routing approach for optimizing medical waste collection based on spatial constraint

Abstract

Medical Solid Wastes (MSWs) are major hazardous materials containing harmful biological or chemical compounds that present public and environmental health risks. The collection and transportation of waste are usually informed by optimized work‐balanced routing based on comprehensive spatial data in urban traffic networks, called a Vehicle Routing Problem (VRP). This may be unsuitable for MSWs as their special category means they impose additional complexity. The present article develops a planar graph‐based cluster‐routing approach for the optimal collection of MSWs informed by a Geospatial Information System (GIS). The problem is first formulated as a mixed integer linear program in road network spatial data, in the context of Tehran city. The work has two key aims: (i) to minimize the total routing cost of MSW collection and transfer to waste landfills; (ii) to balance workload across waste collectors. There are three main contributions of the proposed approach: (i) to simplify the large search space area by converting the road network to a planar graph based on graph theory, spatial parameters, and topological rules; (ii) to use a modified K‐means algorithm for clustering; (iii) to consider average traffic impacts in the clustering stage and momentary traffic in the route planning stage. A planar graph extraction procedure is applied to capture the network sketch (i.e., a directed graph) from the traffic roadway network. An iterative cluster‐first‐route‐second heuristic is employed to solve the proposed routing problem. This heuristic customizes a K‐means algorithm to determine the optimal number and size of clusters (i.e., routes). A Traveling Salesman Problem (TSP) algorithm is applied to regulate the optimal sequence of visits to medical centers. The experimental results show improvements in balancing collectors' workload (i.e., ~4 min reduction in the standard deviation of average travel time) with reductions in travel time (i.e., an average ~1 h for the entire fleet and ~4 min per route). These findings confirm that the proposed methodology can be considered as an approach for optimizing waste collection routes.