Optimization of Waste Management Systems Using Graph Theory: A Case Study of Calabar Metropolis

Abstract

The increasing generation of municipal solid waste in Calabar Metropolis, Cross River State, Nigeria, has created challenges for efficient waste collection, transportation, and disposal. This study applied graph theory and vehicle routing principles to develop an optimized framework for municipal solid waste collection, with the Lemna dumpsite designated as the central disposal node. Global Positioning System (GPS) coordinates were obtained for 70 waste collection stations across Calabar Municipality and Calabar South. The collection network was represented as a weighted graph, with nodes representing collection stations and the dumpsite, and edge weights representing travel distances. Eight collection routes were proposed to organize waste collection and facilitate transportation to the dumpsite. Statistical analysis of the reported route-level distance values revealed a mean of 3.65 km, a median of 3.41 km, a minimum of 1.71 km, and a maximum of 6.53 km. The standard deviation was 1.51 km, while the coefficient of variation as 41.37%, indicating considerable variation in the reported distances across the routes. The proposed routes accounted for 65 of the 70 identified collection stations, representing 92.86% coverage, while five stations remained unassigned. These findings demonstrate the potential of graph-based modelling to support the spatial organization of waste collection activities and identify areas requiring further routing refinement. However, reductions in total travel distance, fuel consumption, and operational costs could not be statistically established because complete route-loop distances and comparable baseline measurements were unavailable. The study recommends incorporating all identified stations, validating road-network distances, and considering vehicle capacity, waste generation, and operating conditions in subsequent optimization. The proposed framework provides a foundation for more systematic and data-driven municipal solid waste collection planning in Calabar Metropolis.