A Fuzzy Cost Optimization Approach in Smart Waste Collection FM/FM/1 Queueing System with Hexagonal Numbers

This study presents a novel approach for managing parameter uncertainty in FM/FM/1 queueing systems through cost optimization using six-point hexagonal fuzzy numbers. By modeling arrival rates, service costs, and waiting costs as hexagonal fuzzy numbers, the proposed method offers a more precise and realistic representation of uncertainty compared to traditional fuzzy models. A unified framework is developed to determine optimal service rates and total costs in both crisp and fuzzy environments, with defuzzification performed via the signed distance method. To demonstrate the practical relevance, a case study on smart waste collection in urban infrastructure is explored. In this scenario, sensor-equipped garbage bins deployed across city zones monitor fill levels and generate service requests upon reaching capacity. The variability in waste accumulation and collection conditions is effectively captured using fuzzy parameters. Numerical and graphical analyses confirm the model’s ability to optimize operations under uncertainty, making it a valuable tool for sustainable and efficient urban service management.