A hybrid approach using deep clustering and Lagrangian relaxation for sustainable waste logistics

Optimizing solid waste management (SWM) is essential for ensuring a sustainable and healthy environment in a city. This study considers a two-echelon solid waste logistics system (2E-SWLS) in a metropolitan city with a fleet of capacitated heterogeneous vehicles. The problem consists of waste collection sites, transfer stations acting as intermediate facilities and dumping yards. The objective is to identify the best locations for transfer stations and optimize the logistics system by minimizing total cost. The problem is formulated as a Mixed Integer Linear Programming (MILP) model. To address large-scale city network complexities, we propose a Cluster-Fix-Optimize Matheuristic (C-F-OM), as the MILP model fails to provide a solution within the given CPU time. This method involves a deep learning-based clustering of sites, determining the transfer station location within each cluster and optimizing the associated operational and logistic decisions while serving as a benchmark solution to the problem. Additionally, we introduce a Lagrangian Relaxation-Fix-Optimize Matheuristic (LR-F-OM) to determine a lower bound for 2E-SWLS. The effectiveness of this lower bound is compared with that of the conventional subgradient method. The upper bound derived from LR-F-OM outperforms the C-F-OM solution and promises significant savings of approximately 50%, when compared to the existing solution approaches in a case study in India by providing insights on facility and logistical configurations for improving the operational efficiency. The study also provides managerial insights on factors such as vehicle fleet heterogeneity, transfer station capacity, demand variations at waste collection sites, and vehicle operational costs on total cost.