Stochastic and Correlated Waste Collection Problem with Time Windows: A Simheuristic Approach

Urban waste collection is hindered by uncertainties and correlations in arc travel times and node waste demands, impacting efficiency and reliability. This study introduces the SCWCPTW model, a variant of SWCP, which treats these variables as correlated random variables. It uniquely accounts for correlations across multiple stochastic components, unlike previous studies that focused on single-component correlations. It incorporates covariance structures into recourse actions by applying proportional penalties to overload and time window violations. A simheuristic combining SA, LNS, and MC is developed to solve the model. Simulation results show that higher variability in stochastic components slows convergence and increases uncertainty, reflecting a more realistic nature in practice. Computational results on modified Solomon benchmarks show that, compared to the deterministic solution (DS), the uncorrelated solution (USS) showed a 6.89% higher cost and 3.73% higher demand, while the correlated solution (CSS) nearly matched DS with only a 0.001% cost difference and a 0.05% demand decrease while achieving higher reliability (0.99). Furthermore, the CSS had lower penalty costs, lower objective costs, and greater reliability (0.99) compared to USS (0.96) when analysed with correlation strength. This indicates that modelling correlations improves cost efficiency and operational robustness without significant computational overhead. Future research directions could extend the proportional penalty approaches to more dynamic penalty structures. Furthermore, the SCWPTW model could be extended to include correlations between travel times and waste demands.