Optimizing multi-vehicle inventory routing problem for waste collection with overflow-level-dependent service times in bins

The growth of urbanization leads to an increase in waste generation in cities. One policy adopted by municipalities for waste management is to provide bins for citizens to dispose of their garbage. However, limited resources can make proper waste management difficult and, together with the population’s behavior, lead to undesirable situations, such as the formation of overflows in bins. When this occurs, collection times vary because operators must clean the site using hand tools. In this study, we approach urban waste collection from bins as a Multi-vehicle Inventory Routing Problem, considering the variability in service times due to overflow. We formulate a mixed integer nonlinear programming model, to which we apply linearization techniques to propose two new linear reformulations. These are solved using a branch-and-cut algorithm, aiming to balance economic and environmental costs by minimizing transportation and overflow costs. The models are compared with each other and the best performing one is selected based on preliminary experiments. This model can optimally solve for medium-sized instances, and the results demonstrate the importance of considering variability in service times in overflow bins, as it is a factor that produces changes in the determination of collection routes.