The waste collection vehicle routing problem is an evolving variant of the vehicle routing problem that could be used to resolve issues that occur while transporting waste to their disposal facilities. Municipal solid waste management is a complex task for municipal authorization owing to a lack of infrastructure, rapid population growth, high levels of urbanisation, an improper segregation system, and inadequate waste vehicles. Furthermore, the problem becomes more complicated and challenging due to the increase in availability and quantity, which has attracted many researchers to do the research work in recent years. In natural world issues, the availability of daily waste in any urban city is determined by a variety of factors, including eating habits, living cultures, and seasonal timing. Due to this reason, the availability of daily waste is considered an uncertainty. In this paper, waste management for fuzzy vehicle routing problems with split delivery and multicompartment vehicles is considered. The objective of this study is to minimise the distance and find the best route. The Branch and Bound algorithm will be used to investigate this issue, and the outcomes are to be compared to those of the Clarke and Wright algorithm.