Optimizing Hauling Vehicle Mix for Debris Removal: A Queueing Theory Approach

This work explores one aspect of debris removal system design, the optimal mix of hauling vehicles, from two perspectives: efficiency and equity. First, the vehicle mix which maximizes the efficiency of the system is determined (i.e., that which minimizes the average wait time). Secondly, the equity of the most efficient mix is considered (i.e., the ratio of wait times between different vehicles). The results suggest that the solution to the optimal mix of hauling vehicles is nominally the same for a wide range of arrival rates for some system configurations. Further, the analysis shows that the optimal solution permanently disadvantages some vehicles for the majority of service rate combinations, however equitable optimal solutions (i.e., those for which all hauling vehicles have the same expected wait times in the system wait time minimizing solution) do exist, though the locus is very small. System configurations which lead to these equitably optimal solutions are highlighted. Policy implications are also presented.