Fleet sizing of automated guided vehicles: a linear programming approach based on closed queuing networks

Abstract

We use multi-class closed queuing networks to model operations of automated guided vehicles in a manufacturing or distribution environment. We approximate the dynamics of the system using the first moment balance equations of the embedded stochastic chain representing the network under the steady-state conditions. These moments account for loaded and empty-travel times, as well as times when vehicles are being loaded/unloaded or waiting to be dispatched. We model the steady-state behaviour of the closed queuing network by a linear program whose optimal value is the estimate of the required fleet-size. The result of the analytical model is compared with those of the simulation studies for a set of numerical examples. The comparison shows that the analytical model provides a good estimate for the required number of vehicles.