Optimal threshold control of empty vehicle redistribution in two depot service systems

In this note, we consider the empty vehicle redistribution problem in a two-depot service system with random demands and uncertain transportation times. It is shown that the optimal stationary policy is of threshold control-type when the long-run average cost is to be minimized. The explicit form of the average cost under threshold controls is presented, which can be used to calculate the optimal threshold values. The sufficient and necessary conditions for the existence of the steady-state are provided. The results are then used to construct suboptimal policies for a more realistic model.