A simple vehicle dispatching policy with non-stationary stochastic arrival rates

This paper provides an impulsive stochastic control approach to the vehicle dispatching problem with non-stationary and stochastic arrival rates. Both necessary and sufficient conditions for optimal dispatches are given with proofs given in appendices. It is shown by means of examples that stationary solutions previously considered are a special case of the theory outlined here. In addition, a discussion of other dispatching rules is included in the conclusion together with their effect on the mathematical optimality of vehicle dispatching.