Optimizing a Stochastic Dynamic Scheduling Problem Using Mathematical Statistics

We investigate analytical cost distributions in the setting of a dynamic stochastic scheduling problem where customers are served from a central location within some given time-frame, for the case where customer locations are uniformly distributed on the boundary of the unit circle. Two distance metrics are considered and analytical expressions for the distribution of the resulting costs are derived, for an infinite planning horizon, using the methods of mathematical statistics. We then investigate the optimization of a threshold-based scheduling strategy, for various choices of the statistic to be optimized: in some cases we can derive exact quantile distributions, allowing optimization of any desired quantile.