A dynamic programming model for assigning customers to priority service classes

A dynamic programming model is presented which optimally assigns n customers to m priority service classes, where customers have heterogeneous demand rates and waiting costs. The model is used to find the vertically efficient assignment of customers to priority classes for both a general service facility and a facility modeled as an M/M/1 priority queue. If the priority model is M/M/1, we prove that all the demand for each customer will be assigned to a single class.