Priority service system optimization under service level constraints

Abstract

We consider a service system that serves one class of customers, which is willing to pay a premium for a faster delivery, with priority over the other class, which is more price sensitive but is willing to wait longer. The demand from one class depends not only on the price and delivery time quoted to it, but also on that offered to the other class. The service provider needs to select the price and delivery time quoted to the two classes, and the required service capacity to meet the quoted delivery times with a certain degree of reliability, so as to maximize its rate (per unit time) of earning profit. This results in a non-linear priority queue optimization model, for which the analytical expression for service level constraint for the low priority customers is unknown. We provide a cutting plane method to solve the problem, where constraints to be satisfied are identified iteratively from results of matrix geometric evaluation of the proposed system alternative, which are then added to the mathematical model for re-optimization.