Note—Optimal Pricing Policy for the Service Facility Offering a Set of Priority Prices - Alperstein, Hanna (Management Science, 1988)
A profit making service facility that offers a set of different prices for the single service it provides is considered. By paying a higher price, the customer buys into a priority class that shortens his stay in the service system. We determine the optimal number of priority classes and the set of prices that affords the service facility a higher revenue than any other set. Relying on Adiri and Yechiali (Adiri, I., U. Yechiali. 1974. Optimal priority-purchasing and pricing decisions in non monopoly and monopoly queues. Oper. Res. 22 1051–1066.) who demonstrated that the customers' optimal priority-purchasing strategy is of the control limit type, we prove that for every set of M(>1) priority prices that are optimal to the service facility, the control limits of all priority classes equal one except the control limit of the highest priority class that is determined by the parameters of the system. We show that the highest priority class also has a control limit of one when the service facility uses the optimal M and optimal priority prices. Thus full optimality results in implementation of the pure LIFO (Last-In-First-Out) service discipline.