Revenue
management for a multi-class single-server queue
Costis Maglaras,
Submitted November 2003
Abstract:
Consider a single-server make-to-order production
firm that offers multiple products to a market of price sensitive users, and
operates in a market with imperfect competition, in which it has power to
influence its vector of demand rates by varying its price menu. This paper
models this system as a multi-class M/M/1 queue with controllable arrival
rates, general demand curves, and quadratic holding costs, and studies the
problem of jointly optimizing over its dynamic pricing and sequencing policies
to maximize the expected revenues minus holding costs. Using fluid and
diffusion approximating models we show the following: as the capacity of the
system and the potential demand grow large: (i) the optimal pricing and
sequencing problems decouple, (ii) optimal prices increase linearly in the
total workload in the system, and (iii) optimal sequencing follows a greedy
``generalized $c\mu$" rule. Numerical results illustrate the accuracy of
these policies by comparing their performance to the optimal one obtained by numerically
solving the associated dynamic program.
Download: dp-mm1.pdf (337 KB)