FRIDAY, September 30, 2005
Probability in Science and Industry Seminar
4:30 P.M., WeH 7500
Marty Reiman
Bell Laboratories, Math Sciences Research Center.
Refreshments at 4:00 in the Math Lounge, WeH 6220.
TITLE:
An Asymptotically-Optimal Dynamic Admission Policy for a Revenue Management Problem
ABSTRACT:
We consider the following canonical revenue management problem, which has been analyzed in the context of airline seat inventory control and has applications to other service industries and supply chain management. There are several resource types (legs), each of which has a fixed capacity (number of seats). There are several customer classes (routes), each with an associated arrival process, price and resource consumption vector. The aim is to make dynamic accept/reject decisions at customer arrival epochs to maximize the total expected revenue obtained over the finite horizon [0,T] subject to not exceeding the capacity of any of the resources.
Motivated by the analysis of so-called fluid and diffusion limits (obtained as resource capacities and arrival rates grow large) of the system, we introduce a certain control policy that involves solving a couple of simple linear programs. We then show that this policy is asymptotically optimal on the so-called diffusion scale, a property that is not shared by other approaches such as booking limits and bid price control.
BIO: Dr. Martin I. Reiman is a distinguished member of technical staff in the Mathematical Sciences Research Center of Bell Labs, Lucent Technologies in Murray Hill, NJ. He has been at Bell Labs since receiving his PhD in operations research from Stanford University in 1977. Dr. Reiman’s research has focused on the analysis, optimization and control of stochastic service (queueing) systems, with an emphasis on fluid and diffusion limits. This work has been motivated by problems in communication, computing and manufacturing systems. He is the vice-chair/chair-elect of the Applied Probability Society of INFORMS and has been an associate editor of the Annals of Applied Probability as well as area editor of Mathematics of Operations Research.
