**COLLEGE OF ADMINISTRATIVE SCIENCES AND ECONOMICS **

**ORCIBS SEMINAR**

**Speaker:**** **Hans Frenk-Sabancı University** **

**Title:** On static and dynamic single leg airline revenue management problems.

**Date:**** ****Friday, 15 March 2019**

**Time **** **** ****11:00-12:30**

**Place: CASE 216**

**Abstract: **In this talk we will give an overview on static and dynamic single leg airline revenue management problems with and without cancellations (cf. Aydin2013, Talluri-van-Ryzin 2005). The aim in these optimization models is to maximize the expected revenue. In all the considered models there are m, m>1 fare classes and the sales of those differently priced fare classes start T time units before the departure time of the airplane. Most well-known examples of fare classes are the economy and business class. It is assumed that during the sales period the fare class requests arrive in the discrete time model according to a non-homogeneous discrete time random arrival process and in the continuous time model according to a continuous time random arrival process. In the static formulation of this problem the airline company determines at the start of the sales period an allocation policy by deciding how many seats will be reserved for the different fare classes. This allocation policy clearly depends on the probability law of the random arrival process of requests. The earliest and most well-known example of such an allocation policy is given by Littlewoods rule for two fare classes and no cancellations allowed. This version of the problem can be solved by computing the expected revenue for a given static policy and using nonlinear (integer) programming techniques an optimal static policy can be easily determined. For the static version having more than two fare classes one may apply different heuristics. Since the objective function depends on the selected class of static policies we also formulate an alternative model with cancellations (cf. Frenk2017) and this model can be solved by dynamic programming techniques. Both static models will be presented in this lecture.

**Short Bio: **Hans Frenk joined the Faculty of Engineering and Natural Sciences at Sabanci University in 2009. He obtained his master degree (1979) from the Mathematics Department of Utrecht University, the Netherlands and his Ph.D degree (1984) from Erasmus University Rotterdam. His Ph.D thesis was on the rate of convergence of the renewal measure to the Lebesgue measure (renewal theory and regenerative processes) for interarrival times having a subexponential distribution using the theory of Banach algebras. Next to this he also obtained a Bachelor degree in Econometrics (1982) from Erasmus University Rotterdam. Before joining Sabanci University he was at IEOR department (UC Berkeley), Mathematics Department Technical University Eindhoven and Econometric Institute Erasmus University Rotterdam. Through the years his main research interest is in optimization, convex and quasiconvex analysis, stochastic processes and stochastic control problems and applying those techniques to problems in Management Science and Engineering (maintenance, inventory control, revenue management and pricing, health care). Recently his research interest is in the statistical estimation of probability laws of stochastic processes. Some of his papers jointly written with coauthors appeared in Production and Operations Management, Management Science, Operations Research, Transportation Science, Advances of Applied Probability, Journal of Applied Probability, Journal of Optimization Theory and Applications. Mathematics of Operations Research, Mathematical Programming and Discrete Applied Mathematics.