Unconstraining Methods in Revenue Management Systems: Research Overview and Prospects

Demand unconstraining is one of the key techniques to the success of revenue management systems. This paper surveys the history of research on unconstraining methods and reviews over 130 references including the latest research works in the area. We discuss the relationship between censored data unconstraining and forecasting and review five alternative unconstraining approaches. These methods consider data unconstraining in various situations such as single-class, multi-class, and multi-flight. The paper also proposes some future research questions to bridge the gap between theory and applications

Global Newton methods for nonlinear programs and variational inequalities: A B-differentiable equation approach

This dissertation presents a modified damped Newton algorithm for solving general variational inequality problems with nonlinear programs and nonlinear complementarity problems as special cases. When these three mathematical problems are formulated as a system of equations, the traditional Newton method will fail because of the presence of some inherent nondifferentiability. The proposed modified damped Newton method, however, insures global convergence and locally quadratic convergence under the assumption of regularity. Numerical experiments show that the algorithm is very efficient and outperforms the traditional Newton method. The research in this dissertation is motivated by J. S. Pang\u27s recent work and is different from his in several respects. It uses a different formulation which makes the structure simpler and is able to exploit the derivative information from both the primal functions and dual variables. In the context of convex nonlinear programming, this formulation maintains the convexity of the subproblems. A significant improvement of this modified algorithm over the basic damped Newton algorithm is that it relaxes the regularity condition to some extent. Under the assumption of weak regularity and some very mild conditions, the modified algorithm is guaranteed to attain a descent direction. Hence, this new algorithm is often suitable for many applications and is shown to preform quite well on an extensive set of test examples

Two Pricing Mechanisms in Sponsored Search Advertising

Sponsored search advertising has grown rapidly since the last decade and is now a significant revenue source for search engines. To ameliorate revenues, search engines often set fixed or variable reserve price to in influence advertisers’ bidding. This paper studies and compares two pricing mechanisms: the generalized second-price auction (GSP) where the winner at the last ad position pays the larger value between the highest losing bid and reserve price, and the GSP with a posted reserve price (APR) where the winner at the last position pays the reserve price. We show that if advertisers’ per-click value has an increasing generalized failure rate, the search engine’s revenue rate is quasi-concave and hence there exists an optimal reserve price under both mechanisms. While the number of advertisers and the number of ad positions have no effect on the selection of reserve price in GSP, the optimal reserve price is affected by both factors in APR and it should be set higher than GSP

Two Pricing Mechanisms in Sponsored Search Advertising

Sponsored search advertising has grown rapidly since the last decade and is now a significant revenue source for search engines. To ameliorate revenues, search engines often set fixed or variable reserve price to in influence advertisers’ bidding. This paper studies and compares two pricing mechanisms: the generalized second-price auction (GSP) where the winner at the last ad position pays the larger value between the highest losing bid and reserve price, and the GSP with a posted reserve price (APR) where the winner at the last position pays the reserve price. We show that if advertisers’ per-click value has an increasing generalized failure rate, the search engine’s revenue rate is quasi-concave and hence there exists an optimal reserve price under both mechanisms. While the number of advertisers and the number of ad positions have no effect on the selection of reserve price in GSP, the optimal reserve price is affected by both factors in APR and it should be set higher than GSP