S. Ilker Birbil

Tractable Open Loop Policies for Joint Overbooking and Capacity Control Over a Single Flight Leg with Multiple Fare Classes

In this paper, we consider the joint overbooking and capacity control problem over a single flight leg with multiple fare classes. The objective is to maximize the net expected revenue, which is given by the difference between the expected revenue from the accepted requests and the expected penalty cost from the denied reservations. We study a class of open loop policies that accept the requests for each fare class with a fixed acceptance probability. In this case, the challenge becomes finding a set of acceptance probabilities that maximize the net expected revenue. We derive a simple expression that can be used to compute the optimal acceptance probabilities, despite the problem of finding the optimal acceptance probabilities being a high dimensional optimization problem. We show that the optimal acceptance probabilities randomize the acceptance decisions for at most one fare class, indicating that the randomized nature of our open loop policies is not a huge practical concern. We bound the performance loss of our open loop policies when compared with the optimal policy. Computational experiments demonstrate that open loop policies perform remarkably well, providing net expected revenues within two percent of the optimal on average.

Approximating the minimum hub cover problem on planar graphs

We study an approximation algorithm with a performance guarantee to solve a new

The set covering problem revisited: an empirical study of the value of dual information

\mathcal {NP}

Application of the cutting stock problem to a construction company: a case study

NP-hard optimization problem on planar graphs. The problem, which is referred to as the minimum hub cover problem, has recently been introduced to the literature to improve query processing over large graph databases. Planar graphs also arise in various graph query processing applications, such as; biometric identification, image classification, object recognition, and so on. Our algorithm is based on a well-known graph decomposition technique that partitions the graph into a set of outerplanar graphs and provides an approximate solution with a proven performance ratio. We conduct a comprehensive computational experiment to investigate the empirical performance of the algorithm. Computational results demonstrate that the empirical performance of the algorithm surpasses its guaranteed performance. We also apply the same decomposition approach to develop a decomposition-based heuristic, which is much more efficient than the approximation algorithm in terms of computation time. Computational results also indicate that the efficacy of the decomposition-based heuristic in terms of solution quality is comparable to that of the approximation algorithm.

Optimizing waste collection in an organized industrial region: a case study

Abstract We propose a new globalization strategy that can be used in unconstrained optimization algorithms to support rapid convergence from remote starting points. Our approach is based on using multiple points at each iteration to build a sequence of representative models of the objective function. Using the new information gathered from those multiple points, a local step is gradually improved by updating its direction as well as its length. We give a global convergence result and also provide the parallel implementation details accompanied with a numerical study. Our numerical study shows that the proposed algorithm is a promising alternative as a globalization strategy.