COMPARING THE SMALL-SAMPLE ESTIMATION ERROR OF CONCEPTUALLY DIFFERENT RISK MEASURES

Motivated by the need to correctly rank risky alternatives in many investment, insurance and operations research applications, this paper uses a generalized location and scale framework from utility theory to propose a simple but powerful metric for comparing the estimation error of conceptually different risk measures. In an illustrative application, we obtain this metric — the probability that a risk measure ranks two assets falsely in finite samples — via Monte Carlo simulation for fourteen popular measures of risk and different distributional settings. Its results allow us to highlight interesting risk measure properties such as their relative quality under varying degrees of skewness and kurtosis. Because of the generality of our approach, the error probabilities derived for classic risk measures can serve as a benchmark for newly proposed measures seeking to replace the classic ones in decision making. It also supports the identification of the most suitable risk measures for a given distributional environment.

Operations Research Problems for Airline Industry

Maintenance routing is one of the most complicated problems of operations research applications for airline industry. In this study, airline industry operations' main applications and subjects are basically mentioned and literature is briefly reviewed. This study is conducted under the headings of; Fleet Assignment, Aircraft Routing, Maintenance Routing and Crew Scheduling. Additionally, network models are explained basically on an example flight program. This study's purpose is to be a guide for the new researchers of this area through operations research applications for airline industry and to introduce maintenance routing problem literature.

The Quadratic Multiknapsack Problem with Conflicts and Balance Constraints

The quadratic multiknapsack problem consists of packing a set of items of various weights into knapsacks of limited capacities with profits being associated with pairs of items packed into the same knapsack. This problem has been solved by various heuristics since its inception, and more recently it has also been solved with an exact method. We introduce a generalization of this problem that includes pairwise conflicts as well as balance constraints, among other particularities. We present and compare constraint programming and integer programming approaches for solving this generalized problem. Summary of Contribution: The quadratic multiknapsack problem consists of packing a set of items of various weights into knapsacks of limited capacities -- with profits being associated with pairs of items packed into the same knapsack. This problem has been solved by various heuristics since its inception, and more recently it has also been solved with an exact method. We introduce a generalization of this problem which includes pairwise conflicts as well as balance constraints, among other particularities. We present and compare constraint programming and integer programming approaches for solving this generalized problem. The problem we address is clearly in the core of the operations research applications in which subsets have to be built and, in particular, we add the concept of fairness to the modeling and solution process by computationally evaluating techniques to take fairness into account. This is clearly at the core of computational evaluation of algorithms.

Operations Research Problems for Airline Industry

Maintenance routing is one of the most complicated problems of operations research applications for airline industry. In this study, airline industry operations' main applications and subjects are basically mentioned and literature is briefly reviewed. This study is conducted under the headings of; Fleet Assignment, Aircraft Routing, Maintenance Routing and Crew Scheduling. Additionally, network models are explained basically on an example flight program. This study's purpose is to be a guide for the new researchers of this area through operations research applications for airline industry and to introduce maintenance routing problem literature.