Fractional location problems

In this paper we analyze some variants of the classical uncapacitated facility location problem with a ratio as an objective function. Using basic concepts and results of fractional programming, we identify a class of one-level fractional location problems which can be solved in polynomial time in terms of the size of the problem. We also consider the fractional two-echelon location problem, which is a special case of the general two-level fractional location problem. For this two-level fractional location problem we identify cases for which its solution involves decomposing the problem into several one-level fractional location problems

An Integrated Approach to Single-Leg Airline Revenue Management: The Role of Robust Optimization

In this paper we introduce robust versions of the classical static and dynamic single leg seat allocation models as analyzed by Wollmer, and Lautenbacher and Stidham, respectively. These robust models take into account the inaccurate estimates of the underlying probability distributions. As observed by simulation experiments it turns out that for these robust versions the variability compared to their classical counter parts is considerably reduced with a negligible decrease of average revenue

Duality theory for convex/quasiconvex functions and its application to optimization

In this paper an intuitive and geometric approach is presented explaining the basic ideas of convex/quasiconvex analysis and its relation to duality theory. As such, this paper does not contain new results but serves as a hopefully easy introduction to the most important results in duality theory for convex/quasiconvex functions on locally convex real topological vector spaces. Moreover, its connection to optimization is also discussed