Locating landfills—Optimization vs. reality

This paper examines the locations of landfills and garbage transfer stations in New Brunswick, one of Canada’s Maritime Provinces. The locations of the existing facilities are then compared to a system of optimized locations. The model used for the optimization is similar to those employed in the analysis of standard hub location models.     

Well‐posedness,smooth dependence and centre manifold reduction for a semilinear hyperbolic system from laser dynamics

We prove existence, uniqueness, regularity and smooth dependence of the weak solution on the initial data for a semilinear, first order, dissipative hyperbolic system with discontinuous coefficients. Such hyperbolic systems have successfully been used to model the dynamics of distributed feedback multisection semiconductor lasers. We show that in a function space of continuous functions the weak solutions generate a smooth skew product semiflow. Using slow fast structure and dissipativity we prove the existence of smooth exponentially attracting invariant centre manifolds for the non‐autonomous model. Copyright © 2006 John Wiley & Sons, Ltd.     

Approximation algorithm for facility location with service installation costs

In this paper, we study the uncapacitated facility location problem with service installation costs depending on the type of service required. We propose a polynomial-time approximation algorithm with approximation ratio 1.808 which improves the previous approximation ratio of 2.391 of Shmoys, Swamy, and Levi.     

Spectral and refractive effects in non-stationary radiative transfer: a theoretical study in dense media

A theoretical study of unsteady radiative heat transfer inside refractive heterogeneous participating media is presented. In the approximation of space-time geometrical optics, some new properties for propagating waves are exhibited. Physically, it is shown that the time dependency of refractive index can give rise to an effect of spectral bounce, whereas space dependency is responsible for the existence of confined trajectories for light. Then, the problem of energy transport is studied: from the shape of Clausius Invariant in unsteady processes, the transient radiative transfer equation is built and the existence of amplification effects for specific intensity is presented.     

Finding the optimal solution to the Huff based competitive location model

In this paper we solve the gravity (Huff) model for the competitive facility location problem. We show that the generalized Weiszfeld procedure converges to a local maximum or a saddle point. We also devise a global optimization procedure that finds the optimal solution within a given accuracy. This procedure is very efficient and finds the optimal solution for 10,000 demand points in less than six minutes of computer time. We also experimented with the generalized Weiszfeld algorithm on the same set of randomly generated problems. We repeated the algorithm from 1,000 different starting solutions and the optimum was obtained at least 17 times for all problems.     

An Improved Branch & Bound Method for the Uncapacitated Competitive Location Problem

In this paper, the problem of locating new facilities in a competitive environment is considered. The problem is formulated as the firm expected profit maximization and a set of nodes is selected in a graph representing the geographical zone. Profit depends on fixed and deterministic location costs and, since customers are independent decision-makers, on the expected market share. The problem is an instance of nonlinear integer programming, because the objective function is concave and submodular. Due to this complexity a branch & bound method is developed for solving small size problems (that is, when the number of nodes is less than 50), while a heuristic is necessary for larger problems. The branch & bound is called data-correcting method, while the approximate solutions are obtained using the heuristic-concentration method.     

Multiple voting location and single voting location on trees

We examine voting location problems in which the goal is to place, based on an election amongst the users, a given number of facilities in a graph. The user preference is modeled by shortest path distances in the graph. A Condorcet solution is a set of facilities to which there does not exist an alternative set preferred by a majority of the users. Recent works generalize the model to additive indifference and replaced user majority by γ-proportion.     

Approximating the two-level facility location problem via a quasi-greedy approach

We propose a quasi-greedy algorithm for approximating the classical uncapacitated 2-level facility location problem (2-LFLP). Our algorithm, unlike the standard greedy algorithm, selects a sub-optimal candidate at each step. It also relates the minimization 2-LFLP problem, in an interesting way, to the maximization version of the single level facility location problem. Another feature of our algorithm is that it combines the technique of randomized rounding with that of dual fitting. This new approach enables us to approximate the metric 2-LFLP in polynomial time with a ratio of 1.77, a significant improvement on the previously known approximation ratios. Moreover, our approach results in a local improvement procedure for the 2-LFLP, which is useful in improving the approximation guarantees for several other multi-level facility location problems. An additional result of our approach is an O(ln (n))-approximation algorithm for the non-metric 2-LFLP, where n is the number of clients. This is the first non-trivial approximation for a non-metric multi-level facility location problem. An extended abstract of this paper appeared in the Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms (SODA), January 2004.     

Diagonal Invariant Ideals of Topologically Graded C*-algebras

We study diagonal invariant ideals of topologically graded C~*-algebras over discrete groups. Since all Toeplitz algebras defined on discrete groups are topologically graded, the results in this paper have improved the first author's previous works on this topic.     

Saddlepoint approximations to studentized bootstrap distributions based onM-estimates

Summary  Saddlepoint methods can provide extremely accurate approximations to resampling distributions. This article applies them to distributions of studentized bootstrap statistics based on robustM-estimates. As examples we consider the studentized versions of Huber’sM-estimate of location, of its initially MAD scaled version, and of Huber’s proposal 2. The studentized version of Huber’s proposal 2 seems to be a preferable measure of location. Remarks on implementation and related problems are given.