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The capacitated single-allocation hub location problem revisited: A note on a classical formulation
(2009)

Denote by G = (N;A) a complete graph where N is the set of nodes and A is the set of edges. Assume that a °ow wij should be sent from each node i to each node j (i; j 2 N). One possibility is to send these °ows directly between the corresponding pairs of nodes. However, in practice this is often neither e±cient nor costly attractive because it would imply that a link was built between each pair of nodes. An alternative is to select some nodes to become hubs and use them as consolidation and redistribution points that altogether process more e±ciently the flow in the network. Accordingly, hubs are nodes in the graph that receive tra±c (mail, phone calls, passengers, etc) from di®erent origins (nodes) and redirect this tra±c directly to the destination nodes (when a link exists) or else to other hubs. The concentration of tra±c in the hubs and its shipment to other hubs lead to a natural decrease in the overall cost due to economies of scale.

Radiotherapy is one of the major forms in cancer treatment. The patient is irradiated with high-energetic photons or charged particles with the primary goal of delivering sufficiently high doses to the tumor tissue while simultaneously sparing the surrounding healthy tissue. The inverse search for the treatment plan giving the desired dose distribution is done by means of numerical optimization [11, Chapters 3-5]. For this purpose, the aspects of dose quality in the tissue are modeled as criterion functions, whose mathematical properties also affect the type of the corresponding optimization problem. Clinical practice makes frequent use of criteria that incorporate volumetric and spatial information about the shape of the dose distribution. The resulting optimization problems are of global type by empirical knowledge and typically computed with generic global solver concepts, see for example [16]. The development of good global solvers to compute radiotherapy optimization problems is an important topic of research in this application, however, the structural properties of the underlying criterion functions are typically not taken into account in this context.

One approach to multi-criteria IMRT planning is to automatically calculate a data set of Pareto-optimal plans for a given planning problem in a first phase, and then interactively explore the solution space and decide for the clinically best treatment plan in a second phase. The challenge of computing the plan data set is to assure that all clinically meaningful plans are covered and that as many as possible clinically irrelevant plans are excluded to keep computation times within reasonable limits. In this work, we focus on the approximation of the clinically relevant part of the Pareto surface, the process that consititutes the first phase. It is possible that two plans on the Parteto surface have a very small, clinically insignificant difference in one criterion and a significant difference in one other criterion. For such cases, only the plan that is clinically clearly superior should be included into the data set. To achieve this during the Pareto surface approximation, we propose to introduce bounds that restrict the relative quality between plans, so called tradeoff bounds. We show how to integrate these trade-off bounds into the approximation scheme and study their effects.

The rotational spinning of viscous jets is of interest in many industrial applications, including pellet manufacturing [4, 14, 19, 20] and drawing, tapering and spinning of glass and polymer fibers [8, 12, 13], see also [15, 21] and references within. In [12] an asymptotic model for the dynamics of curved viscous inertial fiber jets emerging from a rotating orifice under surface tension and gravity was deduced from the three-dimensional free boundary value problem given by the incompressible Navier-Stokes equations for a Newtonian fluid. In the terminology of [1], it is a string model consisting of balance equations for mass and linear momentum. Accounting for inner viscous transport, surface tension and placing no restrictions on either the motion or the shape of the jet’s center-line, it generalizes the previously developed string models for straight [3, 5, 6] and curved center-lines [4, 13, 19]. Moreover, the numerical results investigating the effects of viscosity, surface tension, gravity and rotation on the jet behavior coincide well with the experiments of Wong et.al. [20].

A general multi-period network redesign problem arising in the context of strategic supply chain planning (SCP) is studied. Several aspects of practical relevance in SCP are captured namely, multiple facility layers with different types of facilities, flows between facilities in the same layer, direct shipments to customers, and facility relocation. An efficient two-phase heuristic approach is proposed for obtaining feasible solutions to the problem, which is initially modeled as a large-scale mixed-integer linear program. In the first stage of the heuristic, a linear programming rounding strategy is applied to second initial values for the binary location variables in the model. The second phase of the heuristic uses local search to correct the initial solution when feasibility is not reached or to improve the solution when its quality does not meet given criteria. The results of an extensive computational study performed on randomly generated instances are reported.

In this paper, an extension to the classical capacitated single-allocation hub location problem is studied in which the size of the hubs is part of the decision making process. For each potential hub a set of capacities is assumed to be available among which one can be chosen. Several formulations are proposed for the problem, which are compared in terms of the bound provided by the linear programming relaxation. Di®erent sets of inequalities are proposed to enhance the models. Several preprocessing tests are also presented with the goal of reducing the size of the models for each particular instance. The results of the computational experiments performed using the proposed models are reported.

In the literature, there are at least two equivalent two-factor Gaussian models for the instantaneous short rate. These are the original two-factor Hull White model (see [3]) and the G2++ one by Brigo and Mercurio (see [1]). Both these models first specify a time homogeneous two-factor short rate dynamics and then by adding a deterministic shift function '(·) fit exactly the initial term structure of interest rates. However, the obtained results are rather clumsy and not intuitive which means that a special care has to be taken for their correct numerical implementation.

Selfish Bin Coloring
(2009)

We introduce a new game, the so-called bin coloring game, in which selfish players control colored items and each player aims at packing its item into a bin with as few different colors as possible. We establish the existence of Nash and strong as well as weakly and strictly Pareto optimal equilibria in these games in the cases of capacitated and uncapacitated bins. For both kinds of games we determine the prices of anarchy and stability concerning those four equilibrium concepts. Furthermore, we show that extreme Nash equilibria, those with minimal or maximal number of colors in a bin, can be found in time polynomial in the number of items for the uncapcitated case.

Gegenstand dieser Arbeit ist die Entwicklung eines Wärmetransportmodells für tiefe geothermische (hydrothermale) Reservoire. Existenz- und Eindeutigkeitsaussagen bezüglich einer schwachen Lösung des vorgestellten Modells werden getätigt. Weiterhin wird ein Verfahren zur Approximation dieser Lösung basierend auf einem linearen Galerkin-Schema dargelegt, wobei sowohl die Konvergenz nachgewiesen als auch eine Konvergenzrate erarbeitet werden.