Scheduling the hospital-wide flow of elective patients

In this paper, we address the problem of planning the patient flow in hospitals subject to scarce medical resources with the objective of maximizing the contribution margin. We assume that we can classify a large enough percentage of elective patients according to their diagnosis-related group (DRG) and clinical pathway. The clinical pathway defines the procedures (such as different types of diagnostic activities and surgery) as well as the sequence in which they have to be applied to the patient. The decision is then on which day each procedure of each patient’s clinical pathway should be done, taking into account the sequence of procedures as well as scarce clinical resources, such that the contribution margin of all patients is maximized. We develop two mixed-integer programs (MIP) for this problem which are embedded in a static and a rolling horizon planning approach. Computational results on real-world data show that employing the MIPs leads to a significant improvement of the contribution margin compared to the contribution margin obtained by employing the planning approach currently practiced. Furthermore, we show that the time between admission and surgery is significantly reduced by applying our models.     

On Elastic Solids with Micro-Structure.

Abstract. Based on the general framework of evolutionary equations in the sense of [6,8] and referring to well-posedness results in the context of evolutionary problems from mathematical physics we consider two problems from elasticity theory as particular applications. Our structural perspective is illustrated by showing that the theory of elastic solids with micro-structure can be transparently embedded into the abstract solution theory. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Column generation for vehicle routing problems with multiple synchronization constraints

Synchronization of workers and vehicles plays a major role in many industries such as logistics, healthcare or airport ground handling. In this paper, we focus on operational ground handling planning and model it as an archetype of vehicle routing problems with multiple synchronization constraints, coined as “abstract vehicle routing problem with worker and vehicle synchronization” (AVRPWVS). The AVRPWVS deals with routing workers to ground handling jobs such as unloading baggage or refuelling an aircraft, while meeting each job’s time window. Moreover, each job can be performed by a variable number of workers. As airports span vast distances and due to security regulations, workers use vehicles to travel between locations. Furthermore, each vehicle, moved by a driver, can carry several workers. We propose two mathematical multi-commodity flow formulations based on time-space networks to efficiently model five synchronization types including movement and load synchronization. Moreover, we develop a branch-and-price heuristic that employs both conventional variable branching and a novel variable fixing strategy. We demonstrate that the procedure achieves results close to the optimal solution in short time when compared to the two integer models.     

Finite Element Solution of Conical Diffraction Problems

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R ² coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.     

The mixed Hodge structure on the fundamental group of a punctured Riemann surface

Given a compact Riemann surface of genus and distinct points and on , we consider the non-compact Riemann surface with basepoint . The extension of mixed Hodge structures associated to the first two steps of is studied. We show that it determines the element in , where represents the canonical divisor of as well as the corresponding extension associated to . Finally, we deduce a pointed Torelli theorem for punctured Riemann surfaces.

     

Connectedness and Stability of Julia Sets of the Composition of Polynomials of the Form z2+cn

For a sequence (c_n) of complex numbers, the quadratic polynomialsf_cn(z) := z² + c_n and the sequence (F_n) of iterates F_n := f_cn...f_c1areconsidered. The Fatou set F_(cn) is by definition the set ofall z C^ such that (F_n) is normal in some neighbourhood ofz, while the complement of F_(cn) is called the Julia set J_(cn).The aim of this article is to study the connectedness and stabilityof the Julia set J_(cn) provided that the sequence (c_n) is bounded.     

The Generation of Maximal Triangle-Free Graphs

In this paper we present an efficient algorithm for generating maximal triangle-free graphs. A program based on this algorithm has been used to check a conjecture of Erdo´´s about the local density of triangle-free graphs and turned out to be very powerful for the computation of triangle Ramsey numbers.     

Fast generation of cubic graphs

In this paper an efficient algorithm to generate regular graphs with small vertex valency is presented. The running times of a program based on this algorithm and designed to generate cubic graphs are below two natural benchmarks: (a) If N(n) denotes the number of pairwise non-isomorphic cubic graphs with n vertices and T(n) the time needed for generating the list of all these graphs, then T(n)/N(n) decreases gradually for the observed values of n. This suggests that T(n)/N(n) might be uniformly bounded for all n, ignoring the time to write the outputs, but we are unable to prove this and in fact are not confident about it. (b) For programs that generate lists of non-isomorphic objects, but cannot a priori make sure to avoid the generation of isomorphic copies, the time needed to check a randomly ordered list of these objects for being non-isomorphic is a natural benchmark. Since for large lists (n ≥ 22, girth 3) existing graph isomorphism programs take longer to canonically label all of the N(n) graphs than our algorithm takes to generate them, our algorithm is probably faster than any method which does one or more isomorphism test for every graph. © 1996 John Wiley & Sons, Inc.     

Compact spreads and compact translation planes over locally compact fields

We prove that a spread S over a locally compact nondlscrete field F defines a topological translation plane if and only if the spread is compact. For F=R, this is implicit in Breuning's thesis [Bre], cf. [B 2]. For the proof, we describe the point set of the projective translation plane as a quotient space of some projective space, with identifications taking place in one hyperplane. This is new even for F=R.     

Soliton chaos and lengthscale competition in nonlinear dynamics

Perturbing soliton-bearing completely integrable dynamics can give rise to rich and fascinating behaviour. If the perturbation introduces a lengthscale which is large compared to the spatial extent of the solitons present in the system, the solitons move like particles in an effective potential. Taking into account two-soliton interaction can result in chaotic behaviour called ‘soliton chaos’. In the opposite limit of a small-lengthscale perturbation the solitons acquire a dressing which effectively shields them from the perturbation. If the resulting ‘dressed solitons’ are subject to an additional long-wavelength perturbation they move like renormalised particles. Furthermore they can scatter nearly elastically. If the perturbation contains lengthscales which are comparable to one of the soliton's typical lengthscales then lengthscale competition can occur. Neither the particle approximation nor the dressed-particle approximation for the soliton is valid and complicated spatio-temporal behaviour is observed. We illustrate this scenario by means of the perturbed nonlinear Schrödinger equation. The perturbed sine-Gordon equation and the Ablowitz-Ladik equation are also discussed.