Minimizing the number of apertures in multileaf collimator sequencing with field splitting

In this paper we consider the problem of decomposing a given integer matrix A into an integer conic combination of consecutive-ones matrices with a bound on the number of columns per matrix. This problem is of relevance in the realization stage of intensity modulated radiation therapy (IMRT) using linear accelerators and multileaf collimators with limited width. Constrained and unconstrained versions of the problem with the objectives of minimizing beam-on time and decomposition cardinality are considered. We introduce a new approach which can be used to find the minimum beam-on time for both constrained and unconstrained versions of the problem. The decomposition cardinality problem is shown to be NP-hard and an approach is proposed to solve the lexicographic decomposition problem of minimizing the decomposition cardinality subject to optimal beam-on time

Hierarchical Edge Colorings and Rehabilitation Therapy Planning in Germany

In this paper we give an overview on the system of rehabilitation clinics in Germany in general and the literature on patient scheduling applied to rehabilitation facilities in particular. We apply a class-teacher model developed to this environment and then generalize it to meet some of the specific constraints of inpatient rehabilitation clinics. To this end we introduce a restricted edge coloring on undirected bipartite graphs which is called group-wise balanced. The problem considered is called patient-therapist-timetable problem with group-wise balanced constraints (PTTPgb). In order to specify weekly schedules further such that they produce a reasonable allocation to morning/afternoon (second level decision) and to the single periods (third level decision) we introduce (hierarchical PTTPgb). For the corresponding model, the hierarchical edge coloring problem, we present some first feasibility results

Evaluation of the COSMO-SC turbulence scheme in a shear-driven stable boundary layer

The performance of the COSMOsingle column turbulence scheme (a TKE scheme with a 1.5 order turbulence closure at the hierarchy level 2.5 following Mellor and Yamada) is investigated in the framework of the first GABLS intercomparison case. This is an idealized shear-driven stable boundary layer case with no advection. Overall the COSMO model performs reasonably well compared to the other participating models and the reference Large Eddy Simulations. However, the modification of some model parameters, together with the prescribed high vertical resolution, reveals a problem of numerical stability in the turbulence scheme: for the investigated shear-driven stable boundary layer the vertical diffusivities show unrealistic oscillations. This model deficiency, which has previously been described in literature, is explored in quite substantial detail and possible solutions are evaluated. It is found that under the given conditions the numerical description of the vertical wind gradients is crucial for the stability of the turbulence scheme. It is shown that for the determination of vertical gradients information from grid points beyond the immediately neighboring model levels must be incorporated – as it is common practice in the treatment of horizontal gradients – in order to obtain a numerically stable turbulence scheme. As a first approach vertical wind gradients are filtered using a 5-point filter prior to the evaluation of the stability functions. This approach yields to the overall best performance among all those tested and found in literature. The simulations additionally show that the use of a too high minimum diffusion coefficient (which is introduced in the model in order to avoid too low mixing) leads to losing important structures of the planetary boundary layer, such as the low level jet or a near-surface temperature inversio

Hierarchical Edge Colorings and Rehabilitation Therapy Planning in Germany

In this paper we give an overview on the system of rehabilitation clinics in Germany in general and the literature on patient scheduling applied to rehabilitation facilities in particular. We apply a class-teacher model developed to this environment and then generalize it to meet some of the specific constraints of inpatient rehabilitation clinics. To this end we introduce a restricted edge coloring on undirected bipartite graphs which is called group-wise balanced. The problem considered is called patient-therapist-timetable problem with group-wise balanced constraints (PTTPgb). In order to specify weekly schedules further such that they produce a reasonable allocation to morning/afternoon (second level decision) and to the single periods (third level decision) we introduce (hierarchical PTTPgb). For the corresponding model, the hierarchical edge coloring problem, we present some first feasibility results

Minimizing the Number of Apertures in Multileaf Collimator Sequencing with Field Splitting

In this paper we consider the problem of decomposing a given integer matrix A into a positive integer linear combination of consecutive-ones matrices with a bound on the number of columns per matrix. This problem is of relevance in the realization stage of intensity modulated radiation therapy (IMRT) using linear accelerators and multileaf collimators with limited width. Constrained and unconstrained versions of the problem with the objectives of minimizing beam-on time and decomposition cardinality are considered. We introduce a new approach which can be used to find the minimum beam-on time for both constrained and unconstrained versions of the problem. The decomposition cardinality problem is shown to be NP-hard and an approach is proposed to solve the lexicographic decomposition problem of minimizing the decomposition cardinality subject to optimal beam-on time