In practice, apart from the problem of vehicle routing, schedulers also face the problem of finding feasible driver schedules complying with complex restrictions on drivers' driving and working hours. To address this complex interdependent problem of vehicle routing and break scheduling, we propose a restricted dynamic programming heuristic for the vehicle routing problem with time windows and the full European social legislation on drivers' driving and working hours. The problem we consider includes all rules in this legislation, whereas 1 in the literature only a basic set of rules has been addressed. In addition to this basic set of rules, the legislation contains a set of modifications that allow for more flexibility. To include the legislation in the restricted dynamic programming heuristic, we propose a break scheduling heuristic. Computational results show that our method finds solutions to benchmark instances -which only consider the basic set of rules -with 18% less vehicles and 5% less travel distance than state of the art approaches. Moreover, our results are obtained with significant less computational effort. Furthermore, the results show that including a set of rules on drivers' working hours -which has been generally ignored in the literature -has a significant impact on the resulting vehicle schedules: 3.9% more vehicle routes and 1.0% more travel distance are needed. Finally, using the modified rules of the legislation leads to an additional reduction of 4% in the number of vehicles and of 1.5% regarding the travel distance. Therefore, the modified rules should be exploited in practice.

The cooling rate during material processing until glass transition rate is the key parameter for the production of bulk metallic glasses. But in the past, little attention has been paid to advanced production techniques such as deposition of molten metal sprays or spray forming, which offer elevated cooling rates. In this work, cooling conditions during spray forming were investigated due to its utmost importance for producing amorphous structures. Spray forming is treated in this work as a three step cooling process consisting of droplet flight phase, splat phase and deposit phase. All cooling steps were simulated for different droplet sizes. The surface temperature of the deposit was found to play an important role in the production of metallic glasses via spray forming. The simulation model can be used to find suitable spray conditions for the generation of bulk metallic glasses.

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Porosity is one of the most important quality criteria of spray‐formed materials in the as‐sprayed condition. Typically, spray‐formed sheets have a porous rim close to the substrate and depending on the spray conditions cold or hot porosity may also be present in the core of the deposit. This porosity has to be removed or minimized to make further processing steps such as rolling, forging or extrusion possible. In this paper, the influence of both substrate temperature and deposit surface temperature on porosity in spray‐formed sheets is studied. For this purpose spray forming experiments (sheet size 1000 mm × 250 mm) were carried out using three different materials: aluminium‐bronze, tin‐bronze and a nitriding steel. For the copper‐base alloys preheated steel‐substrates with different temperatures were moved through a scanning spray cone. In the case of steel a ceramic substrate at room temperature was used. In addition to the variation of the substrate temperature, the gas to metal mass flow ratio (GMR) was varied to achieve different deposit surface temperatures. During the run the surface temperature in the deposition zone was measured using a scanning, multi‐wavelength pyrometer. Samples of the deposits were polished and rasterized by light microscopy. The local porosity was characterized by digital image analysis. The influence of the substrate temperature and the GMR on the porosity in the vicinity of the substrate is evaluated and discussed in detail. The impact of the deposit surface temperature on the porosity was analyzed and is discussed as well. It was found that the deposit surface temperature has a strong impact on porosity for spray‐formed sheets. Finally, experimental results were used to develop a new approach to predict the porosity in spray‐formed sheets. The results clearly show the dependence on material properties. This approach can be used to identify process parameters to generate high density sheets in the future.

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