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An uncertain single-machine scheduling problem is considered, where the processing time of a job can take any real value from a given segment. The criterion is to minimise the total weighted completion time of the n jobs, a weight being associated with each given job. We use the optimality box as a stability measure of the optimal schedule and derive an O(n)-algorithm for calculating the optimality box for a fixed permutation of the given jobs. We investigate properties of the optimality box using blocks of the jobs. If each job belongs to a single block, then the largest optimality box may be constructed in time. For the general case, we apply dynamic programming for constructing a job permutation with the largest optimality box. The computational results for finding a permutation with the largest optimality box show that such a permutation is close to an optimal one, which can be determined after completing the jobs when their processing times became known.

Models and optimisation approaches are developed for a flexible job shop scheduling problem with lot streaming and lot sizing of the variable sublots. A two-stage optimisation procedure is proposed...

The problem of scheduling a set of trains traveling through a given railway network consisting of single tracks, sidings and stations is considered. For every train a fixed route and travel times, an earliest departure time at the origin and a desired arrival time at the destination are given. A feasible schedule has to be determined which minimizes total tardiness of all trains at their destinations. This train scheduling problem is modeled as a job-shop scheduling problem with blocking constraints, where jobs represent trains and machines constitute tracks or track sections. Four MIP formulations without time-indexed variables are developed based on two different transformation approaches of parallel tracks and two different types of decision variables leading to job-shop scheduling problems with or without routing flexibility. A computational study is made on hard instances with up to 20 jobs and 11 machines to compare the MIP models in terms of total tardiness values, formulation size and computation time.

Spectral radiance measurements collected in nadir and sideward viewing directions by two airborne passive solar remote sensing instruments, the Spectral Modular Airborne Radiation measurement sysTem (SMART) and the Differential Optical Absorption Spectrometer (mini-DOAS), are used to compare the remote sensing results of cirrus optical thickness τ. The comparison is based on a sensitivity study using radiative transfer simulations (RTS) and on data obtained during three airborne field campaigns: the North Atlantic Rainfall VALidation (NARVAL) mission, the Mid-Latitude Cirrus Experiment (ML-CIRRUS) and the Aerosol, Cloud, Precipitation, and Radiation Interactions and Dynamics of Convective Cloud Systems (ACRIDICON) campaign. Radiative transfer simulations are used to quantify the sensitivity of measured upward radiance I with respect to τ, ice crystal effective radius reff, viewing angle of the sensor θV, spectral surface albedo α, and ice crystal shape. From the calculations it is concluded that sideward viewing measurements are generally better suited than radiance data from the nadir direction to retrieve τ of optically thin cirrus, especially at wavelengths larger than λ = 900 nm. Using sideward instead of nadir-directed spectral radiance measurements significantly improves the sensitivity and accuracy in retrieving τ, in particular for optically thin cirrus of τ ≤ 2. The comparison of retrievals of τ based on nadir and sideward viewing radiance measurements from SMART, mini-DOAS and independent estimates of τ from an additional active remote sensing instrument, the Water Vapor Lidar Experiment in Space (WALES), shows general agreement within the range of measurement uncertainties. For the selected example a mean τ of 0.54 ± 0.2 is derived from SMART, and 0.49 ± 0.2 by mini-DOAS nadir channels, while WALES obtained a mean value of τ = 0.32 ± 0.02 at 532 nm wavelength, respectively. The mean of τ derived from the sideward viewing mini-DOAS channels is 0.26 ± 0.2. For the few simultaneous measurements, the mini-DOAS sideward channel measurements systematically underestimate (−17.6 %) the nadir observations from SMART and mini-DOAS. The agreement between mini-DOAS sideward viewing channels and WALES is better, showing the advantage of using sideward viewing measurements for cloud remote sensing for τ ≤ 1. Therefore, we suggest sideward viewing measurements for retrievals of τ of thin cirrus because of the significantly enhanced capability of sideward viewing compared to nadir measurements.

The Midlatitude Cirrus experiment (ML-CIRRUS) deployed the High Altitude and Long Range Research Aircraft (HALO) to obtain new insights into nucleation, life cycle, and climate impact of natural cirrus and aircraft-induced contrail cirrus. Direct observations of cirrus properties and their variability are still incomplete, currently limiting our understanding of the clouds’ impact on climate. Also, dynamical effects on clouds and feedbacks are not adequately represented in today’s weather prediction models. Here, we present the rationale, objectives, and selected scientific highlights of ML-CIRRUS using the G-550 aircraft of the German atmospheric science community. The first combined in situ–remote sensing cloud mission with HALO united state-of-the-art cloud probes, a lidar and novel ice residual, aerosol, trace gas, and radiation instrumentation. The aircraft observations were accompanied by remote sensing from satellite and ground and by numerical simulations. In spring 2014, HALO performed 16 flights above Europe with a focus on anthropogenic contrail cirrus and midlatitude cirrus induced by frontal systems including warm conveyor belts and other dynamical regimes (jet streams, mountain waves, and convection). Highlights from ML-CIRRUS include 1) new observations of microphysical and radiative cirrus properties and their variability in meteorological regimes typical for midlatitudes, 2) insights into occurrence of in situ–formed and lifted liquid-origin cirrus, 3) validation of cloud forecasts and satellite products, 4) assessment of contrail predictability, and 5) direct observations of contrail cirrus and their distinction from natural cirrus. Hence, ML-CIRRUS provides a comprehensive dataset on cirrus in the densely populated European midlatitudes with the scope to enhance our understanding of cirrus clouds and their role for climate and weather.

A graph is well-indumatched if all its maximal induced matchings are of the same size. We first prove that recognizing whether a graph is well-indumatched is a co-NP-complete problem even for ( 2 P 5 , K 1 , 5 ) -free graphs. We then show that decision problems Independent Dominating Set , Independent Set , and Dominating Set are NP-complete for the class of well-indumatched graphs. We also show that this class is a co-indumatching hereditary class, i.e., it is closed under deleting the end-vertices of an induced matching along with their neighborhoods, and we characterize well-indumatched graphs in terms of forbidden co-indumatching subgraphs. We prove that recognizing a co-indumatching subgraph is an NP-complete problem. We introduce a perfectly well-indumatched graph, in which every induced subgraph is well-indumatched, and characterize the class of these graphs in terms of forbidden induced subgraphs. Finally, we show that the weighted versions of problems Independent Dominating Set and Independent Set can be solved in polynomial time for perfectly well-indumatched graphs, but problem Dominating Set is NP-complete.

A research-level retrieval algorithm for cloud optical and microphysical properties is developed for the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) aboard the Terra satellite. It is based on the operational MODIS algorithm. This paper documents the technical details of this algorithm and evaluates the retrievals for selected marine boundary layer cloud scenes through comparisons with the operational MODIS Data Collection 6 (C6) cloud product. The newly developed, ASTER-specific cloud masking algorithm is evaluated through comparison with an independent algorithm reported in [Zhao and Di Girolamo(2006)]. To validate and evaluate the cloud optical thickness (τ) and cloud effective radius (reff) from ASTER, the high-spatial-resolution ASTER observations are first aggregated to the same 1000 m resolution as MODIS. Subsequently, τaA and reff, aA retrieved from the aggregated ASTER radiances are compared with the collocated MODIS retrievals. For overcast pixels, the two data sets agree very well with Pearson's product-moment correlation coefficients of R > 0.970. However, for partially cloudy pixels there are significant differences between reff, aA and the MODIS results which can exceed 10 µm. Moreover, it is shown that the numerous delicate cloud structures in the example marine boundary layer scenes, resolved by the high-resolution ASTER retrievals, are smoothed by the MODIS observations. The overall good agreement between the research-level ASTER results and the operational MODIS C6 products proves the feasibility of MODIS-like retrievals from ASTER reflectance measurements and provides the basis for future studies concerning the scale dependency of satellite observations and three-dimensional radiative effects.

This study presents and evaluates several candidate approaches for downscaling observations from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) in order to increase the horizontal resolution of subsequent cloud optical thickness (τ) and effective droplet radius (reff) retrievals from the native 3 × 3 km2 spatial resolution of the narrowband channels to 1 × 1 km2. These methods make use of SEVIRI’s coincident broadband high–resolution visible (HRV) channel. For four example cloud fields, the reliability of each downscaling algorithm is evaluated by means of collocated 1 × 1 km2 MODIS radiances, which are re-projected to the horizontal grid of the HRV channel, and serve as reference for the evaluation. By using these radiances smoothed with the spatial response function of the native SEVIRI channels as retrieval input, the accuracy at the SEVIRI standard resolution can be evaluated and an objective comparison of the accuracy of the different downscaling algorithms can be made. For the example scenes considered in this study, it is shown that neglecting high-frequency variations below the SEVIRI standard resolution results in significant random absolute deviations of the retrieved τ and reff of up to ≈ 14 and ≈ 6 μm, respectively, as well as biases. By error propagation, this also negatively impacts the reliability of the subsequent calculation of liquid water path (WL) and cloud droplet number concentration (ND), which exhibit deviations of up to ≈ 89 g m−2 and ≈ 177 cm−3, respectively. For τ, these deviations can be almost completely mitigated by the use of the HRV channel as a physical constraint, and by applying most of the presented downscaling schemes. For the accuracy of reff,the choice of downscaling scheme however is important: deviations are generally of similar magnitude or larger than those for retrievals at the SEVIRI standard resolution, indicative of their limited skill at predicting high–frequency spatial variability in reff. A strong degradation of accuracy of reff is observed for some of the approaches, which also affects subsequent WL and ND estimates. As a result, an approach which constrains the reff to the lower–resolution results is recommended. Overall, this study demonstrates that an increase in horizontal resolution of SEVIRI cloud property retrievals can be reliably achieved by use of its HRV channel, yielding cloud properties which are preferable in terms of accuracy to those obtained from SEVIRI’s standard-resolution. This work advances efforts to mitigate impacts of scale mismatches among channels of multi–resolution instruments on cloud retrievals.

We provide the asymptotic minimax detection boundary for a bump, i.e. an abrupt change, in the mean function of a stationary Gaussian process. This will be characterized in terms of the asymptotic behavior of the bump length and height as well as the dependency structure of the process. A major finding is that the asymptotic minimax detection boundary is generically determined by the value of its spectral density at zero. Finally, our asymptotic analysis is complemented by non-asymptotic results for AR($p$) processes and confirmed to serve as a good proxy for finite sample scenarios in a simulation study. Our proofs are based on laws of large numbers for non-independent and non-identically distributed arrays of random variables and the asymptotically sharp analysis of the precision matrix of the process.

The filling of channels in porous media with particles of a material can be interpreted in a first approximation as a packing of spheres in cylindrical recipients. Numerous studies on micro- and nanoscopic scales show that they are, as a rule, not ideal cylinders. In this paper, the channels, which have an irregular shape and a circular cross-section, as well as the packing algorithms are investigated. Five patterns of channel shapes are detected to represent any irregular porous structures. A novel heuristic packing algorithm for monosized spheres and different irregularities is proposed. It begins with an initial configuration based on an

Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems in Hilbert scales satisfying conditional stability estimates characterized by general concave index functions. For that case, we exploit Tikhonov regularization and provide convergence and convergence rates of regularized solutions for both deterministic and stochastic noise. We further discuss a priori and a posteriori parameter choice rules and illustrate the validity of our assumptions in different model and real world situations.

Recently acquired multibeam echosounder data from the shallowest part (26–53 m depth) of Spitsbergenbanken in the western Barents Sea reveal a variety of bedforms, including megaripples, sandwaves and sandbanks. The bedforms exhibit varying degrees of superimposition and differ in their age of formation and present depositional regime, being either active or moribund. These are the first observations of co-occurring current induced bedforms in the western Barents Sea and provide evidence of a high energy environment in the study area. The bedforms indicate both sediment erosion and transport and confirm that there is enough sand available in this area to maintain them. Such conditions are not known to be common in the western Barents Sea and reflect the unique oceanographic and benthic environment of Spitsbergenbanken. © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license

In this paper we propose a multiscale scanning method to determine active components of a quantity $f$ w.r.t. a dictionary $\mathcal{U}$ from observations $Y$ in an inverse regression model $Y=Tf+\xi$ with linear operator $T$ and general random error $\xi$. To this end, we provide uniform confidence statements for the coefficients $\langle \varphi, f\rangle$, $\varphi \in \mathcal U$, under the assumption that $(T^*)^{-1} \left(\mathcal U\right)$ is of wavelet-type. Based on this we obtain a multiple test that allows to identify the active components of $\mathcal{U}$, i.e. $\left\langle f, \varphi\right\rangle \neq 0$, $\varphi \in \mathcal U$, at controlled, family-wise error rate. Our results rely on a Gaussian approximation of the underlying multiscale statistic with a novel scale penalty adapted to the ill-posedness of the problem. The scale penalty furthermore ensures weak convergence of the statistic's distribution towards a Gumbel limit under reasonable assumptions. The important special cases of tomography and deconvolution are discussed in detail. Further, the regression case, when $T = \text{id}$ and the dictionary consists of moving windows of various sizes (scales), is included, generalizing previous results for this setting. We show that our method obeys an oracle optimality, i.e. it attains the same asymptotic power as a single-scale testing procedure at the correct scale. Simulations support our theory and we illustrate the potential of the method as an inferential tool for imaging. As a particular application we discuss super-resolution microscopy and analyze experimental STED data to locate single DNA origami., Comment: 55 pages, 10 figures, 1 table

The bispectral method retrieves cloud optical thickness (τ) and cloud droplet effective radius (re) simultaneously from a pair of cloud reflectance observations, one in a visible or near-infrared (VIS/NIR) band and the other in a shortwave infrared (SWIR) band. A cloudy pixel is usually assumed to be horizontally homogeneous in the retrieval. Ignoring subpixel variations of cloud reflectances can lead to a significant bias in the retrieved τ and re. In the literature, the retrievals of τ and re are often assumed to be independent and considered separately when investigating the impact of subpixel cloud reflectance variations on the bispectral method. As a result, the impact on τ is contributed only by the subpixel variation of VIS/NIR band reflectance and the impact on re only by the subpixel variation of SWIR band reflectance. In our new framework, we use the Taylor expansion of a two-variable function to understand and quantify the impacts of subpixel variances of VIS/NIR and SWIR cloud reflectances and their covariance on the τ and re retrievals. This framework takes into account the fact that the retrievals are determined by both VIS/NIR and SWIR band observations in a mutually dependent way. In comparison with previous studies, it provides a more comprehensive understanding of how subpixel cloud reflectance variations impact the τ and re retrievals based on the bispectral method. In particular, our framework provides a mathematical explanation of how the subpixel variation in VIS/NIR band influences the re retrieval and why it can sometimes outweigh the influence of variations in the SWIR band and dominate the error in re retrievals, leading to a potential contribution of positive bias to the re retrieval. We test our framework using synthetic cloud fields from a large-eddy simulation and real observations from Moderate Resolution Imaging Spectroradiometer. The predicted results based on our framework agree very well with the numerical simulations. Our framework can be used to estimate the retrieval uncertainty from subpixel reflectance variations in operational satellite cloud products and to help understand the differences in τ and re retrievals between two instruments.

The management of a military supply chain (SC) involves the integration of production, packaging, warehousing, repair, maintenance and transportation of army supplies. In this paper, we focus on the integrated demand-responsive scheduling of maintenance and transportation operations within the SC. We consider a modular representation of a SC, in which the maintenance and transportation operations constitute the corresponding modules. An efficient integration of these operations is carried out by an additional controlling (commanding) module. We describe and analyse the optimisation problems arising in each module. The main contribution of the paper is that the analysis and optimisation of the controlling module permit to enhance the performance of the entire SC. Computational experiments prove the validity and effectiveness of the suggested models.

In this paper, a generalized formulation of a classical single machine scheduling problem is considered. A set of n jobs characterized by their release dates, deadlines and a start time-dependent processing time function p(t) has to be processed on a single machine. The objective is to find a Pareto-optimal set of schedules with respect to the criteria ϕmax and makespan, where ϕmax is a non-decreasing function depending on the completion times of the jobs. We present an approach that allows to find an optimal schedule with respect to different scheduling criteria, such as the minimization of makespan, lateness or weighted lateness, tardiness and weighted tardiness etc. in time polynomially depending on the number of jobs. The complexity of the presented algorithm is O(n3 max{log n, H, P}), where H and P are the complexity of calculating ϕj(t) and p(t), respectively.

This paper is concerned with exponentially ill-posed operator equations with additive impulsive noise on the right hand side, i.e. the noise is large on a small part of the domain and small or zero outside. It is well known that Tikhonov regularization with an $L^1$ data fidelity term outperforms Tikhonov regularization with an $L^2$ fidelity term in this case. This effect has recently been explained and quantified for the case of finitely smoothing operators. Here we extend this analysis to the case of infinitely smoothing forward operators under standard Sobolev smoothness assumptions on the solution, i.e. exponentially ill-posed inverse problems. It turns out that high order polynomial rates of convergence in the size of the support of large noise can be achieved rather than the poor logarithmic convergence rates typical for exponentially ill-posed problems. The main tools of our analysis are Banach spaces of analytic functions and interpolation-type inequalities for such spaces. We discuss two examples, the (periodic) backwards heat equation and an inverse problem in gradiometry., to appear in SIAM J. Numer. Anal

New high-resolution multibeam bathymetry and sub-bottom profile datasets from Fingerdjupet are used for the first detailed geomorphological mapping of the seafloor in this area. The mapped landforms provide evidence for a palaeo-ice stream flowing in a southeasterly direction from Spitsbergenbanken into Fingerdjupet, merging with Bjornoyrenna ice stream, and confirm a theorised palaeo-ice divide located along the bank. The combined landform records and acoustic stratigraphy allow a detailed reconstruction of the glacial dynamics during the last deglaciation. The withdrawal of the Fingerdjupet ice stream from Bjornoyrenna was characterised by rapid retreat, punctuated by periods of stable ice marginal conditions. Five to six major ice margin stillstands and/or readvances associated with the last deglaciation are identified in the seafloor record and acoustic stratigraphy. During these events, large grounding zone wedges were deposited at the ice stream margin. The seabed geomorphology indicates that ice stream dynamics changed as the ice stream retreated from the trough onto the shallower bank. Here, numerous retreat moraines indicate that a grounded ice margin retreated slowly, with several minor stillstands, towards north-northwest. Several controls and/or drivers on the style of ice flow and retreat have been suggested, including catchment size reduction, sea level rise, bedrock topography, drawdown of bank ice and/or migration of the main ice divide over the bank.

In this paper, we consider the single-machine scheduling problem with given release dates and the objective to minimize the maximum penalty which is NP-hard in the strong sense. For this problem, we introduce a dual and an inverse problem and show that both these problems can be solved in polynomial time. Since the dual problem gives a lower bound on the optimal objective function value of the original problem, we use the optimal function value of a sub-problem of the dual problem in a branch and bound algorithm for the original single-machine scheduling problem. We present some initial computational results for instances with up to 20 jobs.

Clear‐sky contamination is a challenging and long‐lasting problem for cloud optical thickness (τ) and effective droplet radius (r(sub eff)) retrievals using passive satellite sensors. This study explores the feasibility of improving both τ and r(sub eff) retrievals for partly cloudy (PCL) pixels by using available subpixel samples in a visible to near‐infrared band, which many satellite sensors offer. Data are provided by high‐resolution reflectance (R) observations and cloud property retrievals by the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) at horizontal resolutions between 30‐960m. For partly cloudy 960‐m observations, the clear‐sky component of the pixels induces significant underestimations of up to 58% for τ, while overestimations in r(sub eff) can exceed 41%. This yields underestimations in the derived liquid water path and cloud droplet number concentration of up to 68% and 72%, respectively. By means of three different assumptions it is shown that subpixel R observations in the visible to near‐infrared band can be used to estimate higher‐resolution R for the second band in the retrieval scheme, as well as the subpixel cloud cover. The estimated values compare well to actually observed ASTER results and are used to retrieve cloud properties, which are unbiased by the clear‐sky component of PCL pixels. While the presented retrieval approach is only evaluated for marine boundary layer clouds, it is computationally efficient and can be easily applied to observations from different imagers. As an example, the PCL retrieval scheme is applied to data by the Moderate Resolution Imaging Spectroradiometer, where similar biases for PCL pixels are observed.

The filling of channels in porous media with particles of a material can be interpreted in a first approximation as a packing of spheres in cylindrical recipients. Numerous studies on micro- and nanoscopic scales show that they are, as a rule, not ideal cylinders. In this paper, the channels, which have an irregular shape and a circular cross-section, as well as the packing algorithms are investigated. Five patterns of channel shapes are detected to represent any irregular porous structures. A novel heuristic packing algorithm for monosized spheres and different irregularities is proposed. It begins with an initial configuration based on an fcc unit cell and the subsequent densification of the obtained structure by shaking and gravity procedures. A verification of the algorithm was carried out for nine sinusoidal axisymmetric channels with different Dmin/Dmax ratio by MATLAB® simulations, reaching a packing fraction of at least 0.67 (for sphere diameters of 5%Dmin or less), superior to a random close packing density. The maximum packing fraction was 73.01% for a channel with a ratio of Dmin/Dmax = 0.1 and a sphere size of 5%Dmin. For sphere diameters of 50%Dmin or larger, it was possible to increase the packing factor after applying shaking and gravity movements.

This edited book presents new results in the area of algorithm development for different types of scheduling problems. In eleven chapters, algorithms for single machine problems, flow-shop and job-shop scheduling problems (including their hybrid (flexible) variants), the resource-constrained project scheduling problem, scheduling problems in complex manufacturing systems and supply chains, and workflow scheduling problems are given. The chapters address such subjects as insertion heuristics for energy-efficient scheduling, the re-scheduling of train traffic in real time, control algorithms for short-term scheduling in manufacturing systems, bi-objective optimization of tortilla production, scheduling problems with uncertain (interval) processing times, workflow scheduling for digital signal processor (DSP) clusters, and many more.

The cloud droplet number concentration (N d) is of central interest to improve the understanding of cloud physics and for quantifying the effective radiative forcing by aerosol‐cloud interactions. Current standard satellite retrievals do not operationally provide N d, but it can be inferred from retrievals of cloud optical depth (τ c) cloud droplet effective radius (r e) and cloud top temperature. This review summarizes issues with this approach and quantifies uncertainties. A total relative uncertainty of 78% is inferred for pixel‐level retrievals for relatively homogeneous, optically thick and unobscured stratiform clouds with favorable viewing geometry. The uncertainty is even greater if these conditions are not met. For averages over 1° ×1° regions the uncertainty is reduced to 54% assuming random errors for instrument uncertainties. In contrast, the few evaluation studies against reference in situ observations suggest much better accuracy with little variability in the bias. More such studies are required for a better error characterization. N d uncertainty is dominated by errors in r e, and therefore, improvements in r e retrievals would greatly improve the quality of the N d retrievals. Recommendations are made for how this might be achieved. Some existing N d data sets are compared and discussed, and best practices for the use of N d data from current passive instruments (e.g., filtering criteria) are recommended. Emerging alternative N d estimates are also considered. First, new ideas to use additional information from existing and upcoming spaceborne instruments are discussed, and second, approaches using high‐quality ground‐based observations are examined., Key Points Satellite cloud droplet concentration uncertainties of 78% for pixel‐level retrievals and 54% for 1 by 1 degree retrievals are estimatedThe effective radius retrieval is the most important aspect for improvement, and more in situ evaluation is neededPotential improvements using passive and active satellite, and ground‐based instruments are discussed

A traditional problem in LCA is how to deal with processes where recycled material is used as an input or where the output of a process is further used as raw material in another product system (open-loop recycling). Allocation is needed to partition the responsibility for the environmental impacts caused by the raw material extraction, the recycling and the final disposal of a material over different product systems in some proportional shares. The norm ISO/DIS 14’04T. 1998 now explicitly allows the use of an economic value as a basis for the allocation of open-loop product systems, where material is recycled into other product systems while undergoing a change in its inherent properties. In a case study for aluminium window frames, an economic allocation procedure for aluminium is developed based on different market prices for secondary materials with different alloy content. Market prices are assumed to reflect the functionality of a material quality within a techno-economic system. Therefore, market prices permit the qualitative description of the degradation of a material over a product system. Based on this qualitative degradation, a ‘relative resource consumption’ can be defined. This relative resource consumption is used to allocate the environmental impacts related to recycled material entering or leaving the product system under study. The results of the new allocation principle are compared to results of a former study on window frames out of various materials, elaborated by EMPA in 1996. The conclusions underline the importance of the recycling of aluminium with a high quality and give some criteria for a more ecological design of aluminium windows. Finally, methodological advantages and obstacles of the presented economic allocation procedure are pointed out.

Goal and Background: The treatment of allocation in the descriptive LCA of wood-based products has been discussed for a long time and different solutions have been presented. In general, it is accepted that the influence of different allocation procedures on the results of LCA of wood-based products can be very significant. This paper is a result of the Cost Action E9 'Life cycle assessment of forestry and forest products' and represents the experience of involved Cost E9 delegates. Objective: Wood is a renewable material that can be used for wood products and energy production. Consistent methodological procedures are needed in order to correctly address the twofold nature of wood as a material and fuel, the multi-functional wood processing generating large quantities of co-products, and reuse or recycling of paper and wood. Ten different processes in LCAs of wood-based products are identified, where allocation questions can occur: forestry, sawmill, wood industry, pulp and paper industry, particle board industry, recycling of paper, recycling of wood-based boards, recycling of waste wood, combined heat and power production, landfill. Methodology: Following ISO 14 041 a step-wise procedure for system boundary setting and allocation are outlined. As a first priority allocation should be avoided by system expansion, thus adding additional functions to the functional unit. Alternatively, the avoided-burden approach can be followed by subtracting substituted functions of wood that are additionally provided. If allocation cannot be avoided, some allocations methods from case studies are described. Conclusions: The following conclusions for allocation in LCA of wood-based products are given. 1) Avoid allocation by expansion of system boundaries by combining material and energy aspects of wood, meaning a combination of LCA of wood products and of energy from wood with a functional unit for products and energy. 2) Substitute energy from wood with conventional energy in the LCA of wood products to get the func-tional unit of the wood product only, but identify the criteria for the substituted energy. 3) Substitution of wooden products with non-wooden products in LCA of bioenergy is not advis able, because the substitution criteria can be too complex. 4) If avoiding allocation is not possible, the reasons should be documented. 5) Different allocation procedures must be analysed and documented. In many cases, it seems necessary to make a sensitivity analysis of different allocation options for different environmental effects. It can also be useful to get the acceptance of the chosen allocation procedure by external experts. 6) Different allocation factors, e.g. mass or economic value, are allowed within the same LCA. 7) For allocation of forestry processes it is necessary to describe the main function of the forest where the raw material is taken out. In some cases different types or functions of forests must be considered and described. 8) Regarding the experiences from the examples, the following most practical allocation for some specific processes are identified: forestry: mass or volume; sawmill: mass or volume and proceeds; wood industry: mass and proceeds

This special issue of Algorithms is devoted to the development of scheduling algorithms based on innovative approaches for solving hard scheduling problems either exactly or approximately. Submissions were welcome both for traditional scheduling problems as well as for new practical applications. The main topics include sequencing and scheduling with additional constraints (setup times or costs, precedence constraints, resource constraints, and batch production environment) and production planning and scheduling problems arising in real-world applications.

In the vehicle routing problem with cross-docking (VRPCD), it is assumed that the selected suppliers and the quantity of the products purchased from each supplier are known. This paper presents an MILP model which incorporates supplier selection and order allocation into the VRPCD in a multi-cross-dock system minimising the total costs, including purchasing, transportation, cross-docking, inventory and early/tardy delivery penalty costs. The sensitivity of the model on the key parameters of the objective function is analysed and the supply decisions are evaluated when the coefficients of the distribution cost are changed. A two-stage solution algorithm (TSSA) is proposed and the results of the TSSA for small-sized instances are compared with the exact solutions. Finally, a large-sized real case of an urban freight transport is solved using the TSSA.

The consideration of blocking constraints refers to the absence of buffers in a production system. A job-shop scheduling problem with a total tardiness objective is NP-hard even without blocking constraints and mathematical programming results indicate the necessity of heuristics. The neighborhood is one of its main components. In contrast to classical job-shop scheduling, a permutation of operations does not necessarily define a feasible schedule. A neighbor is determined by an adjacent pairwise interchange (API) of two operations on a machine and the resulting permutation of operations is modified to regain feasibility while maintaining the given API. The neighborhood is implemented in a simulated annealing and tested on train-scheduling-inspired problems as well as benchmark instances. The heuristic method obtains optimal and near-optimal solutions for small instances and outperforms a given MIP formulation for some of the larger ones.

We investigate a posteriori parameter choice methods for filter based regularizations \(\hat f_\alpha = q_\alpha \left (T^*T\right )T^*Y\) in statistical inverse problems Y = Tf + σξ. Here we assume that T is a bounded linear operator between Hilbert spaces, and ξ is Gaussian white noise.

SYNCHRO-NET is a Horizon 2020 European research project that aims to overcome the stress due to increasing transportation distances, higher complexity, and vulnerability of supply chains. The core of the SYNCHRO-NET solution is an integrated optimisation and simulation eco-NET system that supports stakeholders’ decisions in the transport of goods at strategic and operational levels. In particular, the system enables stakeholders to identify improvement opportunities by quickly analysing and calculating the impacts and benefits of slow/smart steaming and synchro-modality so to enhance sustainability, quality, and reliability. Three case studies considering pan-European and regional trade lanes, as well as commercial activities between Far East and European ports, prove the efficiency and effectiveness of the overall system.

Tessellation methods are a relatively new approach for modeling the structure of a material. In this paper, such structures are interpreted as sphere packing models, where molecules and atoms represent spheres of equal or different size. Based on the review of the literature, it is shown that the tessellation approach is a powerful method for modeling and simulating such structures with desirable metric and topological properties. Two basic tessellation methods are considered more in detail: the Delaunay tessellation and the Voronoi diagram in Laguerre geometry, as well as some of their generalizations. The principal concepts of both tessellation methods are briefly explained for a better understanding of the application details. It is noted that packing models created by tessellation methods are not based on the use of the gravity camp effect, which is a difference to numerical and mathematic programming modeling approaches. Therefore, tessellation methods permit the development of structures without taking into account the gravitation, what is important for modeling the structure on the microscopic and nano levels, where the influence of the gravitation is studied insufficiently. A review of the related literature is given, focusing on the details of the tessellation method and the particle size distribution.

This article considers the problem of scheduling a given set of n jobs on two identical parallel machines with a single server. Each job must be processed on one of the machines. Before processing, the server has to set up the relevant machine. The objective is to minimize the makespan. For this unary NP-hard problem, two fast constructive algorithms with a complexity of O(n2) are presented. The performance of these algorithms is evaluated for instances with up to 10,000 jobs. Computational results indicate that the algorithms have an excellent performance for very large instances so that the obtained objective function values are very close to a lower bound, and in many cases even an optimal solution is achieved. Superiority over all existing algorithms is obtained by sequencing the jobs on the two machines so that the machine idle time and the server waiting time are minimized. In doing so, the characteristics of an optimal solution resulting from its relevant lower bound are taken into account.

International audience; Smart factories Industry 4.0 on the basis of collaborative cyber-physical systems represents a future form of industrial networks. Supply chains in such networks have dynamic structures which evolve over time. In these settings, short-term supply chain scheduling in smart factories Industry 4.0 is challenged by temporal machine structures, different processing speed at parallel machines and dynamic job arrivals. In this study, for the first time, a dynamic model and algorithm for short-term supply chain scheduling in smart factories Industry 4.0 is presented. The peculiarity of the considered problem is the simultaneous consideration of both machine structure selection and job assignments. The scheduling approach is based on a dynamic non-stationary interpretation of the execution of the jobs and a temporal decomposition of the scheduling problem. The algorithmic realisation is based on a modified form of the continuous maximum principle blended with mathematical optimisation. A detailed theoretical analysis of the temporal decomposition and computational complexity is performed. The optimality conditions as well as the structural properties of the model and the algorithm are investigated. Advantages and limitations of the proposed approach are discussed.

During the welding process, the microstructure of the base material changes locally that leads to altering mechanical properties in the weld and the neighboring areas, Heat Affected Zone (HAZ). The constitution of the HAZs also varies spatially as a result of different temperature gradients during heating and cooling cycles. Consequently, the macroscopic material behavior of the HAZ also varies spatially as well and therefore the determination of the mechanical behavior of the welded connection is very challenging. In this study, a hierarchical multiscale approach is presented and applied in order to characterize the material behavior of the Heat Affected Zone (HAZ) in welded connections. First, the metallurgical constituents in particular areas of HAZ have been identified experimentally. Next, several representative volume elements (RVEs) have been constructed using microscopic images. Then employing the computational homogenization methods, the stress–strain curves representing the macroscopic material behavior in respective points of the HAZ have been calculated. Meanwhile, some miniature tensile tests have been performed to experimentally identify the stress–strain behavior in the HAZ. Finally, the numerically calculated stress–strain curves are compared with the measured experimental data and they show a good agreement. The comparison of the results depicts that the proposed multiscale approach is suitable for the characterization of the material properties in welded connections or in general for materials with specially varying microstructures.