A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al. 2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.

First middle-atmospheric zonal wind profile measurements with a new ground-based microwave Doppler-spectro-radiometer

We report on the wind radiometer WIRA, a new ground-based microwave Doppler-spectro-radiometer specifically designed for the measurement of middle-atmospheric horizontal wind by observing ozone emission spectra at 142.17504 GHz. Currently, wind speeds in five levels between 30 and 79 km can be retrieved which makes WIRA the first instrument able to continuously measure horizontal wind in this altitude range. For an integration time of one day the measurement error on each level lies at around 25 m s−1. With a planned upgrade this value is expected to be reduced by a factor of 2 in the near future. On the altitude levels where our measurement can be compared to wind data from the European Centre for Medium-Range Weather Forecasts (ECMWF) very good agreement in the long-term statistics as well as in short time structures with a duration of a few days has been found. WIRA uses a passive double sideband heterodyne receiver together with a digital Fourier transform spectrometer for the data acquisition. A big advantage of the radiometric approach is that such instruments can also operate under adverse weather conditions and thus provide a continuous time series for the given location. The optics enables the instrument to scan a wide range of azimuth angles including the directions east, west, north, and south for zonal and meridional wind measurements. The design of the radiometer is fairly compact and its calibration does not rely on liquid nitrogen which makes it transportable and suitable for campaign use. WIRA is conceived in a way that it can be operated remotely and does hardly require any maintenance. In the present paper, a description of the instrument is given, and the techniques used for the wind retrieval based on the determination of the Doppler shift of the measured atmospheric ozone emission spectra are outlined. Their reliability was tested using Monte Carlo simulations. Finally, a time series of 11 months of zonal wind measurements over Bern (46°57′ N, 7°26′ E) is presented and compared to ECMWF wind data.

On trend estimation under monotone Gaussian subordination with long-memory: application to fossil pollen series

Fossil pollen data from stratigraphic cores are irregularly spaced in time due to non-linear age-depth relations. Moreover, their marginal distributions may vary over time. We address these features in a nonparametric regression model with errors that are monotone transformations of a latent continuous-time Gaussian process Z(T). Although Z(T) is unobserved, due to monotonicity, under suitable regularity conditions, it can be recovered facilitating further computations such as estimation of the long-memory parameter and the Hermite coefficients. The estimation of Z(T) itself involves estimation of the marginal distribution function of the regression errors. These issues are considered in proposing a plug-in algorithm for optimal bandwidth selection and construction of confidence bands for the trend function. Some high-resolution time series of pollen records from Lago di Origlio in Switzerland, which go back ca. 20,000 years are used to illustrate the methods.

Multifractional Poisson process, multistable subordinator and related limit theorems

We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and establish the convergence of a continuous-time random walk to the multifractional Poisson process.

Real-time simulation of large open quantum spin systems driven by dissipation

We consider a large quantum system with spins 12 whose dynamics is driven entirely by measurements of the total spin of spin pairs. This gives rise to a dissipative coupling to the environment. When one averages over the measurement results, the corresponding real-time path integral does not suffer from a sign problem. Using an efficient cluster algorithm, we study the real-time evolution from an initial antiferromagnetic state of the two-dimensional Heisenberg model, which is driven to a disordered phase, not by a Hamiltonian, but by sporadic measurements or by continuous Lindblad evolution.