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.

Influence of time point of calibration on accuracy of continuous glucose monitoring in individuals with type 1 diabetes

Abstract Background and Aims: Data on the influence of calibration on accuracy of continuous glucose monitoring (CGM) are scarce. The aim of the present study was to investigate whether the time point of calibration has an influence on sensor accuracy and whether this effect differs according to glycemic level. Subjects and Methods: Two CGM sensors were inserted simultaneously in the abdomen on either side of 20 individuals with type 1 diabetes. One sensor was calibrated predominantly using preprandial glucose (calibration(PRE)). The other sensor was calibrated predominantly using postprandial glucose (calibration(POST)). At minimum three additional glucose values per day were obtained for analysis of accuracy. Sensor readings were divided into four categories according to the glycemic range of the reference values (low, ≤4 mmol/L; euglycemic, 4.1-7 mmol/L; hyperglycemic I, 7.1-14 mmol/L; and hyperglycemic II, >14 mmol/L). Results: The overall mean±SEM absolute relative difference (MARD) between capillary reference values and sensor readings was 18.3±0.8% for calibration(PRE) and 21.9±1.2% for calibration(POST) (P<0.001). MARD according to glycemic range was 47.4±6.5% (low), 17.4±1.3% (euglycemic), 15.0±0.8% (hyperglycemic I), and 17.7±1.9% (hyperglycemic II) for calibration(PRE) and 67.5±9.5% (low), 24.2±1.8% (euglycemic), 15.5±0.9% (hyperglycemic I), and 15.3±1.9% (hyperglycemic II) for calibration(POST). In the low and euglycemic ranges MARD was significantly lower in calibration(PRE) compared with calibration(POST) (P=0.007 and P<0.001, respectively). Conclusions: Sensor calibration predominantly based on preprandial glucose resulted in a significantly higher overall sensor accuracy compared with a predominantly postprandial calibration. The difference was most pronounced in the hypo- and euglycemic reference range, whereas both calibration patterns were comparable in the hyperglycemic range.

Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R n , with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from [6], and provide a numerical comparison of the two time discretization methods.

CD4-guided scheduled treatment interruptions compared with continuous therapy for patients infected with HIV-1: results of the Staccato randomised trial

BACKGROUND: Stopping antiretroviral therapy in patients with HIV-1 infection can reduce costs and side-effects, but carries the risk of increased immune suppression and emergence of resistance. METHODS: 430 patients with CD4-positive T-lymphocyte (CD4) counts greater than 350 cells per muL, and viral load less than 50 copies per mL were randomised to continued therapy (n=146) or scheduled treatment interruptions (n=284). Median time on randomised treatment was 21.9 months (range 16.4-25.3). Primary endpoints were proportion of patients with viral load less than 50 copies per mL at the end of the trial, and amount of drugs used. Analysis was intention-to-treat. This study is registered at ClinicalTrials.gov with the identifier NCT00113126. FINDINGS: Drug savings in the scheduled treatment interruption group, compared with continuous treatment, amounted to 61.5%. 257 of 284 (90.5%) patients in the scheduled treatment interruption group reached a viral load less than 50 copies per mL, compared with 134 of 146 (91.8%) in the continued treatment group (difference 1.3%, 95% CI-4.3 to 6.9, p=0.90). No AIDS-defining events occurred. Diarrhoea and neuropathy were more frequent with continuous treatment; candidiasis was more frequent with scheduled treatment interruption. Ten patients (2.3%) had resistance mutations, with no significant differences between groups. INTERPRETATION: Drug savings with scheduled treatment interruption were substantial, and no evidence of increased treatment resistance emerged. Treatment-related adverse events were more frequent with continuous treatment, but low CD4 counts and minor manifestations of HIV infection were more frequent with scheduled treatment interruption.

Association between sleep apnea severity and blood coagulability: Treatment effects of nasal continuous positive airway pressure

A prothrombotic state may contribute to the elevated cardiovascular risk in patients with obstructive sleep apnea (OSA). We investigated the relationship between apnea severity and hemostasis factors and effect of continuous positive airway pressure (CPAP) treatment on hemostatic activity. We performed full overnight polysomnography in 44 OSA patients (mean age 47+/-10 years), yielding apnea-hypopnea index (AHI) and mean nighttime oxyhemoglobin saturation (SpO2) as indices of apnea severity. For treatment, subjects were double-blind randomized to 2 weeks of either therapeutic CPAP (n = 18), 3 l/min supplemental nocturnal oxygen (n = 16) or placebo-CPAP (<1 cm H2O) (n = 10). Levels of von Willebrand factor antigen (VWF:Ag), soluble tissue factor (sTF), D-dimer, and plasminogen activator inhibitor (PAI)-1 antigen were measured in plasma pre- and posttreatment. Before treatment, PAI-1 was significantly correlated with AHI (r = 0.47, p = 0.001) and mean nighttime SpO2 (r = -0.32, p = 0.035), but these OSA measures were not significantly related with VWF:Ag, sTF, and D-dimer. AHI was a significant predictor of PAI-1 (R2 = 0.219, standardized beta = 0.47, p = 0.001), independent of mean nighttime SpO2, body mass index (BMI), and age. A weak time-by-treatment interaction for PAI-1 was observed (p = 0.041), even after adjusting for age, BMI, pre-treatment AHI, and mean SpO2 (p = 0.046). Post hoc analyses suggested that only CPAP treatment was associated with a decrease in PAI-1 (p = 0.039); there were no changes in VWF:Ag, sTF, and D-dimer associated with treatment with placebo-CPAP or with nocturnal oxygen. Apnea severity may be associated with impairment in the fibrinolytic capacity. To the extent that our sample size was limited, the observation that CPAP treatment led to a decrease in PAI-1 in OSA must be regarded as tentative.