Learning and forgetting effects on a group scheduling problem

This paper proposes to investigate learning and forgetting effects on the problem of scheduling families of jobs on a single machine to minimize total completion time of jobs. A setup time is incurred whenever the single machine transfers job processing from a family to another family. To analyze the impact of learning and forgetting on this group scheduling problem, we structure three basic models and make some comparisons through computational experiments. The three models, including no forgetting, total forgetting and partial forgetting, assume that the processing time of a job is dependent on its position in a schedule. Some scheduling rules and a lower bound are derived in order to constitute our branch-and-bound algorithm for searching an optimal sequence. In addition, an efficient and simply-structured heuristic is also built to find a near-optimal schedule.     

Local times of continuous N-parameter strong martingales

Let M be a 4N-integrable, real-valued continuous N-parameter strong martingale. By extending Itô-type formulas for M to a function whose 2Nth derivative is Dirac's δ-distribution, Tanaka-type formulas for M are obtained. They represent local time of M with respect to occupation time scaled by the N-fold product of the Stieltjes measure defined by the quadratic variation of M and its kth derivatives in space, where k ≤ N − 1. Applications of Doob's and Burkholder's inequalities give continuity properties: space time continuity for local time, space continuity for the derivatives. In case N is even, for the continuity of the (N − 1)st derivative an additional condition on M is needed which may have a relation to the existence of local times of M w.r.t. different occupation time scales.     

Dependence properties and comparison results for Lévy processes

In this paper we investigate dependence properties and comparison results for multidimensional Lévy processes. In particular we address the questions, whether or not dependence properties and orderings of the copulas of the distributions of a Lévy process can be characterized by corresponding properties of the Lévy copula, a concept which has been introduced recently in Cont and Tankov (Financial modelling with jump processes. Chapman & Hall/CRC, Boca Raton, 2004) and Kallsen and Tankov (J Multivariate Anal 97:1551–1572, 2006). It turns out that association, positive orthant dependence and positive supermodular dependence of Lévy processes can be characterized in terms of the Lévy measure as well as in terms of the Lévy copula. As far as comparisons of Lévy processes are concerned we consider the supermodular and the concordance order and characterize them by orders of the Lévy measures and by orders of the Lévy copulas, respectively. An example is given that the Lévy copula does not determine dependence concepts like multivariate total positivity of order 2 or conditionally increasing in sequence. Besides these general results we specialize our findings for subfamilies of Lévy processes. The last section contains some applications in finance and insurance like comparison statements for ruin times, ruin probabilities and option prices which extends the current literature. Anja Blatter was supported by the Deutsche Forschungsgemeinschaft (DFG).     

Single-machine scheduling against due dates with past-sequence-dependent setup times

Recently Koulamas and Kyparisis [Koulamas, C., Kyparisis, G.J., in press. Single-machine scheduling with past-sequence-dependent setup times. European Journal of Operational Research] introduced past-sequence-dependent setup times to scheduling problems. This means that the setup time of a job is proportionate to the sum of processing times of the jobs already scheduled. Koulamas and Kyparisis [Koulamas, C., Kyparisis, G.J., in press. Single-machine scheduling with past-sequence-dependent setup times. European Journal of Operational Research] were able to show for a number of single-machine scheduling problems with completion time goals that they remain polynomially solvable. In this paper we extend the analysis to problems with due dates. We demonstrated that some problems remain polynomially solvable. However, for some other problems well-known polynomially solution approaches do not guarantee optimality any longer. Consequently we concentrated on finding polynomially solvable special cases.     

Optimal sequencing in the presence of setup times for tow/barge traffic through a river lock

Queues of tow/barges form when a river lock is rendered inoperable due to lock malfunction, a tow/barge accident or adverse lock operating conditions. In this paper, we develop model formulations that allow the queue to be cleared using a number of differing objectives. Of particular interest is the presence of different setup times between successive passages of tow/barges through the lock. Dependent on the objective chosen, we are able to show that certain ordering protocols may be used to markedly reduce the sequencing search space for N tow/barges from the order of N! to 2^N. We present accompanying linear and nonlinear integer programming formulations and carry out computational experiments on a representative set of problems.     

Theoretical assessment of the errors involved in ultrasonic location and sizing of molten weld pools

Ultrasonic transit times may be used to locate the interface between molten weld metal and parent plate as a weld is formed. These transit times will lead to errors in interpretation of the location of the weld interface if account is not taken of the variation of ultrasonic velocity with temperature. We assess the magnitude of these errors using a theoretical model based on the Green's function to obtain the temperature distribution at any time and then convert the temperatures into elastic constants through empirical fits to high temperature data. A ray tracing method and a semi-analytical approach are used to estimate the effects of the changes in elastic constants on the ray paths and transit times. From these theoretical predictions we conclude that the location errors incurred by assuming ultrasonic velocities appropriate to cold metal are less than 0.5 mm for a 3.5 mm radius weld in austenitic steel or in iron. Experimental values tend to be larger than this, possibly suggesting that the solid-liquid interface is not as perfect as in the theoretical model. Under all of the conditions investigated, predicted errors are smaller with compression waves than with shear waves.     

Sorting out the value of spectroscopic tools to assess the Colletotrichum acutatum impact in olive cultivars with different susceptibilities

The olive tree (Olea europaea L.) can be affected by Colletotrichum acutatum, causing a loss of yield and quality of the final products, whilst the incidence of this fungal infection depends on several factors, including cultivar susceptibility. Thus, the effect of C. acutatum infection in cultivars displaying different susceptibilities to this fungal disease (‘Galega Vulgar’ ‐ susceptible, ‘Cobrançosa’ ‐ moderately susceptible, ‘Picual’ ‐ tolerant) has been assessed through spectrophotometric methods and HPLC, while the FTIR spectra of the cuticles have been concomitantly registered, resorting to the ATR accessory. With the support of multivariate analysis, these spectra allowed to discriminate olives with distinct infection times, besides retrieving evidences concerning the different susceptibility of each cultivar, while these observations were reinforced by the spectrophotometric and chromatographic methods. Furthermore, the assessment of the phenolic profile evidenced individual compounds in the distinct cultivars, so as their variations in response to the fungal infection.     

Bounds for the Kirchhoff index of regular graphs via the spectra of their random walks

Using probabilistic tools, we give tight upper and lower bounds for the Kirchhoff index of any d‐regular N‐vertex graph in terms of d, N, and the spectral gap of the transition probability matrix associated to the random walk on the graph. We then use bounds of the spectral gap of more specialized graphs, available in the literature, in order to obtain upper bounds for the Kirchhoff index of these specialized graphs. As a byproduct, we obtain a closed‐form formula for the Kirchhoff index of the d‐dimensional cube in terms of the first inverse moment of a positive binomial variable. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Development of a switchable multidimensional/comprehensive two-dimensional gas chromatographic analytical system

In this study, a new system for analysis using a dual comprehensive two-dimensional gas chromatography/targeted multidimensional gas chromatography (switchable GC × GC/targeted MDGC) analysis was developed. The configuration of this system not only permits the independent operation of GC, GC × GC and targeted MDGC analyses in separate analyses, but also allows the mode to be switched from GC × GC to targeted MDGC any number of times through a single analysis. By incorporating a Deans switch microfluidics transfer module prior to a cryotrapping device, the flow stream from the first dimension column can be directed to either one of two second dimension columns in a classical heart-cutting operation. Both second columns pass through the cryotrap to allow solute bands to be focused and then rapidly remobilized to the respective second columns. A short second column enables GC × GC operation, whilst a longer column is used for targeted MDGC. Validation of the system was performed using a standard mixture of compounds relevant to essential oil analysis, and then using compounds present at different abundances in lavender essential oil. Reproducibility of retention times and peak area responses demonstrated that there was negligible variation in the system over the course of multiple heart-cuts, and proved the reliable operation of the system. An application of the system to lavender oil, as a more complex sample, was carried out to affirm system feasibility, and demonstrate the ability of the system to target multiple components in the oil. The system was proposed to be useful for study of aroma-impact compounds where GC × GC can be incorporated with MDGC to permit precise identification of aroma-active compounds, where heart-cut multidimensional GC-olfactometry detection (MDGC-O) is a more appropriate technology for odour assessment.     

Determination of organic compounds from wood combustion aerosol nanoparticles by different gas chromatographic systems and by aerosol mass spectrometry

Organic compounds in atmospheric nanoparticles have an effect on human health and the climate. The determination of these particles is challenged by the difficulty of sampling, the complexity of sample composition, and the trace-level concentrations of the compounds. Meeting the challenge requires the development of sophisticated sampling systems for size-resolved particles and the optimization of sensitive, accurate and simple analytical techniques and methods. A new sampling system is proposed where particles are charged with a bipolar charger and size-segregated with a differential mobility analyzer. This system was successfully used to sample particles from wood pyrolysis with particle sizes 30–100 nm. Particles were analyzed by four techniques: comprehensive two-dimensional gas chromatography–time-of-flight mass spectrometry, gas chromatography–time-of-flight mass spectrometry, gas chromatography–quadrupole mass spectrometry, and aerosol mass spectrometry (aerosol MS). In the chromatographic techniques, particles were collected on a filter and analyzed off-line after sample preparation, whereas in the aerosol MS, particle analysis was performed directly from the particle source. Target compounds of the samples were polyaromatic hydrocarbons and n-alkanes. The analytical techniques were compared and their advantages and disadvantages were evaluated. The sampling system operated well and target compounds were identified in low concentrations.