Gomory integer programs

 The set of all group relaxations of an integer program contains certain special members called Gomory relaxations. A family of integer programs with a fixed coefficient matrix and cost vector but varying right hand sides is a Gomory family if every program in the family can be solved by one of its Gomory relaxations. In this paper, we characterize Gomory families. Every TDI system gives a Gomory family, and we construct Gomory families from matrices whose columns form a Hilbert basis for the cone they generate. The existence of Gomory families is related to the Hilbert covering problems that arose from the conjectures of Seb?. Connections to commutative algebra are outlined at the end. Received: May 17, 2001 / Accepted: February 7, 2002 Published online: April 24, 2003 RID="⋆" ID="⋆" Research partially supported by NSF grant DMS-0100141.     

Convergence analysis of the local defect correction method for diffusion equations

Summary. This paper is concerned with the convergence analysis of the local defect correction (LDC) method for diffusion equations. We derive a general expression for the iteration matrix of the method. We consider the model problem of Poisson's equation on the unit square and use standard five-point finite difference discretizations on uniform grids. It is shown via both an upper bound for the norm of the iteration matrix and numerical experiments, that the rate of convergence of the LDC method is proportional to H ² with H the grid size of the global coarse grid. Mathematics Subject Classification (2000):65N22, 65N50     

Holding costs under push or pull conditions - The impact of the Anchor Point

Holding costs are traditionally determined from the investment in physical stock during a cycle. An alternative approach instead derives holding costs from Net Present Value (NPV) functions. It is known that applying both frameworks to the same system can lead to different holding cost valuations, but little explanation has been offered. By introducing the Anchor Point in a model, this paper shows, for four different systems, that traditional holding cost models (implicitly) assume pull conditions, while current NPV approaches model push conditions. This explains in part the differences between the methods. It is shown that the Anchor Point concept allows the construction of NPV models under pull conditions, giving results in better correspondence with traditional models. The traditional framework is restricted to pull conditions and important considerations could be easily overlooked, leading to wrong valuations of holding costs. NPV seems superior as such considerations are automatically incorporated. The application to multi-echelon inventory systems provides interesting insights on the roles of echelon stocks and lead-times, and offers potential for future research.     

Using rheometry to determine nucleation density in a colored system containing a nucleating agent

A new suspension-based rheological method was applied to experimentally study the crystallization of a nucleating agent (NA) filled isotactic polypropylene. This method allows for determination of point nucleation densities where other methods fail. For example, optical microscopy can fail because nucleation densities become too high to be counted (materials with effective NA) or crystallites are not easily visible (colored materials), while differential scanning calorimetry does not allow the effect of flow to be studied. Both quiescent and mild-shear-induced crystallization were investigated. The results show that the addition of a nucleating agent increases the nucleation density by six decades for quiescent crystallization. The effect of shear on crystallization in the presence of a nucleating agent was assessed, and it is demonstrated that, at least for this system, the effect of shear is much smaller than the effect of the nucleating agent.     

Digital simulation as an aid to sample scheduling in a routine laboratory for liquid chromatography

A computer model is described to aid decision-making in a routine laboratory for liquid chromatography. The managerial demand was to reduce the delay times of the samples in the laboratory despite an increasing sample input. Knowledge derived from records on the laboratory and from the experience of the laboratory staff is used to develop a simulation model of the laboratory. The model is applied to study the effects of several factors on the performance of the laboratory in order to trace the bottlenecks.     

Effect of alcohol consumption on whole-body protein turnover in healthy adults

The aim of the study was to investigate the whole-body protein turnover, either before or after continuous, moderate ethanol-induced oxidative stress by red wine consumption over a relatively short period in healthy volunteers. Ten healthy adults received an individual regular diet over 20 days. After 10 days, the subjects consumed 0.4 ml ethanol kg(-1) day(-1) as red wine together with dinner over a 10-day period. After 8 and 18 days, respectively, a (15)N-labelled yeast protein was administered in a dosage of 4.2 mg kg(-1) body weight. Urine and faeces were collected over 48 h, respectively. The (15)N-enrichment was measured by isotope ratio mass spectrometry, whereas the protein flux rates were calculated by a three-compartment model. The whole-body protein turnover without/with red wine consumption amounted to 3.73±0.6 and 3.49±0.6 g kg(-1) day(-1) (not significant), respectively. Moderate alcohol consumption does not induce significant short-term changes in the whole-body protein turnover of healthy adults.     

An upper bound on the cycle time of a stochastic marked graph using incomplete information on the transition firing time distributions

Stochastic marked graphs, a special class of stochastic timed Petri nets, are used for modelling and analyzing decision-free dynamic systems with uncertainties in timing. The model allows evaluating the performance of such systems under a cyclic process. Given the probabilistic characteristics of the transition times, the cycle time of the system can be determined from the initial marking. In this contribution, we compute an upper bound on the cycle time of a stochastic marked graph in case the probabilistic characteristics of the transition times are not fully specified.     

Full 3D-3C velocity measurement inside a liquid immersion droplet

We describe a tomographic PIV system for the measurement of the internal flow in a droplet over a stagnant and a moving surface. The flow condition is representative of the flow in an immersion droplet applied in a liquid immersion lithography machine. We quantify the accuracy and reliability of the measurements and compare the shape of the reconstructed measurement volume to shape measurements by means of shadowgraphy. First results indicate the internal flow pattern near the receding contact line, showing a small recirculation region.