A comparison of mixed integer programming formulations of the capacitated lot-sizing problem

We propose a novel mixed integer programming formulation for the capacitated lot-sizing problem with set-up times and set-up carryover. We compare our formulation to two earlier formulations, the Classical and Modified formulations, and a more recent formulation due to Suerie and Stadtler. Extensive computational experiments show that our formulation consistently outperforms the Classical and Modified formulations in terms of CPU time and solution quality. It is competitive with the Suerie–Stadtler (S&S) formulation, but outperforms all other formulations on the most challenging instances, those with low-capacity slack and a dense jobs matrix. We show that some of the differences in the performance of these various formulations arise from their different use of binary variables to represent production or set-up states. We also show that the LP relaxation of our Novel formulation provides a tighter lower bound than that of the Modified formulation. Our experiments demonstrate that, while the S&S formulation provides a much tighter LP bound, the Novel formulation is better able to exploit the intelligence of the CPLEX solution engine.     

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Abstract

A high-bandwidth optical fibre current sensor has been developed at Salford to monitor the waveform of the driving current pulse feeding into a discharge-pumped excimer laser. The sensor is a conventional intrinsic Faraday effect device but overcomes the normal bandwidth-sensitivity limits because the very large electrical current pulse used to drive the excimer laser allows detectable polarization rotation over a 60 cm length of fibre. The performance of the intrinsic sensor is compared with that of a current-viewing resistor, and of a Be₁₂GeO₂₀ crystal sensor.     

铭琪加特纳维尔癌症关顾中心

正铭琪癌症关顾中心旨在为癌症患者以及他们的家人和朋友提供实际上和情绪上的支援服务。自1996年第一所铭琪中心在爱丁堡成立以来,铭琪癌症关顾中心基金会的规模日益扩展,并透过委托世界知名的建筑师发展一系列开创先河的建筑。不论是刻意还是偶然的,当代建筑有时难免会产生冷漠或拒人于千里之外的观感,但每一所铭琪中心——在格拉斯哥、伦敦抑或香港——都希望营造令人宾至如归的感觉,     

Size-dependent deposition of inhaled nanoparticles in the rat respiratory tract using a new nose-only exposure system

Concerns about the potential health effects of exposure to nanomaterials have led to a growing number of in vivo inhalation toxicity studies using nanoparticle aerosols. Estimates of aerosol deposition within the respiratory tract are important for these studies to enable: (a) the interpretation of the results, in particular, the evaluation of dose–response relationships; (b) comparison with the results of other related studies; and (c) the extrapolation of results from animal models to human. Unfortunately, only a limited number of studies have been undertaken to investigate respiratory tract deposition efficiencies for nano-sized aerosol particles. This is of particular importance as deposition efficiencies are predicted to vary significantly over the nano-size range for some elements of the respiratory tract. In this study, female Wistar-Kyoto rats were exposed in a new design nose-only inhalation exposure system to spark generated radioactive iridium-192 nanoparticle aerosols of four particle sizes chosen to cover the majority of the nano-size range (nominal sizes: 10, 15, 35, and 75 nm). The content of iridium-192 in the lung, head, gastrointestinal tract, and various other organs and tissues was measured. Aerosol deposition efficiencies in the whole respiratory tract and components (head airways, lung, alveolar region, and tracheobronchial region) were estimated and compared with the predictions of the Multiple Path Particle Dosimetry (MPPD) model (v2.11). The experimentally derived deposition efficiencies were broadly consistent with, but typically higher than, model predictions and the results of comparable studies in the literature.

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