Hierarchical decomposition is one of the most important methods of dealing with the optimization of large, complex systems. A complex overall problem is reduced into a set of manageable approximate problems or subproblems, these are solved and the solutions used to construct a solution of the original problem.An important class of complex systems is provided by most manufacturing firms, which may be characterized by decision subsystems dealing with finance, personnel, marketing and manufacturing operations. They may have several plants and warehouses, with a large variety of machines and equipment devoted to producing a large number of different products. Moreover, they are subject to deterministic as well as stochastic discrete events, including the acquisition of new equipment, the hiring and layoff of personnel, and frequent machine setups, failures, and repairs.In practice, and by sheer necessity, these systems are managed hierarchically. The early literature provides little justification for the practice other than sheer necessity. To go beyond, it is necessary to show how close to optimal the approximating hierarchical policies are, especially in uncertain environments.SethJ and Zhang's excellent book presents a new hierarchical approach, providing just such a justification for a class of stochastic manufacturing systems in which decisions must be made to optimize an objective function and in which events occur at different time-scales. For example, changes in demand may occur far more slowly than breakdowns and repairs of production machines. In systems of this type, longer-term decisions such as those dealing with capital expansion can be based on the average existing production capacity and an appropriately-modified objective function. These decisions can be expected to be nearly optimal even though the shorter-term capacity fluctuations have been ignored. Once the long-term decisions are in hand, the simpler problem of obtaining production rates can be solved for. Multilevel decisions constructed in this manner are shown by Sethi and Zhang to be asymptotically optimal as the average time between successive short-term events becomes much smaller than that between successive long-term events. It is shown that the order of deviation of the cost of the hierarchical solution from the optimal cost is small. The striking novelty of the approach is that this is done without solving for the optimal solution.Sethi and Zhang formulate various models of manufacturing systems with failure-prone machines that face uncertain demands as stochastic dynamic optimization problems. Partial characterization of their solutions is provided when possible, along with their hierarchical decomposition based on event frequencies. The asymptotic optimal solutions resulting from the decomposition are constructed, along with associated error bounds.
In this note, we will prove that for commuting ergodic measure preserving transformations R,S and T, ifRT 1, ST-I and TR -~ are also ergodic, then the limit 1 lira N Y~=I fl(R"x)fz(S"x)fa(T"x)exists in D-norm. The method used in this note was developed by CONZE, FURSTENBERG, LESIGNE and WEISS. 1991 Mathematics Subject Classification: 28D20.
Previous studies have indicated that some food items and nutrients are associated with uric acid metabolism in humans. However, little is known about the role of dietary patterns in hyperuricaemia. We designed this case-control study to evaluate the associations between dietary patterns and newly diagnosed hyperuricaemia in Chinese adults. A total of 1422 cases and 1422 controls were generated from 14 538 participants using the 1:1 ratio propensity score matching methods. Dietary intake was assessed using a validated self-administered FFQ. Dietary patterns were derived by factor analysis. Hyperuricaemia was defined as concentrations of serum uric acid higher than 7 mg/dl (416·5 μmol/l) for men and 6 mg/dl (357 μmol/l) for women. Three dietary patterns were derived by factor analysis: sweet pattern; vegetable pattern; animal foods pattern. The animal foods pattern characterised by higher intake of an animal organ, seafood and processed meat products was associated with higher prevalence of newly diagnosed hyperuricaemia (P for trend<0·01) after adjustment. Compared with the participants in the lowest quartile of the animal foods pattern, the OR of newly diagnosed hyperuricaemia in the highest quartile was 1·50 (95 % CI 1·20, 1·87). The other two dietary patterns were not associated with the prevalence of newly diagnosed hyperuricaemia after adjustment. In conclusion, a diet rich in animal organ, seafood and processed meat products is associated with higher prevalence of newly diagnosed hyperuricaemia in a Chinese population. Further cohort studies and randomised controlled trials are required to clarify these findings.
Prevalence of both metabolic syndrome (MS) and hyperuricemia are increasing. However, findings regarding their relationships are inconsistent. We aimed to explore correlations between MS and hyperuricemia in a large Chinese population, emphasizing the impacts from gender and age. Data analyses were performed in 17,762 subjects randomly recruited from Tianjin municipality in China. Hyperuricemia was defined as serum uric acid (SUA) >420 μmol/L for men, >360 μmol/L for women. MS was diagnosed by the consensus criterion released in 2009 from a joint collaboration between American Heart Association and other organizations. MS was also diagnosed by Chinese Diabetes Society (CDS) criterion. Total hyperuricemic prevalence was 12.16%, with male significantly higher than female. Total MS prevalence by consensus criterion was much higher than by CDS criterion (25.56% versus 14.09%). Correlation coefficients were much greater in women than in men. SUA was significantly positively related with body mass index and waist circumference. Generally, binary logistic regression models disclosed females with high SUA were twice likely to suffer from MS than males. Young females (≤44 years old) with hyperuricemia had the highest odd ratio of 7.857 by consensus criterion; and after further adjustment by body mass index, this odd ratio was 3.040. SUA and MS were much more closely related in females than in males. Young women with hyperuricemia had the highest risk of MS.
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