The combination of online or semi-online with deterioration jobs has never been researched in scheduling problems. In this paper, two semi-online parallel machine scheduling problems with linear deterioration processi...The combination of online or semi-online with deterioration jobs has never been researched in scheduling problems. In this paper, two semi-online parallel machine scheduling problems with linear deterioration processing time are considered. In the first problem, it is assumed that the deterioration rates of jobs are known in an interval, that is, bj ∈[0, α], where 0 〈α≤ 1 and bj denotes the linear deterioration rate. In the second problem, it is assumed that the largest deterioration rate of jobs is known in advance, that is, b = max1≤j≤n {bj }. For each of the two problems, a heuristic MBLS algorithm is worked out and its worst-case ratio is analyzed. At the same time, the worst-case ratio of the list （LS） algorithm is investigated and it is proved that all the ratios are tight.展开更多
Background: Binary as well as polytomous logistic models are widely used for estimating odds ratios when the exposure of prime interest assumes unordered multiple levels under matched pairs case-control design. In our...Background: Binary as well as polytomous logistic models are widely used for estimating odds ratios when the exposure of prime interest assumes unordered multiple levels under matched pairs case-control design. In our previous studies, we have shown that the use of a polytomous logistic model for estimating cumulative odds ratios when the outcome (response) variable is ordinal (in addition to being polytomous) under matched pairs case-control design. The cumulative odds ratios were estimated based on separate fitting of the model at each of the cutpoint level as compared to less than equal to that level. In this paper we propose an alternative method of estimating the cumulative odds ratios and reanalyze the Los Angeles Endometrial Cancer data in the context of dose levels of conjugated oestrogen exposure and development of endometrial cancer under the matched pair case-control design. Methods: In the present study, the cumulative logit model is fitted using a single multinomial logit model for the data. For this, the full maximum likelihood estimation procedure is adopted. A test for equality of the cumulative odds ratios across the exposure levels is proposed. Results: The analysis revealed that there is a strong evidence of risk for developing endometrial cancer due to oestrogen exposure above each of the three dose level as compared to less than equal to that level. The estimated values at the three cutpoint levels were found to be 6.17, 3.60 and 5.16 respectively. Conclusions: The odds of developing endometrial cancer are very high for the users of any amount of oestrogen, even if it is the least dose, as compared to the non-users.展开更多
考虑带服务等级的三台平行机排序问题.预先赋予每台机器和每个任务一个服务等级(grade of service)标号.每个任务只能被某台服务等级不高于该任务服务等级的机器加工.目标是最小化最大机器完工时间.本文给出了求解这个问题的算法.并证...考虑带服务等级的三台平行机排序问题.预先赋予每台机器和每个任务一个服务等级(grade of service)标号.每个任务只能被某台服务等级不高于该任务服务等级的机器加工.目标是最小化最大机器完工时间.本文给出了求解这个问题的算法.并证明算法的最坏情况界不超过54+12k,其中k是算法中预先给定的迭代次数.已有的算法仅为32.展开更多
文摘The combination of online or semi-online with deterioration jobs has never been researched in scheduling problems. In this paper, two semi-online parallel machine scheduling problems with linear deterioration processing time are considered. In the first problem, it is assumed that the deterioration rates of jobs are known in an interval, that is, bj ∈[0, α], where 0 〈α≤ 1 and bj denotes the linear deterioration rate. In the second problem, it is assumed that the largest deterioration rate of jobs is known in advance, that is, b = max1≤j≤n {bj }. For each of the two problems, a heuristic MBLS algorithm is worked out and its worst-case ratio is analyzed. At the same time, the worst-case ratio of the list （LS） algorithm is investigated and it is proved that all the ratios are tight.
文摘Background: Binary as well as polytomous logistic models are widely used for estimating odds ratios when the exposure of prime interest assumes unordered multiple levels under matched pairs case-control design. In our previous studies, we have shown that the use of a polytomous logistic model for estimating cumulative odds ratios when the outcome (response) variable is ordinal (in addition to being polytomous) under matched pairs case-control design. The cumulative odds ratios were estimated based on separate fitting of the model at each of the cutpoint level as compared to less than equal to that level. In this paper we propose an alternative method of estimating the cumulative odds ratios and reanalyze the Los Angeles Endometrial Cancer data in the context of dose levels of conjugated oestrogen exposure and development of endometrial cancer under the matched pair case-control design. Methods: In the present study, the cumulative logit model is fitted using a single multinomial logit model for the data. For this, the full maximum likelihood estimation procedure is adopted. A test for equality of the cumulative odds ratios across the exposure levels is proposed. Results: The analysis revealed that there is a strong evidence of risk for developing endometrial cancer due to oestrogen exposure above each of the three dose level as compared to less than equal to that level. The estimated values at the three cutpoint levels were found to be 6.17, 3.60 and 5.16 respectively. Conclusions: The odds of developing endometrial cancer are very high for the users of any amount of oestrogen, even if it is the least dose, as compared to the non-users.
文摘考虑带服务等级的三台平行机排序问题.预先赋予每台机器和每个任务一个服务等级(grade of service)标号.每个任务只能被某台服务等级不高于该任务服务等级的机器加工.目标是最小化最大机器完工时间.本文给出了求解这个问题的算法.并证明算法的最坏情况界不超过54+12k,其中k是算法中预先给定的迭代次数.已有的算法仅为32.
