Journal of Combinatorial Optimization - Nowadays, the rapid development of intelligent navigation systems has profound impacts on the routing of traffic users. With the assistance of these... 相似文献
We consider the problem of scheduling a set of jobs with different processing times and sizes on a single bounded parallel-batch machine with periodic maintenance. Because the machine is in batch-processing model and the capacity is fixed, several jobs can be processed simultaneously in a batch provided that the total size of the jobs in the batch doesn’t exceed the machine capacity. And the processing time of a batch is the largest processing time of the jobs contained in the batch. Meanwhile, the production of each batch is non-resumable, that is, if a batch cannot be completed processing before some maintenance, that batch needs to be processed anew once the machine returns available. Our goal is to minimize the makespan. We first consider two special cases where the jobs have the same sizes or the same processing times, both of which are strongly NP-hard. We present two different approximation algorithms for them and show that these two algorithms have the same tight worst-case ratio of 2. We then consider the general case where the jobs have the arbitrary processing times and arbitrary sizes, for which we propose a 17/5-approximation algorithm.
Lifetime Data Analysis - Time-to-event data are often subject to left-truncation. Lack of consideration of the sampling condition will introduce bias and loss in efficiency of the estimation. While... 相似文献
In this paper, we first propose a dependent Dirichlet process (DDP) model using a mixture of Weibull models with each mixture component resembling a Cox model for survival data. We then build a Dirichlet process mixture model for competing risks data without regression covariates. Next we extend this model to a DDP model for competing risks regression data by using a multiplicative covariate effect on subdistribution hazards in the mixture components. Though built on proportional hazards (or subdistribution hazards) models, the proposed nonparametric Bayesian regression models do not require the assumption of constant hazard (or subdistribution hazard) ratio. An external time-dependent covariate is also considered in the survival model. After describing the model, we discuss how both cause-specific and subdistribution hazard ratios can be estimated from the same nonparametric Bayesian model for competing risks regression. For use with the regression models proposed, we introduce an omnibus prior that is suitable when little external information is available about covariate effects. Finally we compare the models’ performance with existing methods through simulations. We also illustrate the proposed competing risks regression model with data from a breast cancer study. An R package “DPWeibull” implementing all of the proposed methods is available at CRAN.
