Concise review of relaxations and approximation algorithms for nonidentical parallel-machine scheduling to minimize total weighted completion times

A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time. Models and relaxations are collected. Most of these problems are NP-hard, in the strong sense, or open problems, therefore approximation algorithms are studied. The review reveals that there exist some potential areas worthy of further research.

Fabrication scheduling on a single machine to minimize the weighted sum of product completion time

In this paper, a fabrication scheduling problem concerning the production of components at a single manufacturing facility was studied, in which the manufactured components are subsequently assembled into a finite number of end products. Each product was assumed to comprise a common component to all jobs and a unique component to itself. Common operations were processed in batches and each batch required a setup time. A product is completed when both its two operations have been processed and are available. The optimality criterion considered was the minimization of weighted flow time. For this scheduling problem, the optimal schedules were described in a weignted shortest processing time first （WSPT） order and two algorithms were constructed corresponding to the batch availability and item availability, respectively.

ABSOLUTE CONTINUITIES OF EXIT MEASURES AND TOTAL WEIGHTED OCCUPATION TIME MEASURES FOR SUPER-α-STABLE PROCESSES

Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xγ and Yγ are discussed.

A New Time-Aware Collaborative Filtering Intelligent Recommendation System

Aiming at the problem that the traditional collaborative filtering recommendation algorithm does not fully consider the influence of correlation between projects on recommendation accuracy,this paper introduces project attribute fuzzy matrix,measures the project relevance through fuzzy clustering method,and classifies all project attributes.Then,the weight of the project relevance is introduced in the user similarity calculation,so that the nearest neighbor search is more accurate.In the prediction scoring section,considering the change of user interest with time,it is proposed to use the time weighting function to improve the influence of the time effect of the evaluation,so that the newer evaluation information in the system has a relatively large weight.The experimental results show that the improved algorithm improves the recommendation accuracy and improves the recommendation quality.

Online Scheduling on Bounded Batch Machines to Minimize the Maximum Weighted Completion Time

We investigate the online scheduling problem on identical parallel-batch machines to minimize the maximum weighted completion time.In this problem,jobs arrive over time and the processing times(of the jobs)are identical,and the batch capacity is bounded.For this problem,we provide a best possible online algorithm with a competitive ratio of(√5+1)/2.Moreover,when restricted to dense-algorithms,we present a best possible dense-algorithm with a competitive ratio of 2.

Assessment and sequencing of air target threat based on intuitionistic fuzzy entropy and dynamic VIKOR

In view of the fact that traditional air target threat assessment methods are difficult to reflect the combat characteristics of uncertain, dynamic and hybrid formation, an algorithm is proposed to solve the multi-target threat assessment problems. The target attribute weight is calculated by the intuitionistic fuzzy entropy(IFE) algorithm and the time series weight is gained by the Poisson distribution method based on multi-times data. Finally,assessment and sequencing of the air multi-target threat model based on IFE and dynamic Vlse Kriterijumska Optimizacija I Kompromisno Resenje(VIKOR) is established with an example which indicates that the method is reasonable and effective.

SOME CENTRAL LIMIT THEOREMS FOR SUPER BROWNIAN MOTION

The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the recurrent case it is a spatially uniform field. The author also give a central limit theorem for the weighted occupation time of the super Brownian motion with underlying dimension number d less than or equal to 3, completing the results of Iscoe (1986).

Predictive-reactive Strategy for Flowshop Rescheduling Problem:Minimizing the Total Weighted Waiting Times and Instability

Due to the fourth revolution experiencing,referred to as Industry 4.0,many production firms are devoted to integrating new technological tools to their manufacturing process.One of them,is rescheduling the tasks on the machines responding to disruptions.While,for static scheduling,the efficiency criteria measure the performance of scheduling systems,in dynamic environments,the stability criteria are also used to assess the impact of jobs deviation.In this paper,a new performance measure is investigated for a flowshop rescheduling problem.This one considers simultaneously the total weighted waiting time as the efficiency criterion,and the total weighted completion time deviation as the stability criterion.This fusion could be a very helpful and significant measure for real life industrial systems.Two disruption types are considered:jobs arrival and jobs cancellation.Thus,a Mixed Integer Linear Programming(MILP)model is developed,as well as an iterative predictive-reactive strategy for dealing with the online part.At last,two heuristic methods are proposed and discussed,in terms of solution quality and computing time.

Discussion of Fan et al.’s paper “Gaining effciency via weighted estimators for multivariate failure time data”

In the analysis of correlated data, it is ideal to capture the true dependence structure to increase effciency of the estimation. However, for multivariate survival data, this is extremely

On States of Total Weighted Occupation Times for Superdiffusions

Suppose X is a superdiffusion in R^d with general branching mechanism ￠. and Y_(D) denotes the total weighted occupation time of X in a bounded smooth domain D. We discuss the conditions on ψ to guarantee that Y_(D) has absolutey continuous states. And for particular ψ(z) = z^(l+, 0<B ≤1. we prove that. in the case d<2 + 2/B. Y_^(D) is absolutely continuous with respect to the Lebesgue measure in D. whereas in the case d>2 + 2/B. it is singular. As we know the absolute continuity and singularity of Y_(D have not been discussed before.

Some Properties of Conditioned Superdiffusion

Some properties of a conditioned superdiffusion are investigated. By a basic property we obtain for it, a class of linear additive functionals, so-called weighted occupation time, is studied. At last, we get an interesting result about its extinctive property.

Rejoinder for Gaining effciency via weighted estimators for multivariate failure time data

We thank all the discussants for their interesting and stimulating contributions. They have touched various aspects that have not been considered by the original articles.

Regularity of the Density for the Total Weighted Occupation Measure of Super-Brownain Motion

Let （Xt） be a super-Brownian motion in a bounded domain D in R^d. The random measure Y^D（.） = ∫o^∞ Xt（.）dt is called the total weighted occupation time of （Xt）. We consider the regularity properties for the densities of a class of yD. When d = 1, the densities have continuous modifications. When d ≥ 2, the densities are locally unbounded on any open subset of D with positive y D （dx）-measure.

Discussion on “Gaining Effciency via Weight Estimators for Multivariate Failure Time Data” by Fan, Zhou and Chen

The survival analysis literature has always lagged behind the categorical data literature in developing methods to analyze clustered or multivariate data. While estimators based on

Outboard abnormal noise source localization method with curved surface projection based on time delay matching and weighting criterion

An improved localization method consisting of ＂filtering-time delay estimationhyperbolic localization＂ is proposed. Combining the empirical mode decomposition（EMD）and time delay estimation method based on generalized average magnitude difference function,the original signals are decomposed into intrinsic mode function（IMF） components. The energy distribution criterion and spectrum consistency criterion are used to select the IMFs, which can represent the physical characteristics of the source signal. Several sets of signals are applied to estimate the time delay, and then a vector matching criterion is proposed to select the correct time delay estimation. Considering the hydrophones location, a shell model is established and projected to a plane according to the quadrant before the hyperbolic localization. Results of mooring and sailing tests show that the proposed method improves the localization accuracy,and reduces the error caused by time delay estimation.

Timing and hamming weight attacks on minimal cost encryption scheme

The timing and Hamming weight attacks on the data encryption standard （DES） cryptosystem for minimal cost encryption scheme is presented in this article. In the attack, timing information on encryption processing is used to select and collect effective plaintexts for attack. Then the collected plaintexts are utilized to infer the expanded key differences of the secret key, from which most bits of the expanded secret key are recovered. The remaining bits of the expanded secret key are deduced by the correlations between Hamming weight values of the input of the S-boxes in the first-round. Finally, from the linear relation of the encryption time and the secret key＇s Hamming weight, the entire 56 bits of the secret key are thoroughly recovered. Using the attack, the minimal cost encryption scheme can be broken with 2^23 known plaintexts and about 2^21 calculations at a success rate a 〉 99%. The attack has lower computing complexity, and the method is more effective than other previous methods.