It is shown that these four types of single machine scheduling problems can be modeled as an assignment problem by mathematical programming method , thus these four types of problems can be solved in polynomial time 用数学规划的方法证明了四类多准则下的单机排序问题可以转化为指派问题，从而这四类问题都多项式时间可解。
This paper continues to survey the progress on semi on - line algorithms on parallel machine scheduling problems and studies the relation between different semi on line scheduling problems 摘要继续介绍半在线平行机排序问题的研究进展。主要介绍第二类、第三类半在线模型。研究两个（或两个以上）半在线模型间关系：复合与限制。文章最后给出了一些待研究的问题。
Fifthly , we use the two models to study the dynamic single - machine scheduling problem rj , chains , prmp wj ( 1 - e - acj ) and develop on - line optimal dispatching rules , which consider only available information R ， ， prec ， pr呷}艺玛( l一。一ac “ )的动态在线调度问题，同样给出了在中断一恢复和两种中断一安装重复模型下的只考虑当前可用信息的在线调度规则
This paper mainly focuses on the air sequencing problem in terminal area . by means of the single - machine scheduling method , the practical problem is reformulated into the cumulative traveling salesman problem with ready times ( ctsr - rt ) 本文主要针对终端区空中交通流量管理中的飞机排序问题，运用单机排序方法，将其转化为一带准备时间的累积旅行商问题( ctsp ? rt ) 。
In this paper we review the new development of scheduling in practice , espacially the machine scheduling with material handling device ( the robotic cell scheduling problem , the automated guided vehicles scheduling problem etc . ) and the hoist scheduling problem 对排序问题的研究在实际应用中的新发展，特别是具有材料搬运装置的机器排序问题和抓钩排序问题作了综述。
We presented a series of heuristic algorithms ga ( 0 < a < 1 ) for single machine scheduling to maximize the expectation of the number of early jobs . the heuristic algorithm ga is suitable for computer data handling , and is useful in practice purpose 对极大化期望按划完工工件数为目标的单台机排序问题，给出了一系列启发式算法g _ ( 0 1 ) ，该算法直观可行，适合用计算机处理，具有一定的实际应用价值。
The main creative results are as follows : 1 . aiming at the limitations of ga on coding while applied to machine scheduling problems , the paper proposed the code expression of job - machine based , the coding is not subjected to the restrictions and is free of modification . 2 主要有如下创新成果：一、针对遗传算法求解最小化完工时间的机器调度问题时编码存在的局限性，提出了基于工件-机器的组合编码方案，该方案不受约束条件的限制，也不需要进行修正。
3 ) the on - line scheduling problem with constrains relationship is studied . we use generalized preemption models to study the dynamic single - machine scheduling problems of minimizing total weighted completion time and develop on - line optimal dispatching rules , which consider only available information 给出了在一般化可中断模型下，考虑任务之间存在优先约束关系时，具有任意的和未知的任务到达时间的最小化加权总完工时间的单机动态排序问题的在线调度规则。
According to the number of processors , scheduling problem can be grouped as single - machine scheduling problem and multi - machine scheduling problem . according to whether the job ' s processing time , released time and the surroundings of the processors are deterministic or stochastic , scheduling problem can be grouped as deterministic scheduling problem and stochastic scheduling problem . according to whether the parameters of the jobs are given before - hand , scheduling problem can be grouped as static scheduling problem and dynamic scheduling problem 按处理机个数将排序问题分为：单机排序问题和多处理机排序问题；根据任务加工时间和到达时间以及处理机的工作环境等数据是确定的或服从某种随机分布可分为：确定性排序问题和随机排序问题；根据所有任务的参数是否是预先给定的可分为：静态排序问题和动态排序问题。
Thirdly , integrating bell - type scheduling investigation of domestic and overseas documents , the paper defines optimized scheduling production of bell - type annealing process as the problem of parallel machine scheduling with resource - constrained and multi - step working procedure , whose optimized function of objective function is given also . furthermore , the author constructs bell - type optimized scheduling model by means of the way combing discrete event simulation with algorithm of intelligent optimization 本文在综合国内外对于罩式炉调度研究的基础上，将罩式炉退火过程优化排产定义为资源受限多步工序并行机器调度问题，并定义了优化目标评价函数；将面向对象的离散事件建模仿真方法和智能优化方法相结合建立了退火炉优化排产模型。
