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1.
具有指数和位置学习效应的机器排序问题   总被引:1,自引:0,他引:1  
本文考虑指数学习效应和位置学习效应同时发生的新的排序模型.工件的实际加工时间不仅依赖于已经加工过工件正常加工时间之和的指数函数,而且依赖于该工件所在的位置.单机排序情形下,对于最大完工时间和总完工时间最小化问题给出多项式时间算法.此外某些特殊情况下,总权完工时间和最大延迟最小化问题也给出了多项时间算法.流水机排序情形,对最大完工时间和总完工时间最小化问题在某些特殊情形下给出多项时间算法.  相似文献   

2.
张新功 《运筹学学报》2013,17(1):98-105
研究具有加工时间之和学习效应下的一个新型成组排序问题,工件的学习效应是之前工件加工时间之和的函数,组学习效应是成组加工所在的位置的函数. 考虑最大完工时间和总完工时间两个问题,证明了这两个问题都是多项式时间可解的,并提出了相应的多项式时间算法.  相似文献   

3.
同时具有学习效应和退化效应的单机排序问题   总被引:1,自引:0,他引:1  
本文给出了一种同时具有一般化学习效应和退化效应的单机排序模型。在此模型中,工件的实际加工时间既与工件所在位置又与其开工时间有关,且工件在加工之后具有一个配送时间。其中学习效应是工件所在位置的函数,退化效应是工件开工时间的函数。证明了极小化最大完工时间和极小化总完工时间问题是多项式可解的,在满足一定的条件下,极小化加权总完工时间和极小化最大延误问题也是多项式可解的。推广了一些已有文献中的结论。  相似文献   

4.
本文主要讨论了工件加工时间具有学习效应和安装时间的单机排序问题。工件的加工时间不仅与之前已加工完的工件加工时间有关,还与工件的加工位置有关。安装时间是依赖于已加工完的工件的实际加工时间的简单函数,即p-s-d形式。本文证明了极小化最大完工时间,极小化总完工时间,极小化完工时间的平方和问题具有多项式算法,也证明了极小化加权总完工时间,极小化最大延误和极小化总误工问题在某些条件下具有多项式算法。  相似文献   

5.
讨论了工件具有安装时间和学习效应的单机排序问题。安装时间是依赖于已加工完的工件的实际加工时间的简单函数,即p-s-d形式。工件的加工时间不仅与已完成工件的加工时间有关,还与工件的加工位置有关。证明了极小化最大完工时间,极小化完工时间k总和,极小化完工时间k次幂的和是多项式可解的,另外还证明了满足一定条件下的极小化加权完工时间和,极小化最大延误和极小化延迟时间和问题是多项式可解的。  相似文献   

6.
考虑带有退化效应和序列相关运输时间的单机排序问题.工件的加工时间是其开工时间的简单线性增加函数.当机器单个加工工件时,极小化最大完工时间、(加权)总完工时间和总延迟问题被证明是多项式可解的,EDD序对于极小化最大延迟问题不是最优排序,另外,就交货期和退化率一致情形给出了一最优算法.当机器可分批加工工件时,分别就极小化最大完工时间和加权总完工时间问题提出了多项式时间最优算法.  相似文献   

7.
研究带有准备时间的单机学习效应模型,其中工件加工时间具有指数时间学习效应,即工件的实际加工时间是已经排好的工件加工时间的指数函数。学习效应模型考虑工件的实际加工时间同时依赖于工件本身的加工时间和已加工工件的累计加工时间,目标函数为最小化总完工时间。这个问题是NP-难的,提出了一个数学规划模型来求解该问题的最优解。通过分析几个优势性质和下界,提出分支定界算法来求解此问题,并设计启发式算法改进分支定界算法的上界值。通过仿真实验验证了分支定界算法在求解质量和时间方面的有效性。  相似文献   

8.
在工业生产中,随着员工操作技能的熟练程度的增加,对于相同的任务越往后加工,所花的时间将会减少。 同时,为了尽早完工,管理者也会考虑给加工工件分配一定量的额外资源来缩短工件加工时间。 本文基于以上实例,讨论了工件的实际加工时间既具有学习效应又依赖所分配资源的单机排序问题。 在问题中,假设工件的学习效应是之前已加工工件正常加工时间和的指数函数。 同时随着分配给工件资源量的增加,工件的实际加工时间呈线性减少,所需费用呈线性增加。对这一排序模型,主要探讨以下五个目标函数:最小化最大完工时间与资源消耗量总费用的和;最小化总完工时间与资源消耗量总费用的和;最小化加权总完工时间与资源消耗量总费用的和;最小化总提前、总延误、总共同交货期与资源消耗量总费用的和以及最小化总提前、总延误、总松弛交货期与资源消耗量总费用的和。 本文对前三个目标函数相应的排序问题给出了多项式时间可求解的算法。 对后两个目标函数所涉及的排序问题借助于指派问题分别给出了时间复杂性为O(n3)的算法。  相似文献   

9.
研究在所有工件的正常加工时间均相同的情况下具有指数学习效应和凸资源约束的单机排序问题.给出了两种模型:在资源消耗总费用有限的情况下,以工件的最大完工时间为目标函数;在工件的最大完工时间有限的情况下,以资源消耗总费用为目标函数.求两种模型下的最优排序和最优资源分配,使得目标函数最小.证明这两个问题都是多项式时间可解的,并给出了相应的算法.  相似文献   

10.
孙丽  马卫民 《运筹与管理》2020,29(3):125-127
本文研究了成组技术下带恶化和综合学习效应的排序问题,工件的加工时间带综合学习效应。对最小化时间表长问题,我们给出了多项式算法,并且证明了带一致关系的最小化总完工时间问题也是多项式可解的。  相似文献   

11.
In this paper we consider the single machine scheduling problems with exponential sum-of-logarithm-processing-times based learning effect. By the exponential sum-of-logarithm-processing-times based learning effect, we mean that the processing time of a job is defined by an exponent function of the sum of the logarithm of the processing times of the jobs already processed. We consider the following objective functions: the makespan, the total completion time, the sum of the quadratic job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.  相似文献   

12.
The paper deals with the single machine scheduling problems with a time-dependent learning effect and deteriorating jobs. By the effects of time-dependent learning and deterioration, we mean that the processing time of a job is defined by function of its starting time and total normal processing time of jobs in front of it in the sequence. It is shown that even with the introduction of a time-dependent learning effect and deteriorating jobs to job processing times, the single machine makespan minimization problem remain polynomially solvable. But for the total completion time minimization problem, the classical shortest processing time first rule or largest processing time first rule cannot give an optimal solution.  相似文献   

13.
In this paper, we analyse the single machine maximum lateness minimization scheduling problem with the processing time based aging effect, where the processing time of each job is described by a non-decreasing function dependent on the sum of the normal processing times of preceded jobs. The computational complexity of this problem was not determined. However, we show it is strongly NP-hard by proving the strong NP-hardness of the single machine maximum completion time minimization problem with this aging model and job deadlines. Furthermore, we determine the boundary between polynomially solvable and NP-hard cases.  相似文献   

14.
In this paper, we analyse the parallel machine makespan minimization problem with the general sum of processing time based learning or aging effects. First, we prove that an optimal solution to the single machine case can be found by priority rules. Next, for the considered parallel machine problem, we construct the exact dynamic programming algorithm that can operate on real-valued job processing times, which is the only exact algorithm for the analysed problem. The computational analysis confirms that it can solve optimally moderate problem instances.  相似文献   

15.
In this paper, we consider the single machine scheduling problems with an actual time-dependent deterioration effect. By the actual time-dependent deterioration effect, we mean that the processing time of a job is defined by increasing function of total actual processing time of jobs in front of it in the sequence. We show that even with the introduction of an actual time-dependent deterioration to job processing times, makespan minimization problem, total completion time minimization problem, the total lateness, and the sum of the quadratic job completion times minimization problem remain polynomially solvable, respectively. We also show that the total weighted completion time minimization problem, the discounted total weighted completion time minimization problem, the maximum lateness minimization problem, and the total tardiness minimization problem can be solved in polynomial time under certain conditions.  相似文献   

16.
In this paper we consider the single-machine scheduling problems with a sum-of-actual-processing-time-based learning effect. By the sum-of-actual-processing-time-based learning effect, we mean that the processing time of a job is defined by a function of the sum of the actual processing time of the already processed jobs. We show that even with the introduction of the sum-of-actual-processing-time-based learning effect to job processing times, the makespan minimization problem, the total completion time minimization problem, the total completion time square minimization problem, and some special cases of the total weighted completion time minimization problem and the maximum lateness minimization problem remain polynomially solvable, respectively.  相似文献   

17.
In this paper we consider the single machine scheduling problem with exponential learning functions. By the exponential learning functions, we mean that the actual job processing time is a function of the total normal processing times of the jobs already processed. We prove that the shortest processing time (SPT) rule is optimal for the total lateness minimization problem. For the following three objective functions, the total weighted completion time, the discounted total weighted completion time, the maximum lateness, we present heuristic algorithms according to the corresponding problems without exponential learning functions. We also analyse the worst-case bound of our heuristic algorithms. It also shows that the problems of minimizing the total tardiness and discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.  相似文献   

18.
In this paper, we analyse the single processor maximum completion time (makespan) minimization problem with distinct release dates of jobs and the sum-of-processing time-based learning effect. We prove that the considered problem is strongly NP-hard, if, in addition to jobs with the same learning ratio, there are jobs with constant job processing times. Such jobs are not affected by learning and model, for instance, required system upgrades or training courses.  相似文献   

19.
This paper considers single machine scheduling problems where the processing time of a job increases as a function of its position in the sequence. In this model, the later a given job is scheduled in the sequence, the longer its processing time. It is shown that the optimal schedule may be very different from that of the classical version of the problem. We introduce polynomial solutions for the makespan minimization problem, the sum of completion times minimization problem and the sum of earliness penalties minimization problem. For two resource constrained problems, based on the analysis of the problems, the optimal resource allocation methods are presented, respectively.  相似文献   

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