恶化率与工件无关的线性加工时间调度问题

讨论恶化率与工件无关的线性加工时间调度问题 .对于工件间具有平行链约束 ,目标函数为极小化最大完工时间的单机问题 ,分别就链不允许中断和链允许中断两种情况给出了最优算法 .对于工件间没有优先约束 ,目标函数为极小化完工时间和的平行机问题 ,证明了工件按基本加工时间不减排列可以得到最优调度 .     

具有优先约束的单机随机排序问题

讨论工件的加工时间为常数,机器发生随机故障的单机随机排序问题,目标函数极小化工件的加权完工时间和的数学期望最小.考虑两类优先约束模型.在第一类模型中,设工件间的约束为串并有向图.证明了模块M的ρ因子最大初始集合I中的工件优先于模块中的其它工件加工,并且被连续加工所得的排序为最优排序,从而将Lawler用来求解约束为串并有向图的单机加权总完工时间问题的方法推广到机器发生随机故障的情况.在第二类模型中,设工件间的约束为出树优先约束.证明了最大家庭树中的工件优先于家庭树中其它的工件加工,并且其工件连续加工所得到的排序为最优排序并给出了最优算法.     

有根森林优先约束的单机随机排序问题

讨论单机随机排序问题,目标函数为确定工件的排列顺序使工件的加权完工时间和的数学期望最小.设工件间的优先约束为有根森林,机器发生随机故障.对此情况,给出了多项式时间的最优算法.     

极小化最大提前完工费用的可中断排序问题

讨论了带截止期限的$n$个工件在单机上加工,工件间存在优先约束,在允许机器空闲的条件下,确定一个工件的可中断排序,极小化最大提前完工费用.首先考虑两种特殊情形:(1)截止期限相同,存在优先约束;(2)截止期限任意,不存在优先约束.针对两种情形分别给出了时间复杂度为$O(n^2)$的算法.在此基础上,考虑普遍情形,即截止期限任意,存在优先约束,也给出了一个时间复杂度为$O(n^2)$的算法.由于工件不允许延迟,问题可能会无可行排序,需先对问题的可行性进行讨论.     

具有凸资源约束的单机指数学习效应问题

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.     

非线性最优化一个可行序列等式约束二次规划算法

本文针对非线性不等式约束优化问题,提出了一个新的可行序列等式约束二次规划算法．在每次迭代中,该算法只需求解三个相同规模且仅含等式约束的二次规划(必要时求解一个辅助的线性规划),因而其计算工作量较小．在一般的条件下,证明了算法具有全局收敛及超线性收敛性．数值实验表明算法是有效的．     

工件间具有串并有向图约束的单机随机排序问题

研究机器发生随机故障的单机排序问题,其中工件间的优先约束为串并有向图,目标函数为极小化加权完工时间和,证明了此问题多项式时间可解,并给出了多项式时间算法.     

一种双目标带约束工件成类的平行机器调度启发式规则

提出了一种快速而有效的启发式规则(fam ily slack,简称FSLACK),来求解极小化总延误时间和极小化最大完工时间两个目标,工件按产品类型成组,带模具数量约束的平行机器生产调度问题.本文提出的FSLACK与EDD、LPT及SLACK进行了比较.随机订单的测试结果表明,本文提出的启发式规则在求解双目标带约束工件成类的平行机器调度问题上是有效的.这表明该算法可以应用在成型加工业的现场作业调度.     

点带约束成本的最短路问题

本文提出了点带约束成本的最短路问题,证明了该问题是ＮＰ－完全的,并利用动态规划给出了一个伪多项式算法,对所有顶点约束成本相同的情况,给出了一个时间复杂性为Ｏ（ｍｎ＾２）的算法,对最小点成本最短路问题,给出了一个时间复杂性为Ｏ（ｎ＾２）的算法。     

机器和工人都有加工资质约束的平行机排序问题研究

研究一类新型的平行机排序问题, 即在机器和工人都是必需的加工资源并且都有加工资质约束的情况下, 如何在一组平行机上进行工件排序(或称调度)以最小化时间表长C_max. 将研究工件加工时间均为单位时间的情况, 通过建立网络流模型以及采用二分搜索技术, 可以在多项式时间内精确地求解上述问题, 算法复杂度为O(n^{3}logn). 同时提供了一种基于双重动态柔性选择\,(DDFS)\,策略的启发式算法,可以获得较好的排序效果, 算法复杂度为O(n^{2}).     

Minimizing the weighted number of tardy jobs and maximum tardiness in relocation problem with due date constraints

The relocation problem addressed in this paper is to determine a reconstruction sequence for a set of old buildings, under a limited budget, such that there is adequate temporary space to house the residents decanted during rehabilitation. It can be regarded as a resource-constrained scheduling problem where there is a set of jobs to be processed on a single machine. Each job demands a number of resources for processing and returns probably a different number of resources on its completion. Given a number of initial resources, the problem seeks to determine if there is a feasible sequence for the successful processing of all the jobs. Two generalizations of the relocation problem in the context of single machine scheduling with due date constraints are studied in this paper. The first problem is to minimize the weighted number of tardy jobs under a common due date. We show that it is NP-hard even when all the jobs have the same tardy weight and the same resource requirement. A dynamic programming algorithm with pseudo-polynomial computational time is proposed for the general case. In the second problem, the objective is to minimize the maximum tardiness when each job is associated with an individual due date. We prove that it is strongly NP-hard. We also propose a pseudo-polynomial time dynamic programming algorithm for the case where the number of possible due dates is predetermined.     

Johnson’s rule,composite jobs and the relocation problem

Two-machine flowshop scheduling to minimize makespan is one of the most well-known classical scheduling problems. Johnson’s rule for solving this problem has been widely cited in the literature. We introduce in this paper the concept of composite job, which is an artificially constructed job with processing times such that it will incur the same amount of idle time on the second machine as that incurred by a chain of jobs in a given processing sequence. This concept due to Kurisu first appeared in 1976 to deal with the two-machine flowshop scheduling problem involving precedence constraints among the jobs. We show that this concept can be applied to reduce the computational time to solve some related scheduling problems. We also establish a link between solving the two-machine flowshop makespan minimization problem using Johnson’s rule and the relocation problem introduced by Kaplan. We present an intuitive interpretation of Johnson’s rule in the context of the relocation problem.     

On the single machine serial batching scheduling problem to minimize total completion time with precedence constraints, release dates and identical processing times

We consider the single machine, serial batching, total completion time scheduling problem with precedence constraints, release dates and identical processing times in this paper. The complexity of this problem is reported as open in the literature. We provide an O(n⁵) time algorithm to solve this problem.     

考虑任务优先约束的同类岸桥作业调度优化

分析了以箱组为任务对象QCSP与以整贝为任务对象QCSP的异同,指出前者更能均衡各岸桥作业负荷,并减少船舶装卸作业时间。考虑到岸桥具有作业效率差异的特点,将其视为同类平行机调度问题,同时结合任务优先约束、岸桥作业不可相互穿越与安全距离等特有约束,建立了更加符合实际的以箱组为任务对象的岸桥作业调度混合整数规划模型,其优化目标是最小化装卸作业的makespan。针对模型求解的复杂度,设计了一种遗传算法,对算法搜索空间进行了讨论,并推导了问题的低界。实验算例表明所建立的模型能够反映岸桥作业调度过程中作业效率差异及任务优先约束现象,其算法能够在允许的运算时间内获得稳定的满意解,并且优化结果要全面优于以整贝为任务对象QCSP的调度方案。     

An Analysis of Partially Clairvoyant Scheduling

Real-time scheduling problems confront two issues not addressed by traditional scheduling models, viz., parameter variability and the existence of complex relationships constraining the executions of jobs. Accordingly, modeling becomes crucial in the specification of scheduling problems in such systems. In this paper, we analyze scheduling algorithms in Partially Clairvoyant Real-time scheduling systems and present a new dual-based algorithm for the feasibility problem in the case of strict relative constraints. We also study the problem of online dispatching in Partially Clairvoyant systems and show that the complexity of dispatching is logarithmically related to the complexity of the schedulability problem.     

A monotone approximation algorithm for scheduling with precedence constraints

We provide a monotone O(m^2/3)-approximation algorithm for scheduling related machines with precedence constraints.     

一类具有资源限制的调度问题

研究了具有线性退化及学习效应作用下的单台机器调度问题,对于工件的到达时间是其资源消耗量的正的严格单调递减函数时,考虑了总资源消耗量限定情形下求最大完工时间最小化问题给出了最优算法.     

具有机器适用限制的分布式置换流水车间问题的模型与算法

考虑具有机器适用限制的多个不同置换流水车间的调度问题. 机器适用限制指的是每个工件只能分配到其可加工工厂集合. 所有置换流水车间拥有的机器数相同但是具有不同的加工能力. 首先, 针对该问题建立了基于位置的混合整数线性规划模型; 进而, 对一般情况和三种特殊情况给出了具有较小近似比的多项式时间算法. 其次, 基于NEH方法提出了启发式算法NEHg, 并给出了以NEHg为上界的分支定界算法. 最后, 通过例子说明了NEHg启发式算法和分支定界算法的计算过程, 并进行大量的实验将NEHg与NEH算法结果进行比较, 从而验证了NEHg算法的有效性.     

An exact algorithm for the precedence-constrained single-machine scheduling problem

This study proposes an efficient exact algorithm for the precedence-constrained single-machine scheduling problem to minimize total job completion cost where machine idle time is forbidden. The proposed algorithm is based on the SSDP (Successive Sublimation Dynamic Programming) method and is an extension of the authors’ previous algorithms for the problem without precedence constraints. In this method, a lower bound is computed by solving a Lagrangian relaxation of the original problem via dynamic programming and then it is improved successively by adding constraints to the relaxation until the gap between the lower and upper bounds vanishes. Numerical experiments will show that the algorithm can solve all instances with up to 50 jobs of the precedence-constrained total weighted tardiness and total weighted earliness–tardiness problems, and most instances with 100 jobs of the former problem.     

带有链优先序的分批排序问题

本文首次就带有优先序的分批排序问题进行了讨论，目标函数为最大完工时间．当优先序为链，一条链上的工件个数为饨，而其它链的工件个数为常数，分批的容量B大于等于链的条数，在这种情况下，问题为多项式可解的．文中并讨论了几种特殊情况的多项式算法．