极小化最大提前完工时间的两平行机排序问题

讨论了在两台同型平行机上,加工带截止期限的n个工件,在机器可空闲条件下,确定一个工件排序,使得最大提前完工时间最小.由于工件不允许延迟,问题可能会无可行排序.先讨论问题的可行性,通过子集和问题归约,证明了判定问题的可行性是NP-complete的.如果问题可行,接着讨论了问题的复杂性,通过划分问题归约,证明了其是NP-complete的.最后,考虑了工件加工时间相等的特殊情形,提出了一个算法在多项式时间内获得最优排序.     

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}).     

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.     

区间图上可带负权的2-中位选址问题

本文研究了区间图上可带负权的2-中位选址问题.根据目标函数的不同,可带负权的$p-$中位选址问题($p\geq 2$)可分为两类：即 MWD 和 WMD 模型;前者是所有顶点与服务该顶点的设施之间的最小权重距离之和,后者是所有顶点与相应设施之间的权重最小距离之和.在本篇论文中,我们讨论了区间图上可带负权2-中位选址问题的两类模型,并分别设计时间复杂度为$O(n^2)$的多项式时间算法.     

无关机上极小化求和问题的平行分批排序（英）

本文我们考虑了无关机上的平行分批排序问题.对于批容量无限的平行批排序模型,目标是极小化总完工时间,我们对$p_{ij}\leq p_{ik}$ $(i=1, \cdots, m; 1\leq j\neq k\leq n)$这种一致性的情况设计了多项式的动态规划算法.对于批容量有限的平行批排序模型,我们讨论了$p_{ij}=p_{i}$ $(i=1, \cdots, m; j=1,\cdots, n)$这种情况, 当不考虑工件可被拒绝时,对极小化加权总完工时间的排序,我们给出了其最优算法;当考虑工件可被拒绝时,对极小化被接收工件的加权总完工时间加上被拒绝工件的总拒绝费用的排序,我们设计了一拟多项时间算法.     

一个约束乘积最大问题的强多项式时间算法

本文讨论了约束乘积最大问题最优解的结构特征,在此基础上给出了一个计算时间为O(n2)的强多项式时间算法,并且对于单边约束的情形给出了复杂度更低(O(nlnn))的强多项式时间算法.     

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.     

连续型单参数指数族参数的经验Bayes检验函数的收敛速度

对独立同分布样本情形的连续型单参数指数族的单边假设检验问题,在线性损失下 导出了单调的Bayes检验函数,构造了相应的经验Bayes(EB)检验函数. 在一定条件下, 获得的经验Bayes检验函数的收敛速度可任意接近$O(n^{-1})$.最后给出了满足定理条件的两个例子.     

具有指数和位置学习效应的机器排序问题

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.     

具有时间与位置相关的两类平行机排序问题

研究带有维修时间限制的时间和位置效应平行机排序问题,涉及同型机和非同类机两种机器类型.工件的实际加工时间同时受到位置效应和时间效应影响,且机器具有维修限制.目标函数由机器负载,总完工时间与总等待时间组成.非同类机情形下,通过将排序问题转化为指派问题,给出多项式时间算法,其算法的时间复杂度为O(n~(k+2))/((k-1)!).同型机情形下通过转化目标函数,使用匹配算法得出排序问题的多项式时间解,其时间复杂度为O((2n+m+n log n)n~(k-1))/((k-1)!).     

基于修正的第二类Chebyshev结点的Newman型有理插值函数对|x|的逼近

Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary sets of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods,one could establish the exact order of approximation for some special nodes.In the present note we consider the sets of interpolation nodes obtained by adjusting the Chebyshev roots of the second kind on the interval [0,1] and then extending this set to [-1,1] in a symmetric way.We show that in this case the exact order of approximation is O（ 1 n 2 ）.     

Extrapolation of Nyström Solutions of Boundary Integral Equations on Non-Smooth Domains

The interior Dirichlet problem for Laplace's equation on a plane polygonal region $\Omega$ with boundary $\Gamma$ may be reformulated as a second kind integral equation on $\Gamma$. This equation may be solved by the Nyström method using the composite trapezoidal rule. It is known that if the mesh has $O(n)$ points and is graded appropriately, then $O(1/n^2)$ convergence is obtained for the solution of the integral equation and the associated solution to the Dirichlet problem at any $x\in \Omega$. We present a simple extrapolation scheme which increases these rates of convergence to $O(1/n^4)$ .     

Single machine bicriteria scheduling with equal-length jobs to minimize total weighted completion time and maximum cost

Bicriteria scheduling problems are of significance in both theoretical and applied aspects. It is known that the single machine bicriteria scheduling problem of minimizing total weighted completion time and maximum cost simultaneously is strongly NP-hard. In this paper we consider a special case where the jobs have equal length and present an $O(n^{3}\log n)$ algorithm for finding all Pareto optimal solutions of this bicriteria scheduling problem.     

Maximization Problems in Single Machine Scheduling

Problems of scheduling n jobs on a single machine to maximize regular objective functions are studied. Precedence constraints may be given on the set of jobs and the jobs may have different release times. Schedules of interest are only those for which the jobs cannot be shifted to start earlier without changing job sequence or violating release times or precedence constraints. Solutions to the maximization problems provide an information about how poorly such schedules can perform. The most general problem of maximizing maximum cost is shown to be reducible to n similar problems of scheduling n?1 jobs available at the same time. It is solved in O(mn+n ²) time, where m is the number of arcs in the precedence graph. When all release times are equal to zero, the problem of maximizing the total weighted completion time or the weighted number of late jobs is equivalent to its minimization counterpart with precedence constraints reversed with respect to the original ones. If there are no precedence constraints, the problem of maximizing arbitrary regular function reduces to n similar problems of scheduling n?1 jobs available at the same time.     

Parallel machine scheduling with a convex resource consumption function

We consider some problems of scheduling jobs on identical parallel machines where job-processing times are controllable through the allocation of a nonrenewable common limited resource. The objective is to assign the jobs to the machines, to sequence the jobs on each machine and to allocate the resource so that the makespan or the sum of completion times is minimized. The optimization is done for both preemptive and nonpreemptive jobs. For the makespan problem with nonpreemptive jobs we apply the equivalent load method in order to allocate the resources, and thereby reduce the problem to a combinatorial one. The reduced problem is shown to be NP-hard. If preemptive jobs are allowed, the makespan problem is shown to be solvable in O(n²) time. Some special cases of this problem with precedence constraints are presented and the problem of minimizing the sum of completion times is shown to be solvable in O(n log n) time.     

优先序约束的排序问题：基于最大匹配的近似算法

本文研究具有加工次序约束的单位工件开放作业和流水作业排序问题,目标函数为极小化工件最大完工时间。工件之间的加工次序约束关系可以用一个被称为优先图的有向无圈图来刻画。当机器数作为输入时,两类问题在一般优先图上都是强NP-困难的,而在入树的优先图上都是可解的。我们利用工件之间的许可对数获得了问题的新下界,并基于许可工件之间的最大匹配设计近似算法,其中匹配的许可工件对均能同时在不同机器上加工。对于一般优先图的开放作业问题和脊柱型优先图的流水作业问题,我们在理论上证明了算法的近似比为$2-\frac 2m$,其中$m$是机器数目。     

优先序约束的排序问题：基于最大匹配的近似算法

本文研究具有加工次序约束的单位工件开放作业和流水作业排序问题，目标函数为极小化工件最大完工时间。工件之间的加工次序约束关系可以用一个被称为优先图的有向无圈图来刻画。当机器数作为输入时，两类问题在一般优先图上都是强NP-困难的，而在入树的优先图上都是可解的。我们利用工件之间的许可对数获得了问题的新下界，并基于许可工件之间的最大匹配设计近似算法，其中匹配的许可工件对均能同时在不同机器上加工。对于一般优先图的开放作业问题和脊柱型优先图的流水作业问题，我们在理论上证明了算法的近似比为$2-\frac 2m$，其中$m$是机器数目。     

Two machine preemptive scheduling problem with release dates,equal processing times and precedence constraints

We consider a scheduling problem with two identical parallel machines and n jobs. For each job we are given its release date when job becomes available for processing. All jobs have equal processing times. Preemptions are allowed. There are precedence constraints between jobs which are given by a (di)graph consisting of a set of outtrees and a number of isolated vertices. The objective is to find a schedule minimizing mean flow time. We suggest an O(n²) algorithm to solve this problem.The suggested algorithm also can be used to solve the related two-machine open shop problem with integer release dates, unit processing times and analogous precedence constraints.     

Single Machine Group Scheduling with Two Ordered Criteria

The problem of scheduling jobs on a single machine is considered. It is assumed that the jobs are classified into several groups and the jobs of the same group have to be processed contiguously. A sequence independent set-up time is incurred between each two consecutively scheduled groups. A schedule is specified by a sequence for the groups and a sequence for the jobs in each group. The quality of a schedule is measured by two critera ordered by their relative importance. The objective is to minimize the maximum cost, the secondary criterion, subject to the schedule is optimal with respect to total weighted completion time, the primary criterion. A polynomial time algorithm is presented to solve this bicriterion group scheduling problem. It is shown that this algorithm can also be modified to solve the single machine group scheduling problem with several ordered maximum cost criteria and arbitrary precedence constraints.