关于P|s_(ij)|C_(max)问题的LPT算法

１引言带相关调整时间的极小化最大完工时间的平行机排序问题可叙述如下:要在ｍ台平行机上加工，Ｊｊ的工时为Ｐｊ，若Ｊｊ紧接在Ｊｊ后加工，则需调整时间ｓｉｊ，目标是求最优排序使工件尽早完工。我们利用Ｇｒａｈａｍ［１］等提出的三参数。问７来表示排序问题。例如。表示工件有到达时间的极小化最大延迟的单机排序问题。本文所考虑的问题则用。来表示，它是由半导体生产的最后阶段提炼出来的。在此阶段，大批集成电路要用检测设备检验以确定它们是否合格，以便把不合格的工件拣出来。但它们要在各自对应的温度下才能检测，为了达到特…     

一个多项式时间可解的自由作业排序问题

一个多项式时间可解的自由作业排序问题俞国胜（上海大学理学院数学系，上海２０１８００）１引言和记号自由作业（ｏＰｅｒｌｓｈｏＰ）排序问题是：有ｎ个工件Ｊ一《ＪＩ，人，··，人｝和。台机器Ｍ一｛ＭＩ，ＭＺ，…；Ｍｔｎ｝，每个工件Ｊｊ需要在机器Ｍｉ上加工，...     

一台机器在加工时间相同准备时间可控时的Lmax问题

一组ｎ个工件需在一台机器上加工，工件ｊ所需的加工时间，应交工时间、准备时间分别为ｐｊ、ｄｊ、ｒｊ＾０，准备时间可压缩量为ｘｊ，０≤ａｊ≤ｒｊ＾０，压缩权因子为ωｊ由最大延误Ｊｍａｘ和压缩费用∑ωｊｘｊ可构成文中（Ｐ１）－（Ｐ３）三个排序问题，在ｄｊ＝０的条件下，引文「１」的作者证明了（Ｐ１）、（Ｐ３）为强ＮＰ－Ｃ的。本文在ｄｊ任意，ｐｊ＝ωｊ＝１的条件下，对（ｐ１）－（Ｐ３）给出了一个伪多项式时间     

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.     

无关机上极小化求和问题的平行分批排序(英文)

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)≤p_(ik)(i=1,…,m;1≤j≠k≤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,…,m;j=1,…,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.     

单机最优交货期决策及工件排序

本文考虑n个独立工件在一台机器上加工的排序问题,每个工件J_i的交货期设置为d_i=kP_i~α(α≥1),目标是寻找工件最优加工时间乘子及工件最优排序S(?),使工件完工时间与交货期的最大偏差最小。给出寻找最优加工时间乘子k(?)及工件最优排序S(?)的方法。     

单位工件的平行机并行分批在线排序问题的算法

本文研究一类批容量有界的并行分批、平行机在线排序问题。模型中有n个相互独立的工件J={J₁,…,J_n}要在m台批处理机上加工。批处理机每次可同时加工至多B(Bj(1≤j≤n)的到达时间为r_j,加工时间为1,工件是否会到达事先未知,而只有等到工件的到达时间才能获知它的到达。目标为最小化工件的最大完工时间。针对该排序问题,本文设计了两个竞争比均达到最好可能的在线算法。     

具有恶化效应和凸资源分配关系的单机排序问题

研究工件加工时间具有恶化效应和凸资源关系的单机排序问题,其中工件的实际加工时间是其正常的加工时间,工件开工时间(具有恶化效应)及消耗资源量的函数。目标为在最大完工时间(总完工时间、总等待时间、完工时间总绝对差与等待时间总绝对差)小于或等于给定常数的条件下找到工件的最优排序和最优的资源分配使工件的总资源消耗量最少。在单机状态下,证明了此问题是多项式时间可解的,并给出了求解该问题的算法和数值实例。     

有关单机两代理排序问题的两个结果

研究了两个单机两代理排序问题. 在第一个两代理排序问题中, 代理A的目标函数为极小化所有工件的加权完工时间总和, 代理B的目标函数为极小化最大工件费用. 在第二个两代理排序问题中, 代理A的目标函数为极小化所有工件的加权完工时间总和, 代理B的目标函数为极小化所有工件的最大完工时间. 证明了第一个问题是强NP-难的, 改进了已有的一般意义NP-难的结果; 对第二个问题给出了一个与现有的动态规划算法不同的动态规划算法.     

一类具有学习效应和安装时间的单机排序问题

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。     

A permutation flow-shop scheduling problem with convex models of operation processing times

The paper is an extension of the classical permutation flow-shop scheduling problem to the case where some of the job operation processing times are convex decreasing functions of the amounts of resources (e.g., financial outlay, energy, raw material) allocated to the operations (or machines on which they are performed). Some precedence constraints among the jobs are given. For this extended permutation flow-shop problem, the objective is to find a processing order of the jobs (which will be the same on each machine) and an allocation of a constrained resource so as to minimize the duration required to complete all jobs (i.e., the makespan). A computational complexity analysis of the problem shows that the problem is NP-hard. An analysis of the structure of the optimal solutions provides some elimination properties, which are exploited in a branch-and-bound solution scheme. Three approximate algorithms, together with the results of some computational experiments conducted to test the effectiveness of the algorithms, are also presented. This revised version was published online in June 2006 with corrections to the Cover Date.     

Shop scheduling problems with multiprocessor tasks on dedicated processors

The computational complexity of shop scheduling problems with multiprocessor tasks on dedicated processors is investigated. The objective is makespan minimization. Preemption of tasks is not allowed. For open and flow-shop problems with three stages, complete classifications into polynomial solvable and NP-hard problems are given. These classifications depend on the compatibility structures of the problems. Furthermore, results for open-shop problems with unit processing times are derived. Finally, it is shown that most of the special cases of the job-shop problem which are polynomially solvable remain polynomially solvable in the multiprocessor task situation.Supported by the Deutsche Forschungsgemeinschaft, Project JoPTAG.     

含有批处理机的三机流水作业加工总长问题的计算复杂性

研究含有批处理机的三台机器流水作业加工总长问题的计算复杂性.不仅考虑了批处理机容量有限的情形,还考虑了批处理机容量无限的情形.证明了当第二台机器是批处理机、其余两台机器是单机时,该问题是NP困难的.至此,含有批处理机的三台机器流水作业加工总长问题在所有情形下的计算复杂性得到了解决.     

A variable neighbourhood search for hybrid flow-shop scheduling problem with rework and set-up times

This paper deals with hybrid flow-shop scheduling problem with rework. In this problem, jobs are inspected at the last stage, and poorly processed jobs were returned and processed again. Thus, a job may visit a stage more than once, and we have a hybrid flow-shop with re-entrant flow. This kind of a shop may occur in many industries, such as final inspection system in automotive manufacturing. The criterion is to minimize the makespan of the system. We developed a 0–1 mixed-integer program of the problem. Since the hybrid flow-shop scheduling problem is NP-hard, an algorithm for finding an optimal solution in polynomial time does not exist. So we generalized some heuristic methods based on several basic dispatching rules and proposed a variable neighbourhood search (VNS) for the problem with sequence-dependent set-up times and unrelated parallel machines. The computational experiments show that VNS provides better solutions than heuristic methods.     

有关流水作业问题的若干结果

我们给出有关流水作业问题的若干结果，并讨论有待研究的一些问题．     

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。     

A Mixed-Integer Goal-Programming Formulation of the Standard Flow-Shop Scheduling Problem

Until recently, the majority of models used to find an optimal sequence for the standard flow-shop problem were based on a single objective, typically makespan. In many applications, the practitioner may also want to consider other criteria simultaneously, such as mean flow-time or throughput time. As makespan and flow-time are equivalent criteria for optimizing machine idle-time and job idle-time, respectively, these additional criteria could be inherently considered as well. The effect of job idle-time, measuring in-process inventory, could be of particular importance.This paper presents an extension of an earlier model developed by the authors, formulating the generalized N job, M machine standard flow-shop problem as a mixed-integer goal-programming model. The formulation was empirically tested through a comparison of the generated optimal solutions to their mathematically derived counterparts. For this, a special flow-shop problem with certain permutation properties was selected. In addition, a randomly chosen problem was solved to show the general applicability of the derived formulation.The model allows the incorporation of the makespan as well as the mean flow-time criteria, instead of optimization being based on a single objective.     

多台机器流水作业中存在调整时间的Lot—streaming问题

多台机器流水作业的Lot-streaming问题（简称LS）,以往的研究都不考虑调整时间,固定分批数,寻找最优分批大小;本文对机器引入调整时间,研究同时决定最优分批数及分批大小,并给出了相应最优算法。     

Reduction of job-shop problems to flow-shop problems with precedence constraints

We study the problem of scheduling N independent jobs in a job-shop environment. Each job must be processed on M machines according to individual routes. The objective is to minimize the maximum completion time of the jobs. First, the job-shop problem is reduced to a flow-shop problem with job precedence constraints. Then, a set of flow-shop algorithms are modified to solve it. To evaluate the quality of these heuristics, several lower bounds on the optimal solution have been computed and compared with the heuristic solutions for 3040 problems. The heuristics appear especially promising for job-shop problems with ‘flow-like’ properties.