需要安装时间的两台多功能机排序问题的计算复杂性

提出需要安装时间的多功能机排序问题,一般情况下,这是NP-困难的;主要研究只有两台机器时一些特殊情况下的计算复杂性.根据加工集合为机器全集的工件组数的不同,分别给出多项式时间算法和分枝定界算法.对各工件组的工件数和加工时间都相等的情况,给出一个多项式时间的最优算法-奇偶算法,从而证明此问题是多项式时间可解的.     

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。     

具有不可用区间且工件可拒绝下的单机重新排序问题的近似方案

本文考虑了机器具有不可用区间且工件可拒绝下的单机重新排序问题,在该问题中,给定一个工件集需在一台机器上加工,每个工件有自己的加工时间和权重,且对该工件集目标函数为极小化总加权完工时间的排序计划已给定,根据该排序计划中每个工件的完工时间已确定每个工件的承诺交付时间。然而,在工件正式开始加工前,原计划用于加工的某段时间区间因临时用于检修机器而导致机器在该时间区间不再可用,需要对工件重新排序。为了确保在新的重新排序中,工件的延误成本不致太大,决策者可以选择拒绝部分工件,但需支付相应的拒绝费用。任务是确定接受工件集和拒绝工件集,并将接受的工件在考虑机器具有不可用区间的条件下重新排序使得接受工件集的总加权完工时间,总拒绝费用及赋权最大延误之和最小。该问题是NP-困难的,对此给出了伪多项式时间动态规划精确算法,利用稀疏技术设计了完全多项式时间近似方案。     

极小化最大完工时间的单机分批加工问题

本文考虑极小化最大完工时间的单机分批加工问题．设有n个工件和一台批加工机器．每个工件有一个释放时间和一个加工时间．批加工机器可以同时加工b(b相似文献   

具有m台通用机和两台专用机的Qm＋2／rj／Cmax问题的改进LS算法

对于实践中存在的机器加工速度不同的,具有两组任务的优化排序问题进行了讨论,在经典的LS算法的基础上提出了一种改进的LS算法,利用＂首先空闲＂准则选择机器,按照工件的到达顺序安排工件,讨论了将两组工件安排在两台速度不同的专用机,m台速度相同的通用机上的Cmax问题,其中工件具有调整时间或安装时间,且工件的调整时间或安装时间均不超过其加工时间的α倍.目标是在最短的时间内完成所有给定的任务.得到了利用该近似算法所得的解TLS与最优解T＊在不同条件下的两个估计,并且证明了这两个估计是紧的。     

工件可自由下线最小化总完工时间的平行分批排序问题

考虑工件可自由下线最小化总完工时间的有界平行分批排序问题. 在该问题中, 一台平行批机器可以同时处理 b 个工件作为一个平行批, 这里b 是批容量, 一个批的加工时间等于分配给这个批的工件的最大加工时间. 关于可自由下线工件, 每一个工件的完工时间等于包含这个工件的批的开工时间与工件的加工时间的和. 也就是, 如果一个批B 有一个开工时间S, 那么包含在批B 中的每一个工件J_j 的开工时间定义为S, 而它的完工时间定义为S+p_j, 这里p_j 是工件J_j 的加工时间. 对此问题, 首先研究最优排序的一些性质. 然后, 基于这些性质, 给出一个运行时间为O(n^{b (b-1)})的动态规划算法.     

基于退化效应的两台机器流水作业可拒绝排序

考虑了工件具有退化效应的两台机器流水作业可拒绝排序问题,其中工件的加工时间是其开工时间的简单线性增加函数.每个工件或者被接收,依次在两台流水作业机器上被加工,或者被拒绝但需要支付一个确定的费用.考虑的目标是被接收工件的最大完工时间加上被拒绝工件的总拒绝费用之和.证明了问题是NP-难的,并提出了一个动态规划算法.最后对一种特殊情况设计了多项式时间最优算法.     

工件可转包加工的排序问题研究

研究工件可以转包加工的单台机排序问题: 有n个工件, 在零时刻已经到达一个单台机处, 每个工件可以由加工者自有的单台机器加工或者转包给其他机器加工. 如果工件被转包加工, 那么其完工时间等于在自有机器上的加工时间, 而产生的加工费用与在自有机器上加工的费用不同. 假设被转包加工的工件的完工时间和加工费用与转包加工机器的总负载没有关系.目标函数是最小化工件最大完工时间与总加工费用的加权和. 该问题已经被证明是NP-难的. 最后给出该问题的伪多项式时间最优算法, 并且提出一个完全多项式时间近似方案(FPTAS).     

工件可自由下线最小化总完工时间的有界平行分批排序

考虑工件可自由下线最小化总完工时间的有界平行分批排序问题.在该问题中,一台平行批机器可以同时处理b个工件作为一个平行批,这里b是批容量,一个批的加工时间等于分配给这个批的工件的最大加工时间.关于可自由下线工件,每一个工件的完工时间等于包含这个工件的批的开工时间与工件的加工时间的和.也就是,如果一个批■有一个开工时间S,那么包含在批■中的每一个工件乃的开工时间定义为S,而它的完工时间定义为S+p_j,这里p_j是工件J_j的加工时间.对此问题,首先研究最优排序的一些性质.然后,基于这些性质,给出一个运行时间为O(n~(b(b-1))的动态规划算法.     

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.     

Scheduling parallel machines with inclusive processing set restrictions and job release times

We consider the problem of scheduling a set of jobs with different release times on parallel machines so as to minimize the makespan of the schedule. The machines have the same processing speed, but each job is compatible with only a subset of those machines. The machines can be linearly ordered such that a higher-indexed machine can process all those jobs that a lower-indexed machine can process. We present an efficient algorithm for this problem with a worst-case performance ratio of 2. We also develop a polynomial time approximation scheme (PTAS) for the problem, as well as a fully polynomial time approximation scheme (FPTAS) for the case in which the number of machines is fixed.     

Approximation algorithms for two-machine flow shop scheduling with batch setup times

In many practical situations, batching of similar jobs to avoid setups is performed while constructing a schedule. This paper addresses the problem of non-preemptively scheduling independent jobs in a two-machine flow shop with the objective of minimizing the makespan. Jobs are grouped into batches. A sequence independent batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. Besides its practical interest, this problem is a direct generalization of the classical two-machine flow shop problem with no grouping of jobs, which can be solved optimally by Johnson's well-known algorithm. The problem under investigation is known to be NP-hard. We propose two O(n logn) time heuristic algorithms. The first heuristic, which creates a schedule with minimum total setup time by forcing all jobs in the same batch to be sequenced in adjacent positions, has a worst-case performance ratio of 3/2. By allowing each batch to be split into at most two sub-batches, a second heuristic is developed which has an improved worst-case performance ratio of 4/3. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.     

带服务器的三台平行机排序问题的复杂性和近似算法

讨论带有两具服务器的三台机的平行机排序问题,在这个问题的实例中,每一个工件都有一个时间长度 安装操作必须要由服务器来完成,每一个服务器在同一时刻只能安装一个工件,用三段式描述表示此问题即为Ｐ３,Ｓ２／ｓｉ＝１／Ｃｍａｘ,证明了此问题为ＮＰ－Ｃ的,分别给出了在在线和离线条件下的近似算法,并且估计了算法的最坏情况界。     

Single-machine ready times scheduling with group technology and proportional linear deterioration

Scheduling research has increasingly taken the concept of deterioration into consideration. In this paper, we study a single machine group scheduling problem with deterioration effect, where the jobs are already put into groups, before any optimization. We assume that the actual processing times of jobs are increasing functions of their starting times, i.e., the job processing times are described by a function which is proportional to a linear function of time. The setup times of groups are assumed to be fixed and known. For some special cases of minimizing the makespan with ready times of the jobs, we show that the problem can be solved in polynomial time for the proposed model. For the general case, a heuristic algorithm is proposed, and the computational experiments show that the performance of the heuristic is fairly accurately in obtaining near-optimal solutions. The results imply that the average percentage error of the proposed heuristic algorithm from optimal solutions is less than 3%.     

Nonpreemptive flowshop scheduling with machine dominance

Flowshop scheduling deals with processing a set of jobs through a set of machines, where all jobs have to pass among machines in the same order. With the exception of minimizing a makespan on two machines, almost all other flowshop problems in a general setup are known to be computationally intractable. In this paper we study special cases of flowshop defined by additional machine dominance constraints. These constraints impose certain relations among the job processing times on different machines and make the studied problems tractable.     

A heuristic for scheduling in a two-stage hybrid flowshop with renewable resources shared among the stages

In this paper we propose a heuristic for solving the problem of resource constrained preemptive scheduling in the two-stage flowshop with one machine at the first stage and parallel unrelated machines at the second stage, where renewable resources are shared among the stages, so some quantities of the same resource can be used at different stages at the same time. Availability of every resource at any moment is limited and resource requirements of jobs are arbitrary. The objective is minimization of makespan. The problem is NP-hard. The heuristic first sequences jobs on the machine at stage 1 and then solves the preemptive scheduling problem at stage 2. Priority rules which depend on processing times and resource requirements of jobs are proposed for sequencing jobs at stage 1. A column generation algorithm which involves linear programming, a tabu search algorithm and a greedy procedure is proposed to minimize the makespan at stage 2. A lower bound on the optimal makespan in which sharing of the resources between the stages is taken into account is also derived. The performance of the heuristic evaluated experimentally by comparing the solutions to the lower bound is satisfactory.     

Tabu search for discrete–continuous scheduling problems with heuristic continuous resource allocation

Problems of scheduling non-preemptable, independent jobs on parallel identical machines under an additional continuous renewable resource to minimize the makespan are considered. Each job simultaneously requires for its processing a machine and an amount (unknown in advance) of the continuous resource. The processing rate of a job depends on the amount of the resource allotted to this job at a time. The problem is to find a sequence of jobs on machines and, simultaneously, a continuous resource allocation that minimize the makespan. A heuristic procedure for allocating the continuous resource is used. The tabu search metaheuristic to solve the considered problem is presented. The results produced by tabu search are compared with optimal solutions for small instances, as well as with the results generated by simple search methods – multi-start iterative improvement and random sampling for larger instances.     

A branch and bound based heuristic for makespan minimization of washing operations in hospital sterilization services

In this paper, we address the problem of parallel batching of jobs on identical machines to minimize makespan. The problem is motivated from the washing step of hospital sterilization services where jobs have different sizes, different release dates and equal processing times. Machines can process more than one job at the same time as long as the total size of jobs in a batch does not exceed the machine capacity. We present a branch and bound based heuristic method and compare it to a linear model and two other heuristics from the literature. Computational experiments show that our method can find high quality solutions within short computation time.     

Fuzzy scheduling of job orders in a two-stage flowshop with batch-processing machines

In this paper, we present a mixed-integer fuzzy programming model and a genetic algorithm (GA) based solution approach to a scheduling problem of customer orders in a mass customizing furniture industry. Independent job orders are grouped into multiple classes based on similarity in style so that the required number of setups is minimized. The family of jobs can be partitioned into batches, where each batch consists of a set of consecutively processed jobs from the same class. If a batch is assigned to one of available parallel machines, a setup is required at the beginning of the first job in that batch. A schedule defines the way how the batches are created from the independent jobs and specifies the processing order of the batches and that of the jobs within the batches. A machine can only process one job at a time, and cannot perform any processing while undergoing a setup. The proposed formulation minimizes the total weighted flowtime while fulfilling due date requirements. The imprecision associated with estimation of setup and processing times are represented by fuzzy sets.