基于到达时间两台并行机上在线批调度

考虑两台同构并行机上在线批调度问题．每个批具有不确定的到达时间,一旦机器可以利用,要在当前可以利用的批中选择出合适的批,并将其中的工件调度到机器上,且工件在加工过程中不允许中断．目标函数是使调度的最大完成时间最小．给出了一个批在线调度ＲＢＬＰＴ算法,即选择当前批中加工时间之和最大的批按ＬＰＴ 规则调度．另外,利用反证法,对算法的最坏情况进行了分析．     

基于到达时间两台并行机上在线批调度

考虑两台同构并行机上在线批调度问题．每个批具有不确定的到达时间,一旦机器可以利用,要在当前可以利用的批中选择出合适的批,并将其中的工件调度到机器上,且工件在加工过程中不允许中断．目标函数是使调度的最大完成时间最小．给出了一个批在线调度ＲＢＬＰＴ 算法,即选择当前批中加工时间之和最大的批按ＬＰＴ 规则调度．另外,利用反证法,对算法的最坏情况进行了分析．

     

释放时间和工期同序的单机连续型批调度问题

本文研究的连续型批处理机调度问题, 是在钢铁工业管坯的加热过程中提出来的. 工件带有释放时间和工期, 工件进入和离开机器是按周期依次进行的. 本文针对单机连续型批调度问题中工件释放时间和工期同序的情况, 分析了极小化最大拖期和拖期工件数等问题的计算复杂性, 证明了两类问题都是强NP-难的. 对于工件的释放时间和加工时间、工期都同序的特殊情况, 分别给出了能够获得对应问题的最优解的多项式算法.     

极小化加权完工时间和的无界批量机器并行调度问题

考虑无界批量机器并行调度中极小化加权完工时间和问题.设有n个工件和m台批加工同型机.每个工件具有一个正权因子、一个释放时间和一个加工时间.每台机器可以同时加工B≥n个工件.一个批次的加工时间是该批次所包含的所有工件的加工时间的最大者.在同一批次中加工的工件有相同的完工时间,即它们的共同开始时间加上该批次的加工时间.给出了一个多项式时间近似方案(PTAS).     

批处理机上具有两类释放时间的工件集竞争调度问题

研究了两个工件集合竞争在一台批处理机上加工的调度问题,其中每个集合的工件具有一个共同的释放时间.批处理机可以同时加工多个工件作为一批,每批的加工时间为该批工件中加工时间的最大值.基于两类释放时间的大小,针对无界批处理机上最小化一个集合工件的最大完工时间、最大延迟以及总完工时间,使得另一个集合工件的最大完工时间不超过给定上界问题,分别给出了最优求解方法.针对有界批处理机上最小化一个集合工件的最大完工时间,使得另一个集合工件的最大完工时间不超过给定上界问题,证明为一般意义NP-难问题,并给出伪多项式时间最优求解方法.     

具有线性恶化加工时间的调度问题

讨论了工件具有线性恶化加工时间的调度问题.在这类问题中,工件的恶化函数为线性 函数.对单机调度问题中目标函数为极小化最大完工时间加权完工时间和,最大延误以及最大费 用等问题分别给出了最优算法.对两台机器极小化最大完工时间的Flowshop问题,证明了利用 Johnson规则可以得到最优调度.对于一般情况,如果同一工件的工序的加工时间均相等,则 Flowshop问题可以转化为单机问题.     

两阶段流水车间批调度问题的蚁群优化算法

针对差异工件(工件尺寸不同)两阶段流水车间的批处理机调度问题,提出一种以最小化加工时间跨度为目标的蚁群优化算法.根据批中工件在每阶段加工时间的相似程度(标准差衡量),得到一个能够提高批中工件加工时间相似水平的启发式信息.同时,改进蚁群算法的编码方案,并引入局部优化算法来提高优化性能.仿真结果表明,与现有算法相比,该算法在工件规模较大的情况下具有较好的求解性能.     

瓶颈指向的启发式算法求解混合流水车间调度问题

针对以最小化时间表长为目标的复杂混合流水车间调度问题,提出了一种将机器布局和工件加工时间特征紧密结合的启发式算法.首先,充分利用各阶段平均机器负荷一般不相等的特点确定瓶颈阶段,构建初始工件排序.其次,针对在瓶颈阶段前加工时间较短而瓶颈阶段后加工时间相对较长的工件,在第1阶段优先开始加工.同时,在瓶颈阶段前的每一个阶段,每当有工件等待加工或同时完工时,优先选择瓶颈阶段前剩余加工时间最短的工件加工;在瓶颈阶段以及瓶颈阶段之后,则优先选择这台机器后剩余加工时间最长的工件加工.最后,采用工件交换和插入操作改进初始调度.用Carlier和Neron的Benchmark算例测试提出的启发式算法.将计算结果与NEH启发式算法进行了比较,平均偏差降低了0.0555%,表明这个启发式算法是有效的.     

基于佳点集遗传算法求解Job—shop调度问题

1.介绍 Job-shop调度问题(JSSP)是极为困难的带约束组合优化问题,是NP难的。典型的Job-shop调度问题可描述为n个工件要在m台机器上加工,每个工件有其特定的加工工序,每道工序加工时间已知,并符合以下假设: (1)每个机器在同一时刻只能加工一个工件。(2)每个工件的工序事先确定。(3)同一工件的两个工序不可同时进行。(4)不允许抢占式执行,即一个工序执行后就不能中断。(5)机器间传送时间为零。典型的调度目标是确定每个机器上工序的加工顺序和各工序的开始时间,以使完成所有工序所需的时间(Makespan)最少。     

带尺寸约束的二机流水车间生产运输协调博弈调度问题

研究二机流水车间生产运输协调调度问题,当工件在第1台机器加工完成后,由1台带有容量限制的运输车分批次运输到第2台机器加工,运输过程考虑工件尺寸约束,目标函数为最小化最大完工时间.考虑到源于不同客户的工件对机器及运输设备的竞争,以工件为博弈方,工件在生产运输过程中等待时间为策略,各工件完工时间为收益,建立非合作博弈模型.通过将问题转化为马尔可夫决策过程,设计线性逼近值函数的Q-learning算法求解纳什均衡调度.实验结果表明Q-learning算法求得的纳什均衡调度具有较好的全局最优性,从而能够在满足客户的利益下,提高企业的生产效率,实现客户与企业的双赢.     

Machine scheduling with job class setup and delivery considerations

We study machine scheduling problems in which the jobs belong to different job classes and they need to be delivered to customers after processing. A setup time is required for a job if it is the first job to be processed on a machine or its processing on a machine follows a job that belongs to another class. Processed jobs are delivered in batches to their respective customers. The batch size is limited by the capacity of the delivery vehicles and each shipment incurs a transport cost and takes a fixed amount of time. The objective is to minimize the weighted sum of the last arrival time of jobs to customers and the delivery (transportation) cost. For the problem of processing jobs on a single machine and delivering them to multiple customers, we develop a dynamic programming algorithm to solve the problem optimally. For the problem of processing jobs on parallel machines and delivering them to a single customer, we propose a heuristic and analyze its performance bound.     

Batching and scheduling in a multi-machine flow shop

We study the problem of batching and scheduling n jobs in a flow shop comprising m, m≥2, machines. Each job has to be processed on machines 1,…,m in this order. Batches are formed on each machine. A machine dependent setup time precedes the processing of each batch. Jobs of the same batch are processed on each machine sequentially so that the processing time of a batch is equal to the sum of the processing times of the jobs contained in it. Jobs of the same batch formed on machine l become available for a downstream operation on machine l+1 at the same time when the processing of the last job of the batch on machine l has been finished. The objective is to minimize maximum job completion time. We establish several properties of an optimal schedule and develop polynomial time algorithms for important special cases. They are improvements over the existing methods with regard to their generality and time efficiency.     

Strong NP-hardness of the single machine multi-operation jobs total completion time scheduling problem

We consider the single machine multi-operation jobs total completion time scheduling problem. Each job consists of several operations that belong to different families. In a schedule, each family of job operations may be processed in batches with each batch incurring a set-up time. A job completes when all of its operations have been processed. The objective is to minimize the sum of the job completion times. In the literature, the computational complexity of this problem is posed as open. We show that the problem is strongly NP-hard even when the set-up times are common and the processing time of each operation is 0 or 1.     

Heuristics for minimizing total completion time and maximum lateness on identical parallel machines with setup times

This paper aims at minimizing the total completion time together with the maximum lateness. Jobs are processed by parallel machines in batches. A setup is required before processing a batch, which is common for all jobs in the batch. Jobs are continuously processed after the setup time. The processing length of a batch is the sum of the setup time and processing times of the jobs it contains. Due to the availability constraint, the completion time of a job is the time when a batch is totally processed. Considering due dates, the jobs need to be processed in a way that the total completion time and the maximum lateness are minimized. This problem is a kind of NP-hard so first we present a constructive heuristic to solve the problem. Then we propose a genetic algorithm whose initial population is formed by using the heuristic approach. Computational experiments are carried out to evaluate the performance of the proposed algorithms.     

A Stronger Complexity Result for the Single Machine Multi-Operation Jobs Scheduling Problem to Minimize the Number of Tardy Jobs

We consider the single machine multi-operation jobs scheduling problem to minimize the number of tardy jobs. Each job consists of several operations that belong to different families. In a schedule, each family of job operations may be processed in batches with each batch incurring a setup time. A job completes when all of its operations have been processed. The objective is to minimize the number of tardy jobs. In the literature, this problem has been proved to be strongly NP-hard for arbitrary due-dates. We show in this paper that the problem remains strongly NP-hard even when the due-dates are common and all jobs have the same processing time.     

A DP algorithm for minimizing makespan and total completion time on a series-batching machine

This paper studies a bicriteria scheduling problem on a series-batching machine with objective of minimizing makespan and total completion time simultaneously. A series-batching machine is a machine that can handle up to b jobs in a batch and the completion time of all jobs in a batch is equal to the finishing time of the last job in the batch and the processing time of a batch is the sum of the processing times of jobs in the batch. In addition, there is a constant setup time s for each batch. For the problem we can find all Pareto optimal solutions in O(n²) time by a dynamic programming algorithm, where n denotes the number of jobs.     

Approximation algorithms for minimizing the total weighted number of late jobs with late deliveries in two-level supply chains

We study a supply chain scheduling problem in which n jobs have to be scheduled on a single machine and delivered to m customers in batches. Each job has a due date, a processing time and a lateness penalty (weight). To save batch-delivery costs, several jobs for the same customer can be delivered together in a batch, including late jobs. The completion time of each job in the same batch coincides with the batch completion time. A batch setup time has to be added before processing the first job in each batch. The objective is to find a schedule which minimizes the sum of the weighted number of late jobs and the delivery costs. We present a pseudo-polynomial algorithm for a restricted case, where late jobs are delivered separately, and show that it becomes polynomial for the special cases when jobs have equal weights and equal delivery costs or equal processing times and equal setup times. We convert the algorithm into an FPTAS and prove that the solution produced by it is near-optimal for the original general problem by performing a parametric analysis of its performance ratio.     

Unbounded parallel-batching scheduling with two competitive agents

We consider the scheduling problems arising when two agents, each with a family of jobs, compete to perform their respective jobs on a common unbounded parallel-batching machine. The batching machine can process any number of jobs simultaneously in a batch. The processing time of a batch is equal to the maximum processing time of the jobs in the batch. Two main categories of batch processing based on the compatibility of job families or agents are distinguished. In the case where job families are incompatible, jobs from different families cannot be placed in the same processing batch while all jobs can be placed in the same processing batch when job families are compatible. The goal is to find a schedule for all jobs of the two agents that minimizes the objective of one agent while keeping the objective of the other agent below or at a fixed value Q. Polynomial-time and pseudo-polynomial-time algorithms are provided to solve various combinations of regular objective functions for the scenario in which job families are either incompatible or compatible.     

Minimizing Mean Completion Time in a Batch Processing System

We consider batch processing jobs to minimize the mean completion time. A batch processing machine can handle up to $B$ jobs simultaneously. Each job is represented by an arrival time and a processing time. Jobs processed in a batch have the same completion time, i.e., their common starting time plus the processing time of their longest job. For batch processing, non-preemptive scheduling is usually required and we discuss this case. The batch processing problem reduces to the ordinary uniprocessor system scheduling problem if $B=1$. We focus on the other extreme case $B=+\infty$. Even for this seemingly simple extreme case, we are able to show that the problem is NP-hard for the weighted version. In addition, we establish a polynomial time algorithm for a special case when there are only a constant number of job processing times. Finally, we give a polynomial time approximation scheme for the general case.