大规模集成电路预烧作业中分批排序问题的数学模型

分批排序(Batch Scheduling)是在半导体生产过程的最后阶段提炼出来的一类重要的排序问题。单机分批排序问题就是n个工件在一台机器上加工,要将工件分批,每批最多可以同时加工B个工件,每批的加工时间等于此批工件中的最大的加工时间。Skutella^[8]1998年把平行机排序的P｜｜∑ω_jC_j和R｜｜∑ω_jC_j表述成二次的0-1整数规划,得到一些令人满意的结果;国内罗守成等^[9]、张倩^[10]给出了单机排序问题1｜｜∑ω_jC_j的数学规划表示,对于用数学规划来研究排序问题是一个很有意义的进展。本文首先介绍总完工时间和最小的带权单机分批排序问题1｜B｜∑ω_jC_j,然后将1｜B｜∑ω_jC_j表示成数学规划的形式,并且用数学规划中的对偶理论证明了SPT序是其特殊情况1｜B=1｜∑C_j的最优解。     

加权折扣单机排序干扰管理模型和算法研究

为解决机器排序中由于干扰事件的发生使初始最优加工时间表无法按计划执行的问题,构建同时考虑原目标和扰动目标的双目标干扰管理模型,对初始最优加工时间表进行调整并对未完工工件进行重排序;在双目标干扰管理模型中,原目标由所有工件的加权折扣完工时间和来度量,扰动目标由重排序后工件完工时间的变化来度量;结合量子比特在表示解的多样性方面的优点和非支配排序遗传算法在处理多目标排序问题上的优点,设计一种量子遗传算法和非支配排序遗传算法相结合的启发式进化算法对构建的模型进行求解。在数值算例中,通过比较若干项针对有效解集的性能指标发现,该混合算法求得的有效解集在多样性和与最优有效前沿的邻近性等方面优于目前得到广泛应用的非支配排序遗传算法,验证了构建的模型和算法对于求解机器排序干扰管理问题的有效性。     

加工能力受限的单机干扰管理研究

针对单机环境下最小化加权折扣加工时间和的排序问题,研究如何应对可预见的干扰事件。由于干扰事件使得机器加工能力受限,初始最优加工时间表不再可行,采用外包的方式来进行干扰管理。构建了排序模型,同时考虑原目标和与初始计划偏离的扰动目标,选择外包工件集并对所有工件进行重排序。为了求解得到的双目标排序问题,基于理想点法设计了一种动态规划算法和量子遗传算法相结合的算法。最后通过一个数值算例说明,该排序模型对于求解加工能力受限的单机干扰管理问题是有效的。     

基于ASRank和MMAS的蚁群算法求解飞机指派问题

本文将航班串的飞机指派问题归结为车辆路径问题,考虑连续航班串之间衔接时间、衔接机场的约束、每架飞机的总飞行时间约束,建立了带有飞行时间约束的车辆路径问题的混合整数规划模型。构造了蚁群系统算法,引入基于排序的蚂蚁系统和最大最小蚂蚁系统算法的信息素更新策略。选取某航空公司7组初始航班串集合进行测试,并对算法中的重要参数进行了分析。实验结果表明,本文设计的模型和算法可以有效地减少连续航班串之间的总衔接时间,在可接受的计算时间内获得满意解。     

考虑加工与运输协同调度的单机排序问题

在考虑加工与运输协同调度的单机排序问题中,每个工件尺寸不同,工件在一台机器加工后,由m辆有容量限制的运输工具运送到同一个顾客处,目标是极小化最后一个送到其顾客的工件的到达时间,本文给出了该问题的一个最优算法,并且证明了该算法的最坏情况界为3/2。     

面向成套订单问题的工艺规划与排序的集成研究

本文从工艺规划与排序的集成优化角度研究了成套订单问题^[1],克服了单独研究工艺规划和排序局部优化的局限性.文章中考虑了同一工件内部各道工序之间存在的优先加工限制,以及工件在不同机器上加工需要转移时间和工序间接连加工需要机器调整时间的情况,建立了成套订单问题的集成排序模型,并提出了针对求解大规模问题的基于遗传算法的启发式算法,最后通过一个算例对所研究的集成排序问题和所提出的算法进行了说明,计算结果表明了算法的有效性.     

等待时间受限的置换流水车间调度启发式算法

针对等待时间受限的置换流水车间调度问题,分析了其可行解与流水车间调度最优解的关系,给出了计算最大完工时间的有向图,证明了等待时间受限的置换流水车间调度问题的可逆性,并以此为基础提出了一种启发式算法.算法首先根据等待时间受限约束与无等待(no-wait)约束的相似特征,生成初始工件序列集;然后利用问题可逆性给出了复杂度为O(n2m)的插入优化机制,进一步优化初始解.数据实验的结果验证了启发式算法的可行性和有效性.     

具有时间转换约束项目网络的时差分析

在传统的网络计划模型中,当所有的紧前工序结束后,当前工序就能够马上开始。但在实践过程中,由于许多工序会受到开始时间的约束,因此工序很少能在满足优先关系约束后的任意时刻开始,而具有时间转换约束的网络则能很好地描述此类问题。本文主要研究在时间转换约束下,不同类型的工序在网络中的时间特性变化情况,并在现有研究基础上,将网络中工序的时间参数由传统的算法转换成具有时间转换约束的时间参数,提出新的机动时间计算公式。最后以案例的形式分析比较传统网络与具有时间转换约束网络的区别,从而体现时间转换约束网络模型的实践价值。     

考虑学习率和搬运时间的人工作业系统生产过程时间组织与优化

在同时考虑员工学习率和运输工序时间的基础上,对该类型人工工序作业系统的批量加工模式生产周期模型及优化问题进行研究。给出批量工件以不同移动方式完成加工的生产周期形式,并详细地对该研究背景下的批量工件以平行顺序移动方式完成加工的生产周期模型进行理论证明。在给定算例的基础上,对仅考虑搬运时间、考虑学习率和搬运时间等两种情况的生产周期进行对比分析。最后,在详细分析工艺工序时间、员工学习率、运输工序时间、增加峰工艺工序员工人数等优化措施对批量工件生产周期优化效果影响的基础上,提出针对不同移动方式完成加工的批量工件进行生产周期优化的策略,为该类型制造系统正确进行现场改善提供可以借鉴的准则。     

三台平行机排序的一个复合半在线问题的算法

本文讨论一个三台平行机半在线排序问题.对预先知道工件的总加工时间和最大的工件的加工时间的复合半在线模型,我们证明了不存在半在线算法,其竞争比为4/3,并给出了一个竞争比为7/5的半在线算法,两者的差距小于0.067.     

一类新型批处理机调度问题的理论分析

钢卷在冷轧生产中,为了改进其性能,需要在罩式炉进行退火,退火过程由加热、保温和降温三段组成,而这三段处理时间由于工艺上的要求不能归结为一个时间,这与传统批处理机调度有明显的差别.对新型批处理机的总加权完成时间最小化问题建立了非线性整数规划模型,开发了基于动态规划的启发式算法.通过理论分析,获得该算法的误差性能比为3.对于三段中的某一段板卷的处理时间相同的情况,证明了启发式算法的误差性能比是2,而且证明是紧界.对于三段中的某二段板卷的处理时间相同的情况,证明了启发式算法是最优算法.对启发式算法扩展到带有任意段的加工时间的一般情况进行了性能分析.     

MINIMIZING TOTAL WEIGHTED COMPLETION TIME ON A SINGLE BATCH PROCESSING MACHINE

We study the problem of scheduling jobs on a single batch processing machine to minimize the total weighted completion time. A batch processing machine is one that can process a number of jobs simultaneously as a batch. The processing time of a batch is given by the processing time of the longest job in the batch. We present a branch and bound algorithm to obtain optimal solutions and develop lower bounds and dominance conditions. We also develop a number of heuristics and evaluate their performance through extensive computational experiments. Results show that two of the heuristics consistently generate high-quality solutions in modest CPU times.     

Single machine scheduling problems with subcontracting options

In this paper, we study a scheduling model as follows: there are n jobs which can be processed in house on a single machine or subcontracted to a subcontractor. If a job is subcontracted, its processing cost is different from the in-house cost and its delivery lead time is a stepwise function of the total processing time of outsourced jobs. Two objective functions are studied (1) to minimize the weighted sum of the maximal completion time and the total processing cost and (2) to minimize the weighted sum of the number of tardy jobs and the total processing cost. For the first problem, we prove that it is NP-hard and get a pseudo-polynomial time algorithm. For the second problem, we prove that it is NP-hard and get a pseudo-polynomial time algorithm for a special case.     

A note on special optimal batching structures to minimize total weighted completion time

A batch is a subset of jobs which must be processed jointly in either serial or parallel form. The algorithmic aspects of the batching scheduling problems have been extensively studied in the literature. This paper presents necessary and sufficient conditions of the existence of optimal batch sequences for the single machine, batching, total weighted completion time scheduling problems on two batching ways: (1) all jobs form one batch; (2) each batch contains a single job. This kind of conditions can help us to recognize some special optimal schedules quickly. Research supported by NSFC (10671183).     

Online scheduling to minimize the total weighted completion time plus the rejection cost

We consider the online scheduling on a single machine, in which jobs are released over time and each job can be either accepted and scheduled on the machine or rejected under a certain rejection cost. The goal is to minimize the total weighted completion time of the accepted jobs plus the total rejection cost of the rejected jobs. For this problem, we provide an online algorithm with a best possible competitive ratio of 2.     

Batch-Processing Scheduling with Setup Times

The problem is to minimize the total weighted completion time on a single batch-processing machine with setup times. The machine can process a batch of at most B jobs at one time, and the processing time of a batch is given by the longest processing time among the jobs in the batch. The setup time of a batch is given by the largest setup time among the jobs in the batch. This batch-processing problem reduces to the ordinary uni-processor scheduling problem when B = 1. In this paper we focus on the extreme case of B = +, i.e. a batch can contain any number of jobs. We present in this paper a polynomial-time approximation algorithm for the problem with a performance guarantee of 2. We further show that a special case of the problem can be solved in polynomial time.     

A note on the complexity of the problem of two-agent scheduling on a single machine

We consider a two-agent scheduling problem on a single machine, where the objective is to minimize the total completion time of the first agent with the restriction that the number of tardy jobs of the second agent cannot exceed a given number. It is reported in the literature that the complexity of this problem is still open. We show in this paper that this problem is NP-hard under high multiplicity encoding and can be solved in pseudo-polynomial time under binary encoding. When the first agent's objective is to minimize the total weighted completion time, we show that the problem is strongly NP-hard even when the number of tardy jobs of the second agent is restricted to be zero.     

Scheduling a single semi-continuous batching machine

This paper addresses a new problem, called semi-continuous batch scheduling, which arises in the heating-operation of tube-billets in the steel industry. Each heating furnace can be regarded as a semi-continuous batching machine, which can handle up to C jobs simultaneously. The jobs in the same batch enter and leave the machine semi-continuously, which differs from the traditional batching machine scheduling where the jobs in same batch have a starting time and a finishing time. In this paper the processing time of a batch depends on the capacity of the semi-continuous batching machine, the longest processing time of jobs in the batch and its size. The objectives are to schedule jobs on the machine so that the makespan and the total completion time are minimized. A schedule for a semi-continuous batching machine consists of a batching and sequencing for the batches. We propose the optimal properties of two different objective functions and present the different dynamic programming algorithms with a running time of O(n²), respectively.     

Single-machine scheduling problems with general truncated sum-of-actual-processing-time-based learning effect

We study single machine scheduling problems with general truncated sum-of-actual-processing-time-based learning effect. In the general truncated learning model, the actual processing time of a job is affected by the sum of actual processing times of previous jobs and by a job-dependent truncation parameter. We show that the single machine problems to minimize makespan and to minimize the sum of weighted completion times are both at least ordinary NP-hard and the single machine problem to minimize maximum lateness is strongly NP-hard. We then show polynomial solvable cases and approximation algorithms for these problems. Computational experiments are also conducted to show the effectiveness of our approximation algorithms.