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.     

最小化完成时间和加惩罚值和的批调度问题

考虑如下单机并行批调度问题:给定一些工件,每个工件有给定的处理时间以及惩罚值(可以拒绝处理某些工件,惩罚值为拒绝处理工件所付出的代价).给定一个可同时处理多个工件的批处理器.同时处理的工件形成一个批.同一批处理的工件具有相同的开始时间和结束时间,即开始时间加上这一批中所有工件的最大给定处理时间.判断如何选择要处理的工件,给这些工件分批以及给批排序使得目标函数值最小.对目标函数是被处理工件的完成时间之和加上被拒绝工件的惩罚值之和的情况,通过给出一个动态规划算法,证明当批容量为常量时问题是多项式时间可解的.     

具有空闲时间的云制造作业车间调度方法

针对云制造企业的剩余能力利用问题,研究具有空闲时间的车间调度方法.构建云制造作业车间的调度框架,以最小化工期为目标,考虑设备空闲时间,提出工序加工时间序列的确定方法和空闲时间段的更新策略,采用基于工件的精简编码和改进的二阶粒子群算法求解工件最优调度顺序.仿真结果验证了所提出调度方法的可行性.与已有算法的对比分析表明,改进算法具有良好的搜索性能.     

两台等级平行机上部分处理时间已知的半在线调度

工作环境为两台处理速度相同的平行机M1,M2,工件具有两种不同的等级gj=1或2,等级gj=1的工件只能在第1台机器上处理,等级gj=2的工件两台机都能处理.已知等级gj=1的工件的处理时间之和,目标是最小化最大完工时间.主要思路为第一台机器预留出等级gj=1的工件的总处理时间,分析过程中只对等级gj=2的工件进行讨论.文章的三种半在线等级调度问题分别为已知最优处理时间,即已知C opt的情况,可得竞争比大于等于4/3,并有竞争比为4/3的半在线算法;已知工件的最大处理时间,可得竞争比大于等于4/3,同样有算法得出竞争比为4/3;对已知最优处理时间和工件最大处理时间的半在线问题,得到竞争比大于等于6/5,并且找到了相应的算法竞争比小于等于6/5.     

带有线性恶化工件和释放时间的两个代理单机调度问题

研究了带有简单线性恶化工件和释放时间的两个代理单机调度问题. 所有工件在一台机器上加工, 每个代理有各自依赖于自己工件的优化目标. 针对工件释放时间相同与不同两种情况, 研究了有约束的优化模型, 即找到调度最小化一个代理的目标函数而使得另一个代理的目标函数不超过一个给定的上界. 当工件具有相同的释放时间, 我们主要考虑的目标函数有: 总加权完工时间和总加权拖期工件数. 当工件具有不同释放时间, 我们考虑的目标函数有: 最大完工时间、总完工时间以及拖期工件数. 对于每一个问题, 我们分析了问题的计算复杂性. 此外, 对于NP难问题的一些特殊情况本文分析了最优解性质, 基于这些性质给出了最优算法.     

传搁时间约束下的运输与批处理机生产协调调度

针对炼钢模铸系统钢锭高温运作的特点,提出带有传搁时间约束的生产前运输与批处理机生产协调的调度问题.工件的加工时间依赖于其传搁时间,每批工件的加工时间为该批工件中加工时间最大值.目标函数为最小化总完工时间与生产费用的线性组合.通过复杂性分析,证明该问题是强NP难解问题.建立混合整数规划模型,基于动态规划提出两种特殊情况的最优算法,设计原问题的启发式算法并进行最坏情况下性能比分析.实验仿真结果验证了所提出启发式算法的有效性与稳定性.     

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.     

两台流水机器协调分解调度问题

研究钢管加工流程中一类新型两台机器流水车间调度问题,工件在第一台机器上加工后被分解成多个子工件.对于最小化最大完成时间的情况,给出一个多项式时间的最优算法;对于最小化最大完成时间与惩罚费用之和的情况,给出一个拟多项式时间的动态规划算法;对于考虑生产前运输的最小化最大完成时间的情况,分析了问题的复杂性.证明了第一种情况的最优算法可作为后两种情况的2-近似算法.数值实验表明了算法的有效性.     

两台流水机器协调分解调度问题

研究钢管加工流程中一类新型两台机器流水车间调度问题,工件在第一台机器上加工后被分解成多个子工件.对于最小化最大完成时间的情况,给出一个多项式时间的最优算法;对于最小化最大完成时间与惩罚费用之和的情况,给出一个拟多项式时间的动态规划算法;对于考虑生产前运输的最小化最大完成时间的情况,分析了问题的复杂性.证明了第一种情况的最优算法可作为后两种情况的2-近似算法.数值实验表明了算法的有效性.

     

带机器人制造单元的作业车间调度仿真

针对带有机器人制造单元的作业车间调度优化问题, 在若干加工机器上可以加工具有特定加工工序的若干工件, 并且搬运机器人可以将工件在装卸载站与各加工机器间进行搬运. 在实际生产过程中, 由于不确定性, 特别是带有存货的加工单元, 要求工件的完工时间在一个时间窗内, 而不是一个特定的时间点. 因此针对此情况的作业车间, 考虑到其在求解问题过程中的复杂性和约束性等特点, 研究了在时间窗约束下, 目标值为最小化工件完成时间提前量和延迟量的总权重. 提出了一种将文化基因算法与邻域搜索技术(变邻域下降搜索)相结合的改进元启发式算法, 在求得最优目标值的同时, 可得到最优值的工件加工序列及机器人搬运序列. 通过实验结果表明, 所提出的算法有效且优于传统文化基因算法与遗传算法.     

Due date setting with supply constraints in systems using MRP

We propose a new model for quoting due dates in a make-to-order environment where customers request due dates. The model incorporates inventory costs, fill rate issues, and service level issues. In particular, we consider order delay costs that measure the positive difference between the due date requested by the customer and the due date committed by the supplier. The underlying two-stage production model assumes that production is constrained primarily by an uncertain procurement process, as is the case in many assembly systems. This simplification results in a news vendor-like formulation that enables us to obtain a simple approximately optimal due date setting policy that is well suited to MRP environments. The model also yields several interesting policy conclusions. For example, in environments where the importance of service level performance does not reach a certain threshold relative to the importance of order acceptance, the optimal policy is to always quote the requested due date. A special case of our formulation of the problem is to minimize lead-times. However, we show that a lead-time minimization often yields longer quoted due dates than our general formulation.     

Two due date assignment problems with position-dependent processing time on a single-machine

The focus of this study is to analyze single-machine scheduling and due date assignment problems with position-dependent processing time. Two generally positional deterioration models and two frequent due date assignment methods are investigated. The objective functions include the cost of changing the due dates, the total cost of positional weight earliness, and the total cost of the discarded jobs that cannot be completed by their due dates. We conclude that the problems are polynomial time solvable. Significantly enough, after assessing the special case of each problem, this research found out that they can be optimally solved by lower order algorithms.     

Preemptive Scheduling on Uniform Parallel Machines with Controllable Job Processing Times

In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan.     

An Exact Method to Minimize the Number of Tardy Jobs in Single Machine Scheduling

This paper considers the problem of scheduling n jobs on a single machine to minimize the number of tardy (or late) jobs. Each job has a release date, a processing time and a due date. The general case with non-equal release dates and different due dates is considered. Using new and efficient lower bounds and several dominance rules, a branch and bound scheme is proposed based on the definition of a master sequence, i.e. a sequence containing at least one optimal sequence. With this procedure, 95% of 140-job instances are optimally solved in a maximum of one-hour CPU time.     

Comparative study of the applicability of fuzzy multi-objective linear programming models through cost-effective analysis for mold manufacturing

The mold-manufacturing process consists of prototype design, production, assembly, and testing. As products tend to vary, have short due dates, and life cycles, are highly precise and must be responsiveness to customers, production system planning is complex and the relationship between outsourcing capability and in-house capacity is crucial to mold-manufacturing. Differentiation of core operations vs. non-core operations in internal vs. external environments and time control are essential for mold manufacturing when planning production systems. To analyze the cost-effectiveness of capacity planning and its relationship to suppliers, this work applies a novel fuzzy multi-objective linear programming model. Considered factors are order quantity allocation, due dates, manufacturing quantity, capacity, defect rates, back-log, and the purchasing discount. The applicability of three fuzzy theories is assessed using total costs, punishment costs, and crashing costs. Implementation results demonstrate the potentials for cost-effective capacity planning and outsourcing, and identify the applicability of these fuzzy theories to a specific mold-manufacturing case.     

Minimizing the number of late jobs on a single machine under due date uncertainty

We study the problem of minimizing the number of late jobs on a single machine where job processing times are known precisely and due dates are uncertain. The uncertainty is captured through a set of scenarios. In this environment, an appropriate criterion to select a schedule is to find one with the best worst-case performance, which minimizes the maximum number of late jobs over all scenarios. For a variable number of scenarios and two distinct due dates over all scenarios, the problem is proved NP-hard in the strong sense and non-approximable in pseudo-polynomial time with approximation ratio less than 2. It is polynomially solvable if the number s of scenarios and the number v of distinct due dates over all scenarios are given constants. An O(nlog?n) time s-approximation algorithm is suggested for the general case, where n is the number of jobs, and a polynomial 3-approximation algorithm is suggested for the case of unit-time jobs and a constant number of scenarios. Furthermore, an O(n ^s+v?2/(v?1) ^v?2) time dynamic programming algorithm is presented for the case of unit-time jobs. The problem with unit-time jobs and the number of late jobs not exceeding a given constant value is solvable in polynomial time by an enumeration algorithm. The obtained results are related to a min-max assignment problem, an exact assignment problem and a multi-agent scheduling problem.     

Due date assignments and scheduling a single machine with a general earliness/tardiness cost function

We study three different due date assignment problems in scheduling a single machine which differ from each other based upon the objective function and due date assignment method being used. Two different objective functions are considered. The first is a cost function that includes earliness, tardiness and due date assignment penalties and the second is a function that includes penalties due to the number of tardy jobs and due date assignments. We assume that the earliness, tardiness and due date assignment penalties are continuous and non-decreasing functions of the corresponding duration. The goal is to minimize each objective function for two different due date assignment methods. The first is a method in which the assigned due dates are restricted to be equal while the second is a method that allows us to assign different due dates to different jobs.     

Finite capacity scheduling systems: Performance issues and comparisons

This study examines the flowtime, schedule stability and delivery performance results for finite capacity scheduling (FCS) systems. Two common schedule construction approaches, blocked-time and event-driven, are compared. A production shop simulation model facilitates the testing of these two approaches using either internally or externally specified due dates. Also, various due-date dependent loading rules are used in schedule construction. The results show that using the event-driven schedule construction approach along with internally specified due dates works best. Flowtime, flowtime variability and mean tardiness are lower when comparing the event-driven approach to the blocked-time approach as well as when comparing internally to externally set due dates. Schedule stability results are less consistent, with performance being largely a function of the loading rule when the blocked-time approach is used.     

A PSO and a Tabu search heuristics for the assembly scheduling problem of the two-stage distributed database application

The assembly flowshop scheduling problem has been addressed recently in the literature. There are many problems that can be modeled as assembly flowshop scheduling problems including queries scheduling on distributed database systems and computer manufacturing. The problem has been addressed with respect to either makespan or total completion time criterion in the literature. In this paper, we address the problem with respect to a due date-based performance measure, i.e., maximum lateness. We formulate the problem and obtain a dominance relation. Moreover, we propose three heuristics for the problem: particle swarm optimization (PSO), Tabu search, and EDD. PSO has been used in the areas of function optimization, artificial neural network training, and fuzzy system control in the literature. In this paper, we show how it can be used for scheduling problems. We have conducted extensive computational experiments to compare the three heuristics along with a random solution. The computational analysis indicates that Tabu outperforms the others for the case when the due dates range is relatively wide. It also indicates that the PSO significantly outperforms the others for difficult problems, i.e., tight due dates. Moreover, for difficult problems, the developed dominance relation helps reduce error by 65%.