无空闲占优机器的加工时间可变流水作业排序

研究了基于实际应用背景提炼出的工件加工时间是其开工时间的线性函数的无空闲流水作业排序问题。在机器分别具有某些优势关系的情形下,探讨了目标函数为极小化最大完工时间和极小化总完工时间之和的情况。对于每种情况,分别给出了工件按某种规则排序为最优序的多项式时间算法。     

两个带有分批费用的平行分批排序问题的算法

本文研究两个带有分批费用的平行分批排序问题.平行分批是将工件集分割成若干批在机器上成批加工,机器可同时加工在一批的多个工件,每批的加工时间等于该批中最大的加工时间.假设每分一批都产生一个固定的分批费用,本文目标是将工件分成若干批且排出各批的加工顺序,使目标值最优.这里假定工件和批处理机都在零时刻到达,一旦开始加工就不允许中断.本文利用动态规划方法分别给出下面两个问题的多项式时间算法:一是最小化总加权完工时间与分批费用之和;二是最小化最大延迟与分批费用之和.     

总迟后相关的两个工况代理的单机排序问题

研究了两个代理的单机排序问题.其中一个代理以工件总迟后相关的为目标函数(总迟后和加权总迟后),第二个代理以最大费用函数为目标函数.排序问题的目标就是寻找一个序列,使得在第二个代理的目标函数不超过给定的上界的情况下,第一个代理的目标函数最小.对于总迟后的情形,并给出拟多项式时间的动态规划算法.当第一个代理中的工件具有相等工期时,考虑了加权总迟后问题,并给出了一个多项式时间算法.最后对于总迟后问题给数值实验.     

工件可拒绝的两个代理排序问题的全多项式时间近似方案

本文研究单处理机上工件可拒绝的两个代理的排序问题。在此问题中,有两个代理A和B,分别有各自的工件集和费用函数。代理A的工件可以被接收,也可以被拒绝,但要支付一定的拒绝费用。代理B的工件要全部接收。代理A的费用函数是他的接收工件的最大完工时间与拒绝工件的拒绝费用之和,代理B的费用函数是他的工件的最大延迟。排序问题的目标是在满足代理B的费用函数不超过一定数量的前提下,使得代理A的费用函数达到最小。对于该问题给出了一个全多项式时间近似方案。     

同时最优化时间表长与总完工时间的双代理单机序列分批排序问题（英文）

本文研究在一台序列分批处理机上同时最优化A代理的时间表长和B代理的总完工时间的双代理排序问题.在序列分批的背景下,工件被分批加工(但不同代理的工件不能在同一批中加工,且每个代理都希望最小化仅依赖于各自工件完工时间的费用函数)且一批的加工时间等于这一批中所有工件的加工时间和.而且在一个新批开始加工前,机器有一个常数的安装时间.此外,根据批容量,序列分批模型又被分成有界模型和无界模型.在本文中,我们对所研究问题的有界模型和无界模型分别给出了一个多项式时间算法.     

同时最优化时间表长与总完工时间的双代理单机序列分批排序问题（英）

本文研究在一台序列分批处理机上同时最优化$A$代理的时间表长和$B$代理的总完工时间的双代理排序问题．在序列分批的背景下，工件被分批加工（但不同代理的工件不能在同一批中加工，且每个代理都希望最小化仅依赖于各自工件完工时间的费用函数）且一批的加工时间等于这一批中所有工件的加工时间和．而且在一个新批开始加工前，机器有一个常数的安装时间．此外，根据批容量，序列分批模型又被分成有界模型和无界模型．在本文中，我们对所研究问题的有界模型和无界模型分别给出了一个多项式时间算法．     

一类具有三重指标的分批排序问题

本文研究现代排序问题一具有三重指标的批容量无限制平行分批排序问题。第一指标为最大延迟,第二指标为最大完工时间,第三指标为关于工件完工时间的任意正规函数。本文通过分析前两个指标最优解的性质给出了此问题的多项式时间算法。     

单台机器排序问题关于加工时间的反问题

本文研究单台机器总完工时间排序问题关于加工时间的反问题,研究尽量"小"地调整工件的加工时间使给定工件的加工次序成为最优的排序。我们考虑尽量"小"地调整是分别使最大带权相对离差的绝对值为最小、使总的带权相对离差的绝对值为最小或者使总的带权相对离差的平方为最小等三种情况。通过把问题转化成数学规划,我们分别指出这三种情况下的三个反问题都可以在多项式时间内求解。     

单机带调整时间加权成套订单数问题遗传算法研究

通过大量的企业调研,提出了一类新的目标排序问题--单机带调整时间加权成套订单数排序问题:n个工件来自m个订单,分属B个不同类别,不同类之间的工件连续加工有调整时间,各工件有自己的交货期,一个订单中所有工件均按期完工则该订单成套完工,目标为加权成套延迟订单数最小.提出两类问题并且通过数学模型进行表述,设计相应的遗传算法,仿真结果表明该算法是可行而有效的.     

考虑公共交货期窗口问询的退化工件排序问题

工件的实际加工时间是其开始加工时间的线性递增函数,且不同的工件有不同的退化率。所有工件需要在相同的时间间隔内完工。以此模型为基础,研究了同时确定最优的交货期窗口和最优的工件加工顺序以最小化提前工件个数、延误工件个数以及交货期窗口问询产生的总成本的单机排序问题。分析了最优决策具有的特征,并基于上述性质提出了求解问题的多项式时间最优算法。利用随机产生的算例说明了最优算法的应用。     

Generating all efficient solutions of a rescheduling problem on unrelated parallel machines

In this paper, we consider a rescheduling problem where a set of jobs has already been assigned to unrelated parallel machines. When a disruption occurs on one of the machines, the affected jobs are rescheduled, considering the efficiency and stability measures. Our efficiency measure is the total flow time and stability measure is the total reassignment cost caused by the differences in the machine allocations in the initial and new schedules. We propose a branch and bound algorithm to generate all efficient solutions with respect to our efficiency and stability measures. We improve the efficiency of the algorithm by incorporating powerful reduction and bounding mechanisms. Our computational tests on large sized problem instances have revealed the satisfactory behaviour of our algorithm.     

Rescheduling with controllable processing times for number of disrupted jobs and manufacturing cost objectives

We consider a machine rescheduling problem that arises when a disruption such as machine breakdown occurs to a given schedule. Machine unavailability due to a breakdown requires repairing the schedule as the original schedule becomes infeasible. When repairing a disrupted schedule a desirable goal is to complete each disrupted job on time, i.e. not later than the planned completion time in the original schedule. We consider the case where processing times of jobs are controllable and compressing the processing time of a job requires extra processing cost. Usually, there exists a nonlinear relation between the processing time and manufacturing cost. We solve a bicriteria rescheduling problem that trades off the number of on-time jobs and manufacturing cost objectives. We give a mixed-integer second-order cone programming formulation for the problem. We develop a heuristic search algorithm to generate efficient solutions for the problem. Heuristic algorithm searches solution space by moving and swapping jobs among machines. We develop cost change estimates for job moves and swaps so that the heuristic implements only promising moves and hence generates a set of efficient solutions in reasonably short CPU times.     

Minimizing earliness–tardiness on a single burn-in oven with a common due date and maximum allowable tardiness constraint

This paper considers a scheduling problem for a single burn-in oven in the semiconductor manufacturing industry where the oven is a batch processing machine with restricted capacity. The batch processing time is set by the longest processing time among those of all the jobs contained in the batch. All jobs are assumed to have the same due date. The objective is to minimize the sum of the absolute deviations of completion times from the due date (earliness–tardiness) of all jobs under the constraint that the maximum tardiness should be less than or equal to the maximum allowable time value. We suggest several two-phase heuristic algorithms for this problem. In the first phase, some heuristic algorithms are developed without maximum allowable tardiness constraint. If the schedule from the first phase violates the maximum tardiness constraint, then the schedule is changed to satisfy maximum allowable tardiness constraint in the second phase. The suggested heuristics are based on genetic algorithms and dominance properties of optimal schedules. We present the results of computational experiments that clearly show the solution quality obtained by the suggested heuristics.     

Rescheduling parallel machines with stepwise increasing tardiness and machine assignment stability objectives

Nervousness in machine assignments during rescheduling can cause problems for the implementation of a scheduling system. This paper examines rescheduling due to the arrival of new jobs to the system. Parallel machine scheduling problems with stepwise increasing tardiness cost objectives, non-zero machine ready times, constraints that limit machine reassignments, and machine reassignment costs are considered. Simulation experiments and individual scheduling problems indicate that nervousness can be controlled at a low cost in some parallel machine scheduling environments. The rescheduling problems in the simulation are solved with a branch-and-price algorithm. Significant gains in schedule stability can be achieved by selecting the alternative optimal solution with the fewest machine reassignments.     

Minimizing the makespan for the two-machine scheduling problem with a single server: Two algorithms for very large instances

This article considers the problem of scheduling a given set of n jobs on two identical parallel machines with a single server. Each job must be processed on one of the machines. Before processing, the server has to set up the relevant machine. The objective is to minimize the makespan. For this unary NP-hard problem, two fast constructive algorithms with a complexity of O(n²) are presented. The performance of these algorithms is evaluated for instances with up to 10,000 jobs. Computational results indicate that the algorithms have an excellent performance for very large instances so that the obtained objective function values are very close to a lower bound, and in many cases even an optimal solution is achieved. Superiority over all existing algorithms is obtained by sequencing the jobs on the two machines so that the machine idle time and the server waiting time are minimized. In doing so, the characteristics of an optimal solution resulting from its relevant lower bound are taken into account.     

Scheduling with shutdowns and sequence dependent set-up times

This paper considers a single machine scheduling problem with ready and due times constraints on jobs, shutdown constraints on the machine and sequence dependent set-up times among jobs. The shutdown is a disruptive event such as holiday, breaks or machine maintenance, and has a prespecified period when the machine will be interrupted. If no pre-emption is allowed for jobs, shutdown constraints divide the planning horizon into disconnected time windows. An optimization algorithm based on the branch-and-bound method is developed to minimize the maximum tardiness for solving the problem. This paper further develops the post-processing algorithm that manipulates the starting time of the shutdown period so as to reduce the obtained maximum tardiness. The post-processing algorithm can determine plural schedules to reduce the maximum tardiness, and the production manager will select the objective schedule among them for the interest of overall efficiency. Computational results for the proposed algorithms will indicate that the post-processing algorithm can improve upon the original solution and the problems with multiple shutdowns and with set-up times varying widely can be satisfactorily solved.     

Comparing the impact of different rescheduling strategies on the entropic-related complexity of manufacturing systems

The primary objective of this paper is to compare five rescheduling strategies according to their effectiveness in reducing entropic-related complexity arising from machine breakdowns in manufacturing systems. Entropic-related complexity is the expected amount of information required to describe the state of the system. Previous case studies carried out by the authors have guided computer simulations, which were carried out in Arena 5.0 in combination with MS Excel. Simulation performance is measured by: (1) entropic-related complexity measures, which quantify: (a) the complexity associated with the information content of schedules, and (b) the complexity associated with the variations between schedules; and (2) mean flow time. The results highlight two main points: (a) the importance of reducing unbalanced machine workloads by using the least utilised machine to process the jobs affected by machine breakdowns, and (b) low disruption strategies are effective at reducing entropic-related complexity; this means that applying rescheduling strategies in order to manage complexity can be beneficial up to a point, which, in low disruption strategies, is included in their threshold conditions. The contribution of this paper is two-fold. First, it extends the application of entropic-related complexity to every schedule generated through rescheduling, whereas previous work only applied it to the original schedule. Second, recommendations are proposed to schedulers for improving their rescheduling practice in the face of machine breakdowns. Those recommendations vary according to the manufacturing organisations’ product type and scheduling objectives. Further work includes: (a) preparing a detailed workbook to measure entropic-related complexity at shop-floor level; and (b) extending the analysis to other types of disturbances, such as customer changes.     

Analytical models to predict the performance of a single-machine system under periodic and event-driven rescheduling strategies

This article presents initial results in the search for analytical models that can predict the performance of one-machine systems under periodic and event-driven rescheduling strategies in an environment where different job types arrive dynamically for processing and set-up must incur when production changes from one product type to another. The scheduling algorithm considered uses a first-in firstout dispatching rule to sequence jobs and it also groups jobs with similar types to save set-up time. The analytical models can estimate important performance measures like average flow time and machine utilization, which can then be used to determine optimal rescheduling parameters. Simulation experiments are used to show that the analytical models accurately predict the performance of the single machine under the scheduling algorithm proposed.     

Group scheduling with deteriorating jobs and allotted resource under limited resource availability constraint

This study considers a single machine group scheduling problem with deteriorating jobs and resource allocation (controllable processing times). The objective is to have the resource availability limited within a given range, and to minimize the maximum completion time (i.e. the makespan). For two special cases, it is proved that the problem can be solved in polynomial time. For the general case, an heuristic algorithm and a branch-and-bound algorithm are proposed. Computational results show that the proposed heuristic algorithm is generally effective.     

Scheduling a Single Machine to Minimize the Weighted Number of Tardy Jobs

In this paper the problem of scheduling jobs on a single machine to minimize the weighted number of tardy jobs is examined. It contains the framework for a new branch-and-bound procedure as well as the first extensive computational study of the problem. Results indicate that large problems, e.g. 50 jobs, can be solved in just a few seconds of computer time. Further, the computational results provide insight into how various problem parameters affect the solution difficulty of particular problems.