云制造中带学习效应平行机排序问题的最优可中断算法

研究了云制造环境下一类带有学习效应的m台平行机排序问题.每台机器都有一个不同的单位时间加工费用,目标是在不超过给定的总费用情况下,从m台机器中选取若干机器加工工件,极小化最大完工时间.考虑了机器加工费用依赖于时间变化的学习效应函数.分别针对基于指数函数和幂函数的两类学习效应函数,分析了最优排序的性质并给出了最优可中断算法.     

具有周期维护最小化时间表长的两台平行机调度问题(英文)

本文讨论了具有周期维护的两台平行机调度问题,目标函数为最小化时间表长.设T为维护周期,t为每次对机器维护需要的时间,当t≤T/3时,本文证明了对于该问题由LPT算法得到的最坏误差界为2.     

具有学习效应和加工时间可控的平行机排序问题

本文研究了一类不相关平行机的排序问题,在该问题中工件的加工时间既具有学习效应,又资源可控,也就是说在该问题模型中,工件的实际加工时间为其正常的加工时间、加工过程中工件所处位置以及加工时间可控这些变量的函数。该研究的目的是为使得总机器负载和总的控制费用的加权和最小以及总的完工时间和总的控制费用的加权和最小。文章通过对问题的相关性质的分析和证明找到了一个解决问题的最优化算法,并且也证明了在处理机的数量给定的条件下,该问题的时间复杂性为O(n^m+2),最后也给出了相应的数值例子来阐述该问题。     

两台平行机的实时到达在线排序

本文考虑一的的在线平行机排序模型－－实时到达在线问题,该模型中,工件是陆续到达的,工件的个数及到达时间是事先未知的,而且只有当工件到达,才知其加工时间,所求目标是使所有工件都加工完的时间达到最小,对两台平行机的情形,Ｃｈｅｎ与Ｖｅｓｔｊｅｎｓ给出近似比为３／２的线ＬＰＴ算法,并证明了不存在近似小于（５－√５）／２的算法,我们利用黄金分割数设计了一个 算法,其近似比不超过（１８－√５）／１１。     

一类带核的平行机排序问题

研究了一类工件具有相似加工时间的带核的平行机排序问题,运用ＬＰＴ算法求解,得到ＬＰＴ算法界的精确估计并对问题的某些情形,给出了界紧的例子。     

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。     

可拆分平行机排序问题研究

平行机排序问题是把n个产品安排到m台机器上加工，使其总费用最小．通常的平行机排序问题都假设（C1）：任何产品不能在不同机器上同时加工．但是，如果把产品的加工时间看成一个产品量的需求，就可以假设（C2）：允许同一产品拆分在不同机器上同时加工．本文首先回顾了C1假设下平行机排序问题已有的结果，然后基于假设C2，讨论了各种费用目标下问题的算法及其复杂性．在没有生产准备时间的情况下，给出了一些问题的多项式算法和线性规划方法．在有独立生产准备时间的情况下，给出了P／split／Cmax问题的启发式算法及其算法分析．     

带服务器的三台平行机排序问题的复杂性和近似算法

本文研究了带服务器的三台平行机排序问题的复杂性，并给出了一个最好的在线近似算法．     

具有时间与位置相关的两类平行机排序问题

研究带有维修时间限制的时间和位置效应平行机排序问题,涉及同型机和非同类机两种机器类型.工件的实际加工时间同时受到位置效应和时间效应影响,且机器具有维修限制.目标函数由机器负载,总完工时间与总等待时间组成.非同类机情形下,通过将排序问题转化为指派问题,给出多项式时间算法,其算法的时间复杂度为O（n^k+2/（k-1）!）.同型机情形下通过转化目标函数,使用匹配算法得出排序问题的多项式时间解,其时间复杂度为O（（2n+m+n log n）n^k-1/（k-1）!）.     

Approximation algorithms for scheduling unrelated parallel machines

We consider the following scheduling problem. There arem parallel machines andn independent jobs. Each job is to be assigned to one of the machines. The processing of jobj on machinei requires timep _ij . The objective is to find a schedule that minimizes the makespan.Our main result is a polynomial algorithm which constructs a schedule that is guaranteed to be no longer than twice the optimum. We also present a polynomial approximation scheme for the case that the number of machines is fixed. Both approximation results are corollaries of a theorem about the relationship of a class of integer programming problems and their linear programming relaxations. In particular, we give a polynomial method to round the fractional extreme points of the linear program to integral points that nearly satisfy the constraints.In contrast to our main result, we prove that no polynomial algorithm can achieve a worst-case ratio less than 3/2 unlessP = NP. We finally obtain a complexity classification for all special cases with a fixed number of processing times.A preliminary version of this paper appeared in theProceedings of the 28th Annual IEEE Symposium on the Foundations of Computer Science (Computer Society Press of the IEEE, Washington, D.C., 1987) pp. 217–224.     

Minimizing makespan and total completion time for parallel batch processing machines with non-identical job sizes

This paper considers the scheduling problem of parallel batch processing machines with non-identical job sizes. The jobs are processed in batches and the machines have the same capacity. The models of minimizing makespan and total completion time are given using mixed integer programming method and the computational complexity is analyzed. The bound on the number of feasible solutions is given and the properties of the optimal solutions are presented. Then a polynomial time algorithm is proposed and the worst case ratios for minimizing total completion time and makespan is proved to be 2 and (8/3–2/3 m) respectively. To test the proposed algorithm, we generate different levels of random instances. The computational results demonstrate the effectiveness of the algorithm for minimizing the two objectives.     

Minimizing makespan for two parallel machines with job limit on each availability interval

We consider the problem of scheduling jobs on two parallel machines that are not continuously available for processing. The machine is not available after processing a fixed number of jobs in order to make precision adjustment of machines such as in wafer manufacturing, to reload the feeder in printed circuit board production, or to undertake any other maintenance works such as cleaning and safety inspections. The objective of the problem is to minimize the makespan. Two different scheduling horizons are investigated for this problem. For the short-term scheduling horizon, we consider only the time period before the unavailability interval, while for the long-term horizon, machines are allowed to restart processing after the unavailability interval. For both cases, which are strongly NP-hard, exact optimization algorithms based on the branch and bound method are proposed. Although the algorithms have exponential time complexities, computational results show that they can solve optimally the various-sized problems in reasonable computation time.     

Scheduling open shops with parallel machines

The parallel shop and the open shop are two machine environments that have received much attention in the literature of scheduling theory. A common generalization—the open shop with parallel machines—is considered in this paper. Polynomial-time algorithms are presented for obtaining minimum-length preemptive schedules for three cases. Open shops with single-operation machines of equal speed are scheduled with essentially no more difficulty than an ordinary open shop. Open shops with multiple-operation machines of equal speed are scheduled with the aid of a sequence of network flow computations. The general open shop problem with parallel machines of arbitrary speeds can be solved by linear programming, in much the same way as an optimal preemptive schedule can be found for unrelated parallel machines.     

Scheduling deteriorating jobs with a learning effect on unrelated parallel machines

In this study we consider unrelated parallel machines scheduling problems with learning effect and deteriorating jobs, in which the actual processing time of a job is a function of joint time-dependent deterioration and position-dependent learning. The objective is to determine the jobs assigned to corresponding each machine and the corresponding optimal schedule to minimize a cost function containing total completion (waiting) time, total absolute differences in completion (waiting) times and total machine load. If the number of machines is a given constant, we show that the problems can be solved in polynomial time under the time-dependent deterioration and position-dependent learning model.     

Scheduling open shops with parallel machines to minimize total completion time

This paper explores scheduling a realistic variant of open shops with parallel machines per working stage. Since real production floors seldom employ a single machine for each operation, the regular open shop problem is very often in practice extended with a set of parallel machines at each stage. The purpose of duplicating machines in parallel is to either eliminate or to reduce the impact of bottleneck stages on the overall shop efficiency. The objective is to find the sequence which minimizes total completion times of jobs. We first formulate the problem as an effective mixed integer linear programming model, and then we employ memetic algorithms to solve the problem. We employ Taguchi method to evaluate the effects of different operators and parameters on the performance of memetic algorithm. To further enhance the memetic algorithm, we hybridize it with a simple form of simulated annealing as its local search engine. To assess the performance of the model and algorithms, we establish two computational experiments. The first one is small-sized instances by which the model and general performance of the algorithms are evaluated. The second one consists of large-sized instances by which we further evaluate the algorithms.     

Scheduling on parallel identical machines to minimize total tardiness

This paper focuses on the problem of scheduling n independent jobs on m identical parallel machines for the objective of minimizing total tardiness of the jobs. We develop dominance properties and lower bounds, and develop a branch and bound algorithm using these properties and lower bounds as well as upper bounds obtained from a heuristic algorithm. Computational experiments are performed on randomly generated test problems and results show that the algorithm solves problems with moderate sizes in a reasonable amount of computation time.     

Fast LP models and algorithms for identical jobs on uniform parallel machines

Scheduling n identical jobs on m uniform parallel machines to minimize scheduling work is very common in practice. The case of identical jobs is common in manufacturing systems, in which many products have identical designs or processing times on the same machine. Factories often buy new equipment but retain their slower, older equipment; this results in machines having different processing speeds.