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。     

具有时间与位置相关及维修限制的单机排序问题

考虑时间和位置相关的单机排序问题, 且机器具有退化的维修限制. 工件的实际加工时间是工件加工位置相关的函数, 目标函数为最大完工时间和总完工时间两个函数, 并利用匹配算法给出这两个问题的多项式时间算法. 最后得出工件满足一定条件时最大完工时间满足组平衡规则.     

机器具有准备时间的双目标平行机排序问题

本文讨论机器具有准备时间的双目标平行机排序问题，目标函数为完工时间和最优条件下极小化最大完工时间．通过对SPT排序的性质的分析，给出了最优排序的下界．在此基础上证明了SPT排序的误差界为3／2，并且是紧界．     

极小化最大提前完工时间的两平行机排序问题

讨论了在两台同型平行机上,加工带截止期限的n个工件,在机器可空闲条件下,确定一个工件排序,使得最大提前完工时间最小.由于工件不允许延迟,问题可能会无可行排序.先讨论问题的可行性,通过子集和问题归约,证明了判定问题的可行性是NP-complete的.如果问题可行,接着讨论了问题的复杂性,通过划分问题归约,证明了其是NP-complete的.最后,考虑了工件加工时间相等的特殊情形,提出了一个算法在多项式时间内获得最优排序.     

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)!).     

可拆分有调整时间的平行机排序问题的一个算法

考虑有独立调整时间的同型号平行机排序问题,极小化最迟完工时间,产品允许拆分,同一产品被拆分后各部分可以在不同机器上同时加工,该问题是ＮＰ－ｈａｒｄ问题。本文首先给出该问题的一个启发式算法ＭＬ,然后证明了其最坏情况估计不超过７／４－１／ｍ（ｍ≥２）。     

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。     

带机器准备时间的平行机ordinal排序及近似算法

本文研究带机器准备时间的m台平行机ordinal在线排序问题。讨论了在极小化最大机器完工时间和极小化最大工件完工时间两种目标下的不同下界和相应的在线近似算法。对第一个目标，我们得到了3/2的下界和最坏情况界为2-1/m的近似算法。对第二个目标，我们得到了最坏情况为m的最好近似算法。我们还对一些特殊情况进行了分析。     

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．     

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 interfering job sets on parallel machines

We consider bicriteria scheduling on identical parallel machines in a nontraditional context: jobs belong to two disjoint sets, and each set has a different criterion to be minimized. The jobs are all available at time zero and have to be scheduled (non-preemptively) on m parallel machines. The goal is to generate the set of all non-dominated solutions, so the decision maker can evaluate the tradeoffs and choose the schedule to be implemented. We consider the case where, for one of the two sets, the criterion to be minimized is makespan while for the other the total completion time needs to be minimized. Given that the problem is NP-hard, we propose an iterative SPT–LPT–SPT heuristic and a bicriteria genetic algorithm for the problem. Both approaches are designed to exploit the problem structure and generate a set of non-dominated solutions. In the genetic algorithm we use a special encoding scheme and also a unique strategy – based on the properties of a non-dominated solution – to ensure that all parts of the non-dominated front are explored. The heuristic and the genetic algorithm are compared with a time-indexed integer programming formulation for small and large instances. Results indicate that the both the heuristic and the genetic algorithm provide high solution quality and are computationally efficient. The heuristics proposed also have the potential to be generalized for the problem of interfering job sets involving other bicriteria pairs.     

Scheduling three chains on two parallel machines

We consider the problem of scheduling n tasks subject to chain-precedence constraints on two identical machines with the objective of minimizing the makespan. The problem is known to be strongly NP-hard. Here, we prove that it is binary NP-hard even with three chains. Furthermore, we characterize the complexity of this case by presenting a pseudopolynomial time algorithm and a fully polynomial time approximation scheme.     

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.     

带学习效应的两台平行机时间表长问题

研究机器带学习效应, 目标函数为时间表长的两台平行机排序问题, 问题是NP-难的. 首先建立了求解该问题最优解的整数规划模型. 其次, 基于模拟退火算法给出了该问题的近似算法SA, 并证明了该算法依概率1 全局收敛到最优解. 最后, 通过数值模拟对所提出的算法进行了性能分析. 数值模拟结果表明, 近似算法SA可以达到最优值的99%, 准确度高, 算法较有效.     

Scheduling jobs on parallel machines with sequence-dependent setup times

Consider a number of jobs to be processed on a number of identical machines in parallel. A job has a processing time, a weight and a due date. If a job is followed by another job, a setup time independent of the machine is incurred. A three phase heuristic is presented for minimizing the sum of the weighted tardinesses. In the first phase, as a pre-processing procedure, factors or statistics which characterize an instance are computed. The second phase consists of constructing a sequence by a dispatching rule which is controlled through parameters determined by the factors. In the third phase, as a post-processing procedure, a simulated annealing method is applied starting from a seed solution which is the result of the second phase. In the dispatching rule of the second phase there are two parameters of which the values are dependent on the particular problem instance at hand. Through extensive experiments rules are developed for determining the values of the two parameters which make the priority rule work effectively. The performance of the simulated annealing procedure in the third phase is evaluated for various values of the factors.     

Maximizing the minimum completion time on parallel machines

We propose an exact branch-and-bound algorithm for the problem of maximizing the minimum machine completion time on identical parallel machines. The proposed algorithm is based on tight lower and upper bounds as well as an effective symmetry-breaking branching strategy. Computational results performed on a large set of randomly generated instances attest to the efficacy of the proposed algorithm.      

Scheduling jobs with release dates on parallel batch processing machines

In this paper we consider the problem of scheduling jobs with release dates on parallel unbounded batch processing machines to minimize the maximum lateness. We show that the case where the jobs have deadlines is strongly NP-hard. We develop a polynomial-time approximation scheme for the problem to minimize the maximum delivery completion time, which is equivalent to minimizing the maximum lateness from the optimization viewpoint.     

An improved on-line algorithm for scheduling on two unrestrictive parallel batch processing machines

We consider the problem of on-line scheduling a set of n jobs on two parallel batch processing machines. The objective is to minimize the makespan. We provide an algorithm for the problem that is better than one given in the literature, improving the competitive ratio from to .