带有拒绝的单机和同型机排序问题

研究了带有拒绝的单机和同型机排序问题. 对于单机情形, 工件的惩罚费用是对应加工时间的\alpha倍.如果工件有到达时间, 目标为最小化时间表长与惩罚费用之和, 证明了这个问题是可解的.如果所有工件在零时刻到达, 目标为最小化总完工时间与惩罚费用之和, 也证明了该问题是可解的.对于同型机排序问题, 研究了工件分两批在线实时到达的情形, 目标为最小化时间表长与惩罚费用之和.针对机器台数2和m, 分别给出了竞争比为2和4-2/m的在线算法.     

带有链优先序的分批排序问题

本文首次就带有优先序的分批排序问题进行了讨论，目标函数为最大完工时间．当优先序为链，一条链上的工件个数为饨，而其它链的工件个数为常数，分批的容量B大于等于链的条数，在这种情况下，问题为多项式可解的．文中并讨论了几种特殊情况的多项式算法．     

各机器具有相同加工时间的Flow Shop 成组排序问题

本文讨论了m台机器的Folw Shop成组排序问题，工件在不同机器上的加工时间相同，目标函数为极小化完工时间和。给出了一个多项式时间可解的最优算法。     

具有资源约束的工期指派排序问题

研究在资源有限情况下,工件加工具有学习效应和凸资源依赖的单机排序问题,其中工件的实际加工时间与正常的加工时间,工件所排位置,学习因子及资源分配量都有关,为资源消耗量的一个凸函数.在模型中,讨论了两种情形::共同交货期(CON),共同松弛交货期(SLK).目标为确定工件的排序,资源分配和工件的工期,使得工件的提前、延误、工期费用的总和最小.在分配资源量有限情况下,证明了这两个问题都是多项式时间可解的,并给出了相应的算法.     

工件加工时间增加的排序问题(1‖Cmax)

讨论了工件加工时间随工件开工时间线性增加的排序问题,考虑的目标函数是最大完工时间,证明了加工时间是简单线性增加情况下最大完工时间问题是多项式时间可解的,对于加工时间是一般线性增加情况,研究了最优排序的性质,同时证明了两种特殊情况下最大完工时间问题也是多项式时间可解的。     

延误工件个数与最大加工时间压缩比例之和的可控排序

研究工件加工时间可控的排序问题，讨论的目标函数是延误工件个数与最大加工时间压缩比例之和，证明这一问题是多项式时间可解的。     

单机两组工件继列分批与平行分批混合排序

研究单机两组工件继列分批与平行分批混合排序.在问题中有两组工件J^A和JA和J^B.A-工件可以在平行批中进行加工,B-工件可以在继列批中进行加工.对若干正则目标函数给出了多项式时间算法.主要结果如下:·排序问题1|s-p-batch,s(B),(∞,∞)|L_(max)在O(n_An_Bn)时间可解.·排序问题1|s-p-batch,s(B),(∞,b(B))|∑C_j在O(n_An_Bn)时间可解.·排序问题1|s-p-batch,p_j=1,s(B),(b(A),b(B))|∑w_jC_j在O(n_An_Bn)时间可解.·排序问题1|s-p-batch,s(B),(∞,b(B))|f_(max)可以在时间界为O(log(max_jf_j(M))×(nlogM+n_An_Bn))内可解.其中,M是工件完工时间的一个上界.     

需要安装时间的两台多功能机排序问题的计算复杂性

提出需要安装时间的多功能机排序问题,一般情况下,这是NP-困难的;主要研究只有两台机器时一些特殊情况下的计算复杂性.根据加工集合为机器全集的工件组数的不同,分别给出多项式时间算法和分枝定界算法.对各工件组的工件数和加工时间都相等的情况,给出一个多项式时间的最优算法-奇偶算法,从而证明此问题是多项式时间可解的.     

平行机物流排序的近似算法

本文研究一个两阶段物流排序问题,即第一阶段工件在平行机上加工,在第二阶段这些被加工过的工件以某种运输方式分批运送到预先指定的目的地.优化的目标是使工件带权送到的时间与运输费用的总和为最小.应用动态规划及组合优化方法,分别研究“满足一致性条件”和一般情形下该问题的多项式时间近似算法,并分析算法的性能比.     

基于加工时间之和学习效应下的单机成组排序问题

研究具有加工时间之和学习效应下的一个新型成组排序问题,工件的学习效应是之前工件加工时间之和的函数,组学习效应是成组加工所在的位置的函数. 考虑最大完工时间和总完工时间两个问题,证明了这两个问题都是多项式时间可解的,并提出了相应的多项式时间算法.     

Single machine scheduling subject to deadlines and resource dependent processing times

The problem of scheduling n jobs on a single machine is studied. Each job has a deadline and a processing time which is a linear decreasing function of the amount of a common resource allocated to the job. The objective is to find simultaneously a sequence of the jobs and a resource allocation so as the deadlines are satisfied and the total weighted resource consumption is minimized. The problem is shown to be solvable in O(n log n) time if the resource is continuously divisible. If the resource is discrete, then the problem is proved to be binary NP-hard. Some special cases are solvable in O(n log n) time. A fully polynomial approximation scheme is presented for the general problem with discrete resource.     

Two-machine flowshop scheduling to minimize the number of tardy jobs

We consider the two-machine flowshop problem with the objective of minimizing the total number of tardy jobs. Since this problem is known to be strongly NP-hard, algorithms are described for four polynomially solvable special cases. In addition, several heuristic algorithms are developed to find optimal or near optimal schedules. Results of computational tests in solving problems up to 60 jobs are reported and directions for future research are provided.     

Two-machine flow shop scheduling with deteriorating jobs: minimizing the weighted sum of makespan and total completion time

This paper considers a two-machine flow shop scheduling problem with deteriorating jobs in which the processing times of jobs are dependent on their starting times in the sequence. The objective is to minimize the weighted sum of makespan and total completion time. To analyse the problem, we propose a mixed integer programming model, and discuss several polynomially solvable special cases. We also present a branch-and-bound algorithm with several dominance rules, an upper bound and a lower bound. Finally, we present results of computational experiments conducted to evaluate the performance of the proposed model and the exact algorithm.     

Minimizing the weighted number of early and tardy jobs in a stochastic single machine scheduling problem

We study a static stochastic single machine scheduling problem in which jobs have random processing times with arbitrary distributions, due dates are known with certainty, and fixed individual penalties (or weights) are imposed on both early and tardy jobs. The objective is to find an optimal sequence that minimizes the expected total weighted number of early and tardy jobs. The general problem is NP-hard to solve; however, in this paper, we develop certain conditions under which the problem is solvable exactly. An efficient heuristic is also introduced to find a candidate for the optimal sequence of the general problem. Our illustrative examples and computational results demonstrate that the heuristic performs well in identifying either optimal sequences or good candidates with low errors. Furthermore, we show that special cases of the problem studied here reduce to some classical stochastic single machine scheduling problems including the problem of minimizing the expected weighted number of early jobs and the problem of minimizing the expected weighted number of tardy jobs which are both solvable by the proposed exact or heuristic methods.     

Minimizing the makespan in a two-machine cross-docking flow shop problem

This paper studies a two-machine cross-docking flow shop scheduling problem in which a job at the second machine can be processed only after the processing of some jobs at the first machine has been completed. The objective is to minimize the makespan. We first show that the problem is strongly NP-hard. Some polynomially solvable special cases are provided. We then develop a polynomial approximation algorithm with an error-bound analysis. A branch-and-bound algorithm is also constructed. Computational results show that the branch-and-bound algorithm can optimally solve problems with up to 60 jobs within a reasonable amount of time.     

工件带简单线性恶化函数和共同交货期单机排序问题

本文研究单机排序问题,其中工件加工时间具有简单线性恶化函数.同时,所有工件均具有一个给定共同交货期.目标函数为最小化提前有奖延误受罚之和.在逆一致性条件下,给出了求解该排序问题的一个伪多项式时间动态规划算法.同时借助于几何舍入技巧,对求解这类排序问题给出了一个充分多项式时间的近似算法(FPTAS)。     

Single Machine Group Scheduling with Two Ordered Criteria

The problem of scheduling jobs on a single machine is considered. It is assumed that the jobs are classified into several groups and the jobs of the same group have to be processed contiguously. A sequence independent set-up time is incurred between each two consecutively scheduled groups. A schedule is specified by a sequence for the groups and a sequence for the jobs in each group. The quality of a schedule is measured by two critera ordered by their relative importance. The objective is to minimize the maximum cost, the secondary criterion, subject to the schedule is optimal with respect to total weighted completion time, the primary criterion. A polynomial time algorithm is presented to solve this bicriterion group scheduling problem. It is shown that this algorithm can also be modified to solve the single machine group scheduling problem with several ordered maximum cost criteria and arbitrary precedence constraints.     

带有退化效应和序列相关运输时间的排序问题

考虑带有退化效应和序列相关运输时间的单机排序问题. 工件的加工时间是其开工时间的简单线性增加函数. 当机器单个加工工件时, 极小化最大完工时间、(加权)总完工时间和总延迟问题被证明是多项式可解的, EDD序对于极小化最大延迟问题不是最优排序, 另外, 就交货期和退化率一致情形给出了一最优算法. 当机器可分批加工工件时, 分别就极小化最大完工时间和加权总完工时间问题提出了多项式时间最优算法.     

Single-machine scheduling with linear decreasing deterioration to minimize earliness penalties

We consider a single-machine scheduling problem with linear decreasing deterioration in which the due dates are determined by the equal slack (SLK) method. By the linear decreasing deterioration, we mean that the job’s processing time is a decreasing function of its starting time. The objective is to minimize the total weighted earliness penalty subject to no tardy jobs. We prove that two special cases of the problem remain polynomially solvable. The first case is the problem with equally weighted monotonous penalty objective function and the other case is the problem with weighted linear penalty objective function.     

Scheduling a single machine to minimize earliness penalties subject to the SLK due-date determination method

This paper considers a single machine scheduling problem. There are n jobs to be processed on a single machine. The problem is to minimize total earliness penalties subject to no tardy jobs. The problem is NP-complete if the due-dates are arbitrary. We study the problem when the due-dates are determined by the equal slack (SLK) method. Two special cases of the problem are solved in polynomial time. The first one is the problem with equally weighted monotonous penalty objective function. The second one is the problem with weighted linear penalty objective function.