一个具有两类工件的多目标排序的多项式时间算法

本文考虑具有两个工件集的单机排序问题.第一个工件集J1以完工时间和为目标函数,第二个工件集J2以最大加权完工时间为目标函数.问题的目标是寻找一种排序,使得两个目标函数的加权和达到最小.本文证明该问题可在O(n1n2(n1 n2))时间内求解.     

有关单机两代理排序问题的两个结果

研究了两个单机两代理排序问题. 在第一个两代理排序问题中, 代理A的目标函数为极小化所有工件的加权完工时间总和, 代理B的目标函数为极小化最大工件费用. 在第二个两代理排序问题中, 代理A的目标函数为极小化所有工件的加权完工时间总和, 代理B的目标函数为极小化所有工件的最大完工时间. 证明了第一个问题是强NP-难的, 改进了已有的一般意义NP-难的结果; 对第二个问题给出了一个与现有的动态规划算法不同的动态规划算法.     

一个具有退化的两个代理的排序问题

考虑两个代理的带有退化的单机排序问题.第一个代理J以完工时间和为目标函数,第二个代理J以最大延迟为目标函数,并且两个代理的加工时间是按时间退化的,所谓按时间退化就是每个工件的加工时间是其开始加工时间的函数.问题的目标是寻找一种排序,使得两个代理的目标函数之和达到最小.证明该问题可在O(n_1n_2(n_1+n_2))时间内求解.     

具有错位限制且工件可退化的单机重新排序问题

重新排序问题是在原始工件已经按照某种最优规则排列时有一批新的工件到达,新工件的安排使得原始工件重新排序而产生错位.考虑了加权序列错位以及加权时间错位限制条件下具有退化工件,目标函数为最小化总完工时间和最小化总延误时间问题.工件的位置错位和时间错位限制条件下具有退化工件,目标函数为最小化总完工时间和最小化最大延迟问题.其中退化效应是指其实际加工时间是开工时间的非减函数,工件的位置错位是指重新排序过程中原始工件在原始最优序列与新到达工件所构成的新序列的加工位置之差,工件的时间错位是指重新排序过程中原始工件在原始最优序列与新到达工件所构成的新序列的完工时间之差.对以上两类问题,当权重系数或者错位限制满足特殊情况时,最优排序是原始工件集和新工件集中的工件按照退化率非减的序列排列,基于动态规划方法给出了以上几个问题的多项式时间算法或者是拟多项式算法.     

具有凸资源约束的单机指数学习效应问题

研究在所有工件的正常加工时间均相同的情况下具有指数学习效应和凸资源约束的单机排序问题.给出了两种模型:在资源消耗总费用有限的情况下,以工件的最大完工时间为目标函数;在工件的最大完工时间有限的情况下,以资源消耗总费用为目标函数.求两种模型下的最优排序和最优资源分配,使得目标函数最小.证明这两个问题都是多项式时间可解的,并给出了相应的算法.     

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.     

具有不可用区间且工件可拒绝下的单机重新排序问题的近似方案

本文考虑了机器具有不可用区间且工件可拒绝下的单机重新排序问题,在该问题中,给定一个工件集需在一台机器上加工,每个工件有自己的加工时间和权重,且对该工件集目标函数为极小化总加权完工时间的排序计划已给定,根据该排序计划中每个工件的完工时间已确定每个工件的承诺交付时间。然而,在工件正式开始加工前,原计划用于加工的某段时间区间因临时用于检修机器而导致机器在该时间区间不再可用,需要对工件重新排序。为了确保在新的重新排序中,工件的延误成本不致太大,决策者可以选择拒绝部分工件,但需支付相应的拒绝费用。任务是确定接受工件集和拒绝工件集,并将接受的工件在考虑机器具有不可用区间的条件下重新排序使得接受工件集的总加权完工时间,总拒绝费用及赋权最大延误之和最小。该问题是NP-困难的,对此给出了伪多项式时间动态规划精确算法,利用稀疏技术设计了完全多项式时间近似方案。     

机器带准备时间的同类机分批排序算法

讨论了两类机器带准备时间的同类机分批排序问题.对工件无到达时间及有常数个到达时间,目标函数为极小化加权总完工时间这两类问题进行研究,给出了两个最优算法,并对算法及其计算复杂性给予了分析与证明.     

具有学习和退化效应的单机干扰管理问题

针对工件同时具有学习和退化效应、机器具有可用性限制这一问题,建立可预见性单机干扰管理模型。在这一模型中,工件的加工时间是既与工件所排的加工位置又与工件开始加工的时间有关的函数。同时,在生产过程中由于机器发生故障或定期维修等扰动事件导致机器在某段时间内不能加工工件。目标是在同时考虑原目标函数和由扰动造成的偏离函数的情况下,构建一个新的最优时间表序列。根据干扰度量函数的不同研究了两个问题,第一个问题的目标函数是极小化总完工时间与总误工时间的加权和;第二个问题的目标函数是极小化总完工时间与总提前时间的加权和。对于所研究的问题,首先证明了最优排序具有的性质,然后建立了相应的拟多项式时间动态规划算法。     

具有优先约束的单机随机排序问题

讨论工件的加工时间为常数,机器发生随机故障的单机随机排序问题,目标函数极小化工件的加权完工时间和的数学期望最小.考虑两类优先约束模型.在第一类模型中,设工件间的约束为串并有向图.证明了模块M的ρ因子最大初始集合I中的工件优先于模块中的其它工件加工,并且被连续加工所得的排序为最优排序,从而将Lawler用来求解约束为串并有向图的单机加权总完工时间问题的方法推广到机器发生随机故障的情况.在第二类模型中,设工件间的约束为出树优先约束.证明了最大家庭树中的工件优先于家庭树中其它的工件加工,并且其工件连续加工所得到的排序为最优排序并给出了最优算法.     

Single machine scheduling with a general exponential learning effect

In this paper we consider the scheduling problem with a general exponential learning effect and past-sequence-dependent (p-s-d) setup times. By the general exponential learning effect, we mean that the processing time of a job is defined by an exponent function of the total weighted normal processing time of the already processed jobs and its position in a sequence, where the weight is a position-dependent weight. The setup times are proportional to the length of the already processed jobs. We consider the following objective functions: the makespan, the total completion time, the sum of the δ ? 0th power of completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.     

Single machine scheduling with exponential learning functions

In this paper we consider the single machine scheduling problem with exponential learning functions. By the exponential learning functions, we mean that the actual job processing time is a function of the total normal processing times of the jobs already processed. We prove that the shortest processing time (SPT) rule is optimal for the total lateness minimization problem. For the following three objective functions, the total weighted completion time, the discounted total weighted completion time, the maximum lateness, we present heuristic algorithms according to the corresponding problems without exponential learning functions. We also analyse the worst-case bound of our heuristic algorithms. It also shows that the problems of minimizing the total tardiness and discounted total weighted completion time are polynomially solvable under some agreeable conditions on the problem parameters.     

Single machine scheduling with exponential sum-of-logarithm-processing-times based learning effect

In this paper we consider the single machine scheduling problems with exponential sum-of-logarithm-processing-times based learning effect. By the exponential sum-of-logarithm-processing-times based learning effect, we mean that the processing time of a job is defined by an exponent function of the sum of the logarithm of the processing times of the jobs already processed. We consider the following objective functions: the makespan, the total completion time, the sum of the quadratic job completion times, the total weighted completion time and the maximum lateness. We show that the makespan minimization problem, the total completion time minimization problem and the sum of the quadratic job completion times minimization problem can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem and the maximum lateness minimization problem can be solved in polynomial time under certain conditions.     

单可变资源最小化加权完工时间和排序问题的强NP-困难性

Baker和Nuttle提出了下述单可变资源排序问题：$n$个工件利用某个单资源进行加工使得工件的完工时间的某个函数达到最小,而资源的可利用率是随着时间而变化的.当最小化的目标函数是工件的加权完工时间和时,Baker和Nuttle猜测该问题是NP-困难的.最近,Yuan、Cheng 和 Ng 证明该问题在一般意义下是NP-困难的,但是问题的精确复杂性仍然是悬而未决的.本文我们证明了该问题是强NP-困难的.     

Two-parallel machines scheduling with rate-modifying activities to minimize total completion time

This paper considers the two-parallel machines scheduling problem with rate-modifying activities. In this model, each machine has a rate-modifying activity that can change the processing rate of machine under consideration. Hence the actual processing times of jobs vary depending on whether the job is scheduled before or after the rate-modifying activity. We need to make a decision on when to schedule the rate-modifying activities and the sequence of jobs to minimize some objective function. We provide polynomial and pseudo-polynomial time algorithms to solve the total completion time minimization problem and total weighted completion time minimization problem under agreeable ratio condition.     

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.