The unbounded parallel-batch scheduling with rejection

In this paper, we consider the unbounded parallel-batch scheduling with rejection. A job is either rejected, in which case a certain penalty has to be paid, or accepted and processed in batches on a machine. The processing time of a batch is defined as the longest processing time of the jobs contained in it. Four problems are considered: (1) to minimize the sum of the total completion time of the accepted jobs and the total rejection penalty of the rejected jobs; (2) to minimize the total completion time of the accepted jobs subject to an upper bound on the total rejection penalty of the rejected jobs; (3) to minimize the total rejection penalty of the rejected jobs subject to an upper bound on the total completion time of the accepted jobs; (4) to find the set of all the Pareto optimal schedules. We provide a polynomial-time algorithm for the first problem. Furthermore, we show that all the other three problems are binary NP-hard and present a pseudo-polynomial-time algorithm and a fully polynomial-time approximation scheme for them.     

Parallel-batch scheduling with deterioration and rejection on a single machine

The single machine parallel-batch scheduling with deteriorating jobs and rejection is considered in this paper.A job is either rejected,in which a rejection penalty should be paid,or accepted and processed on the machine.Each job's processing time is an increasing linear function of its starting time.The machine can process any number of jobs simultaneously as a batch.The processing time of a batch is equal to the largest processing time of the jobs in the batch.The objectives are to minimize the makespan and the total weighted completion time,respectively,under the condition that the total rejection penalty cannot exceed a given upper bound Q.We show that both problems are NP-complete and present dynamic programming algorithms and fully polynomial time approximation schemes(FPTASs) for the considered problems.     

具有老化效应的单机共同工期安排和工件可拒绝排序问题

研究共同工期安排和具有老化效应的单机排序问题。在整个加工过程中,工件的实际加工时间是与其所在位置和工件本身老化率相关的函数,生产商可以通过支付一定的处罚费用而拒绝加工某些工件。鉴于生产过程中出现老化效应,通过采取维修活动来提高生产率。目标是划分接受工件集和拒绝工件集,确定接受工件集中工件的加工次序和维修活动安排的位置,以极小化接受工件的提前、延误、工期与拒绝工件的总处罚费用的加权和。对这一问题,首先将其转化为指派问题并构造了最优多项式时间算法;其次,证明了目标函数满足一定条件下的问题的更一般形式能够在多项式时间内得到最优解;最后,对本文问题的一个特殊情况,设计了具有更低时间复杂度的多项式动态规划算法。     

Vector scheduling with rejection on a single machine

In this paper, we study a vector scheduling problem with rejection on a single machine, in which each job is characterized by a d-dimension vector and a penalty, in the sense that, jobs can be either rejected by paying a certain penalty or assigned to the machine. The objective is to minimize the sum of the maximum load over all dimensions of the total vector of all accepted jobs, and the total penalty of rejected jobs. We prove that the problem is NP-hard and design two approximation algorithms running in polynomial time. When d is a fixed constant, we present a fully polynomial time approximation scheme.     

Single machine group scheduling under decreasing linear deterioration

This paper considers single machine scheduling problems with group technology (GT) and deteriorating jobs. A sequence independent setup is required to process a job from a different group and jobs in each group are processed together. We consider the case of jobs whose processing times are a decreasing function of their starting time. The objectives of scheduling problems are to minimize the makespan and the total completion time, respectively. We also provide polynomial time algorithms to solve these problems.     

可转包的双目标单机排序问题（英文）

Scheduling with outsourcing is studied in this paper. It is assumed that both manufacturer and subcontractor have a single machine to process n jobs. The manufacturer needs to determine simultaneously a set of outsourced jobs and the schedule of the jobs in-house such that two criterias, i.e., outsourcing cost and production cost, are minimized.The production cost is measured by the number of tardy jobs or the total tardiness of jobs in-house, and the outsourcing cost is proportional to the total processing time of jobs outsourced. Two kinds of problems with different criterias are considered. We analyze the computational complexity and provide pseudo-polynomial time optimization algorithms for the NP-hard version of the problems.     

Considerations of single-machine scheduling with deteriorating jobs

This paper considers some scheduling problems with deteriorating jobs. The objectives are to minimize the makespan, the total completion time, the total absolute deviation of completion time, the earliness, tardiness, and due date penalty, the sum of earliness penalties subject to no tardy jobs, respectively. We also explore two resource constrained scheduling problems: how to minimize the resource consumption with makespan constraints and how to minimize the makespan with the total resource consumption constraints. Several polynomial time algorithms are proposed to optimally solve the problems with the above objective functions.     

Machine scheduling with a rate-modifying activity

Motivated by a problem commonly found in electronic assembly lines, this paper deals with the problem of scheduling jobs and a rate-modifying activity on a single machine. A rate-modifying activity is an activity that changes the production rate of the equipment under consideration. Hence the processing times of jobs vary depending on whether the job is scheduled before or after the rate-modifying activity. The decisions under consideration are when to schedule the rate-modifying activity and the sequence of jobs to optimize some performance measure.In this paper, we develop polynomial algorithms for solving problems of minimizing makespan, and total completion time respectively. We also develop pseudo-polynomial algorithms for solving problems of total weighted completion time under the agreeable ratio assumption. We prove that the problem of minimizing maximum lateness is NP-hard and also provide a pseudo-polynomial time algorithm to solve it optimally.     

Single machine scheduling with release dates and rejection

In this paper, we consider the single machine scheduling problem with release dates and rejection. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the machine. The objective is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. We show that the problem is NP-hard in the ordinary sense. Then we provide two pseudo-polynomial-time algorithms. Consequently, two special cases can be solved in polynomial-time. Finally, a 2-approximation algorithm and a fully polynomial-time approximation scheme are given for the problem.     

On-line integrated production–distribution scheduling problems with capacitated deliveries

In on-line integrated production–distribution problems, customers release jobs to a manufacturer that has to process the jobs and deliver them to the customers. The jobs are released on-line, that is, at any time there is no information about future jobs. Processed jobs are grouped into batches, which are delivered to the customers as single shipments. The total cost (to be minimized) is the sum of the total weighted flow time and the total delivery cost. Such on-line integrated production–distribution problems have been studied for the case of uncapacitated batches. We consider the capacitated case with an upper bound on the size of a batch. For several versions of the problem, we present efficient on-line algorithms, and use competitive analysis to study their worst-case performance.     

Single machine SLK/DIF due window assignment problem with job-dependent linear deterioration effects

We consider single machine scheduling problems with deteriorating jobs and SLK/DIF due window assignment, where the deteriorating rates of jobs are assumed to be job-dependent. We consider two different objectives under SLK and DIF due window assignment, respectively. The first objective is to minimise total costs of earliness, tardiness, due window location and due window size, while the second objective is to minimise a cost function that includes number of early jobs, number of tardy jobs and the costs for due window location and due window size. We study the optimality properties for all problems and develop algorithms for solving these problems in polynomial time.     

On-line scheduling of unit time jobs with rejection: minimizing the total completion time

We consider on-line scheduling of unit time jobs on a single machine with job-dependent penalties. The jobs arrive on-line (one by one) and can be either accepted and scheduled, or be rejected at the cost of a penalty. The objective is to minimize the total completion time of the accepted jobs plus the sum of the penalties of the rejected jobs.We give an on-line algorithm for this problem with competitive ratio . Moreover, we prove that there does not exist an on-line algorithm with competitive ratio better than 1.63784.     

Some Generalisations of the Time Minimising Assignment Problem

The time minimising assignment problem is the problem of finding an assignment of n jobs to n facilities, one to each, which minimises the total time for completing all the jobs. The usual assumption made in these problems is that all the jobs are commenced simultaneously. In this paper two generalisations of this assumption are considered, and algorithms are presented to solve these general problems. Numerical examples are worked out illustrating the algorithms.     

具有退化工件和老化效应的单机可拒绝排序问题

研究同时具有退化工件和老化效应的单机可拒绝排序问题,即工件的实际加工时间是与其开工时间和所在位置有关的函数,同时生产商可以通过支付一定的处罚费用而拒绝加工某些工件。在生产加工过程中,考虑对机器进行选择性维修活动来提高加工的效率;机器进行维修活动后将恢复到初始状态,老化效应也将重新开始。目标是确定拒绝哪些工件、何时进行维修活动以及接受工件集中工件的次序,以便极小化接受加工工件的最大完工时间与拒绝加工工件总处罚费用的和。证明得到了所研究的问题是NP-难解的,并给出了解决问题的一个全多项式时间近似方案(FPTAS)算法。     

Rescheduling problems with deteriorating jobs under disruptions

In this paper, we consider two single-machine rescheduling problems with linear deteriorating jobs under disruption. By a deteriorating jobs, we mean that the actual processing time of the job is an increasing function of its starting time. The two problems correspond to two different increasing linear function. Rescheduling means a set of original jobs has already been scheduled to minimize some classical objective, then a new set of jobs arrives and creates a disruption. We consider the rescheduling problem to minimize the total completion time under a limit of the disruption from the original scheduling. For each problem, we consider two versions. For each version, the polynomial algorithms are proposed, respectively.     

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.     

Single machine scheduling and due date assignment with positionally dependent processing times

We consider single machine scheduling and due date assignment problems in which the processing time of a job depends on its position in a processing sequence. The objective functions include the cost of changing the due dates, the total cost of discarded jobs that cannot be completed by their due dates and, possibly, the total earliness of the scheduled jobs. We present polynomial-time dynamic programming algorithms in the case of two popular due date assignment methods: CON and SLK. The considered problems are related to mathematical models of cooperation between the manufacturer and the customer in supply chain scheduling.     

工作有到达时间且拒绝工件总个数受限的单机平行分批排序问题的近似算法

考虑了工件有到达时间且拒绝工件总个数不超过某个给定值的单机平行分批排序问题.在该问题中,给定一个工件集和一台可以进行批处理加工的机器.每个工件有它的到达时间和加工时间;对于每个工件来说要么被拒绝要么被接受安排在机器的某一个批次里进行加工;一个工件如果被拒绝,则需支付该工件对应的拒绝费用.为了保证一定的服务水平,要求拒绝工件的总个数不超过给定值.目标是如何安排被接受工件的加工批次和加工次序使得其最大完工时间与被拒绝工件的总拒绝费用之和最小.该问题是NP-难的,对此给出了伪多项式时间动态规划精确算法,2-近似算法和完全多项式时间近似方案.     

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 group scheduling with time-dependent learning effect and position-based setup time learning effect

As to learning effect, it may be more appropriate to assume that position-based learning takes place during machine setups only, while sum-of-processing-time-based learning occurs in considering the experience that workers have gained from producing jobs. Thus, in this paper, we consider sum-of-processing-time-based learning on job processing time and position-based learning on setup time in single-machine group scheduling problems. The objectives are to minimize the makespan and the total completion time, respectively. We provide two polynomial time algorithms to solve the makespan minimization problems. On the other hand, we also provide two polynomial time algorithms to solve the total completion time minimization problems under certain conditions.