Bounded single-machine parallel-batch scheduling with release dates and rejection

We consider the bounded single-machine parallel-batch scheduling problem with release dates and rejection. A job is either rejected, in which case a certain penalty has to be paid, or accepted and then processed on the machine. The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. When the jobs have identical release dates, we present a polynomial-time algorithm. When the jobs have a constant number of release dates, we give a pseudo-polynomial-time algorithm. For the general problem, we provide a 2-approximation algorithm and a polynomial-time approximation scheme.     

A dynamic-programming-based exact algorithm for general single-machine scheduling with machine idle time

This paper proposes an efficient exact algorithm for the general single-machine scheduling problem where machine idle time is permitted. The algorithm is an extension of the authors’ previous algorithm for the problem without machine idle time, which is based on the SSDP (Successive Sublimation Dynamic Programming) method. We first extend our previous algorithm to the problem with machine idle time and next propose several improvements. Then, the proposed algorithm is applied to four types of single-machine scheduling problems: the total weighted earliness-tardiness problem with equal (zero) release dates, that with distinct release dates, the total weighted completion time problem with distinct release dates, and the total weighted tardiness problem with distinct release dates. Computational experiments demonstrate that our algorithm outperforms existing exact algorithms and can solve instances of the first three problems with up to 200 jobs and those of the last problem with up to 80 jobs.     

带有线性恶化工件和释放时间的两个代理单机调度问题

研究了带有简单线性恶化工件和释放时间的两个代理单机调度问题. 所有工件在一台机器上加工, 每个代理有各自依赖于自己工件的优化目标. 针对工件释放时间相同与不同两种情况, 研究了有约束的优化模型, 即找到调度最小化一个代理的目标函数而使得另一个代理的目标函数不超过一个给定的上界. 当工件具有相同的释放时间, 我们主要考虑的目标函数有: 总加权完工时间和总加权拖期工件数. 当工件具有不同释放时间, 我们考虑的目标函数有: 最大完工时间、总完工时间以及拖期工件数. 对于每一个问题, 我们分析了问题的计算复杂性. 此外, 对于NP难问题的一些特殊情况本文分析了最优解性质, 基于这些性质给出了最优算法.     

Optimality proof of the Kise–Ibaraki–Mine algorithm

Kise, Ibaraki and Mine (Operations Research 26:121–126, 1978) give an O(n ²) time algorithm to find an optimal schedule for the single-machine number of late jobs problem with agreeable job release dates and due dates. Li, Chen and Tang (Operations Research 58:508–509, 2010) point out that their proof of optimality for their algorithm is incorrect by giving a counter-example. In this paper we give a correct proof of optimality for their algorithm.     

A branch and bound algorithm for minimizing makespan on a single machine with unequal release times under learning effect and deteriorating jobs

We present a single-machine problem with the unequal release times under learning effect and deteriorating jobs when the objective is minimizing the makespan. In this study, we introduced a scheduling model with unequal release times in which both job deterioration and learning exist simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution. A heuristic algorithm is proposed to obtain a near-optimal solution. The computational experiments show that the branch-and-bound algorithm can solve instances up to 30 jobs, and the average error percentage of the proposed heuristic is less than 0.16%.     

Fast approximation algorithms to minimize a special weighted flow-time criterion on a single machine with a non-availability interval and release dates

This paper is the first attempt to successfully design efficient approximation algorithms for the single-machine weighted flow-time minimization problem when jobs have different release dates and weights equal to their processing times under the assumption that one job is fixed (i.e., the machine is unavailable during a fixed interval corresponding to the fixed job). Our work is motivated by an interesting algorithmic application to the generation of valid inequalities in a branch-and-cut method. Our analysis shows that the trivial FIFO sequence can lead to an arbitrary large worst-case performance bound. Hence, we modify this sequence so that a new 2-approximation solution can be obtained for every instance and we prove the tightness of this bound. Then, we propose a fully polynomial-time approximation algorithm with efficient running time for the considered problem. Especially, the complexity of our algorithm is strongly polynomial.     

Deteriorating job scheduling to minimize the number of late jobs with setup times

Deteriorating jobs scheduling problems have been widely studied recently. However, research on scheduling problems with deteriorating jobs has rarely considered explicit setup times. With the current emphasis on customer service and meeting the promised delivery dates, we consider a single-machine scheduling problem to minimize the number of late jobs with deteriorating jobs and setup times in this paper. We derive some dominance properties, a lower bound, and an initial upper bound by using a heuristic algorithm to speed up the search process of the branch-and-bound algorithm. Computational experiments show that the algorithm can solve instances up to 1000 jobs in a reasonable amount of time.     

Scheduling with job release dates, delivery times and preemption penalties

We consider in this paper the single-machine preemptive scheduling problem with job release dates, delivery times and preemption penalties, where each time a job is started, whether initially or after preemption, a job-dependent setup must take place. First, we prove that the problem is strongly NP-hard. Then, we present a dynamic programming algorithm and a polynomial time approximation scheme.     

Exact algorithms for single-machine scheduling with time windows and precedence constraints

We study a single-machine scheduling problem that is a generalization of a number of problems for which computational procedures have already been published. Each job has a processing time, a release date, a due date, a deadline, and a weight representing the penalty per unit-time delay beyond the due date. The goal is to schedule all jobs such that the total weighted tardiness penalty is minimized and both the precedence constraints as well as the time windows (implied by the release dates and the deadlines) are respected. We develop a branch-and-bound algorithm that solves the problem to optimality. Computational results show that our approach is effective in solving medium-sized instances, and that it compares favorably with existing methods for special cases of the problem.     

Optimal release time on a stochastic single machine

The job release times are usually treated as given information in most scheduling research. However, in practice, the release time can be a controlled variable. It should be controlled carefully for many reasons. Jobs released to the shop floor too early would result in carrying costs (e.g. cost incurred by having unnecessary capital tied up in inventory). On the other hand, jobs released too late would cause machines and other resources to be idle and miss the due dates. With proper job release control, the best trade-off can be achieved, In this paper we consider a single-machine scheduling problem in which the processing times are stochastic. In particular, two models are under consideration. Model I assumes no unreleased jobs in the system while Model II relaxes this assumption. Procedures are developed for both models to determine the optimal release time for the arriving job. The objective is to minimize the weighted average of the expected flow time and the expected make-span