Single machine batch scheduling with release times

Motivated by a high-throughput logging system, we investigate the single machine scheduling problem with batching, where jobs have release times and processing times, and batches require a setup time. Our objective is to minimize the total flow time, in the online setting. For the online problem where all jobs have identical processing times, we propose a 2-competitive algorithm and we prove a corresponding lower bound. Moreover, we show that if jobs with arbitrary processing times can be processed in any order, any online algorithm has a linear competitive ratio in the worst case. A preliminary version of a part of this paper was presented at the 31st International Symposium on Mathematical Foundations of Computer Science (MFCS 2006). We gratefully acknowledge reviewers’ comments that helped to improve the presentation of this work. Supported by the Swiss SBF under contract no. C05.0047 within COST-295 (DYNAMO) of the European Union. Research carried out while B. Weber was affiliated with the Institute of Theoretical Computer Science, ETH Zurich.     

Single machine scheduling problems with subcontracting options

In this paper, we study a scheduling model as follows: there are n jobs which can be processed in house on a single machine or subcontracted to a subcontractor. If a job is subcontracted, its processing cost is different from the in-house cost and its delivery lead time is a stepwise function of the total processing time of outsourced jobs. Two objective functions are studied (1) to minimize the weighted sum of the maximal completion time and the total processing cost and (2) to minimize the weighted sum of the number of tardy jobs and the total processing cost. For the first problem, we prove that it is NP-hard and get a pseudo-polynomial time algorithm. For the second problem, we prove that it is NP-hard and get a pseudo-polynomial time algorithm for a special case.     

Single machine scheduling with general positional deterioration and rate-modifying maintenance

We present polynomial-time algorithms for single machine problems with generalized positional deterioration effects and machine maintenance. The decisions should be taken regarding possible sequences of jobs and on the number of maintenance activities to be included into a schedule in order to minimize the overall makespan. We deal with general non-decreasing functions to represent deterioration rates of job processing times. Another novel extension of existing models is our assumption that a maintenance activity does not necessarily fully restore the machine to its original perfect state. In the resulting schedules, the jobs are split into groups, a particular group to be sequenced after a particular maintenance period, and the actual processing time of a job is affected by the group that job is placed into and its position within the group.     

Single machine scheduling with non-availability interval and optional job rejection

This paper studies the single machine scheduling problem with availability constraints and optional job rejection. We consider the non-resumable and resumable variants, and show that the problems remain ordinary NP-hard, even with the rejection possibility extension, by presenting pseudo-polynomial dynamic-programming (DP) solutions. We also present an enhanced running time implementation of the algorithm of Kellerer and Strusevich (Algorithmica 57(4):769–795, 2010) for the resumable scenario without job rejection. This solution is adapted to efficiently solve the machine non-availability problem with a floating interval and the problem of two competing agents on a single machine, with and without optional job rejection. Numerical experiments support the efficiency of our DP implementation.

     

Single machine scheduling: A comparison of two solution procedures

Recent research on the single machine scheduling problem has focused on the treatment of multiple scheduling objectives. Most works have used some combination of mean flowtime, maximum tardiness, or total tardiness as scheduling criteria. Previous research has largely ignored earliness as a scheduling criterion. This paper presents a model that employs the criteria of flowtime as a measure of work-in-process (WIP) inventory and total job earliness to represent finished goods inventory. Total tardiness is used to represent customer satisfaction. The three criteria are used to form a single, weighted-sum objective function for guiding the choice of the best processing sequence. Two procedures are presented that might be used to solve this problem. The first is an enumeration scheme using bounding and dominance criteria that have been developed to aid efficient solution, and the second is a mixed integer linear programming (LP) formulation. Computational experience with the two models is also presented.     

Single machine lot scheduling with non-uniform lot capacities and processing times

Journal of Combinatorial Optimization - In this paper, we investigate the single machine lot scheduling problem in which each lot contains one or more jobs (or part of jobs). Jobs with different...     

Single machine group scheduling to minimize mean flow time subject to due date constraints

This paper considers a single machine group scheduling problem. All jobs are classified into groups and the jobs within a group are processed contiguously on the machine. A sequence-independent setup time is incurred between each two consecutively scheduled groups. This paper presents a solution procedure which utilizes Smith's algorithm and a proposed modified Smith's algorithm to find an optimal job sequence and an optimal group sequence which minimizes the mean flow time of jobs subject to the constraint that no jobs are tardy. The complexity of the algorithm is shown to have a polynomial running time in the number of groups and jobs.     

Related machine scheduling with machine speeds satisfying linear constraints

Journal of Combinatorial Optimization - We propose a related machine scheduling problem in which the processing times of jobs are given and known, but the speeds of machines are variables and must...     

On-line machine scheduling with batch setups

We study a class of scheduling problems with batch setups for the online-list and online-time paradigms. Jobs are to be scheduled in batches for processing. All jobs in a batch start and complete together, and a constant setup is prior to each batch. The objective is to minimize the total completion time of all jobs. We primarily consider the special cases of these problems with identical processing times, for which efficient on-line heuristics are proposed and their competitive performance is evaluated.     

On single machine scheduling with resource constraint

The single machine scheduling with resource constraint is a nonlinear combinatorial optimization problem in cloud computing applications. Given a set of jobs and certain resource, the problem is to find a permutation of jobs and a distribution of resource to optimize certain objective function. The processing time of each job is a nonlinear function with respect to the resource assigned to it. In this paper, we propose a naive algorithm and study a subproblem in the algorithm that suppose the permutation of jobs is also given, how to find a resource distribution to minimize the total weighted flow time. We found a polynomial-time optimal solution for a special case and an approximation solution in general case.     

Single process plan scheduling with genetic algorithms

AIn this paper, a genetic algorithm model for scheduling manufacturing resources is developed for the case when there is only one process plan available per job, hence there is no routeing flexibility. The scheduling objectives considered are minimizing the makespan and mean flow time. Genetic algorithms design issues are discussed and the working of the employed genetic operators is explained in detail. Parameters for the genetic algorithms used for single process plan scheduling SPPS problems are set through extensive experimentation. Finally, the genetic algorithms approach is compared with several other approaches in terms of optimality of solution and computAuthors: ing time. It was observed that in most cases the genetic algorithms approach performed better than other approaches both in terms of finding an optimal or near optimal solution as well as computing time.     

Online lazy bureaucrat scheduling with a machine deadline

The lazy bureaucrat scheduling problem was first introduced by Arkin et al. (Inf Comput 184:129–146, 2003). Since then, a number of variants have been addressed. However, very little is known on the online version. In this note we focus on the scenario of online scheduling, in which the jobs arrive over time. The bureaucrat (machine) has a working time interval. Namely, he has a deadline by which all scheduled jobs must be completed. A decision is only based on released jobs without any information on the future. We consider two objective functions of [min-makespan] and [min-time-spent]. Both admit best possible online algorithms with competitive ratio of \(\frac{\sqrt{5}+1}{2}\approx 1.618\).     

Parallel machine scheduling subject to auxiliary resource constraints

This paper is motivated by scheduling photolithography machines in semiconductor manufacturing wherein reticle requirements are the auxiliary resource constraints. As the problem is NP hard, two different heuristic solution approaches are developed. The performance of our network-based mathematical model and heuristics are evaluated through an extensive set of problem instances. The best performing heuristic method typically produces solutions that are 1.72% above optimal. If this method is used as the seed solution for a Tabu search-based post processing algorithm, schedules that are 0.78% above the optimal solution, on average, are possible.     

A pairwise interchange algorithm for parallel machine scheduling

This paper considers the problem of non-preemptive scheduling n tasks on m identical parallel processors to minimize makespan for simultaneous arrivals. Based on a pairwise interchange method, an efficient algorithm ispresented which is able to give a near-optimal schedule in a short time through suitable pairwise interchange between tasks, after an initial solution is constructed. The behaviour of the algorithm is discussed. Testing results prove its high performance in comparison with available simple heuristic procedures. Finally, the algorithm is generalized for the problems of non-identical processors and non-simultaneous arrivals.     

Multi-objective scheduling of two-job families on a single machine

This paper presents a preliminary analysis of the typical scheduling environment in semiconductor manufacturing involving multiple job families, and where more than one objective such as cycle time, machine utilization and the due-date accuracy needs to be simultaneously considered. In this study, the NP-hard problem of scheduling N independent jobs on a single testing machine with due dates and sequence-dependent setup times is addressed, where the multiple objectives are to minimize average cycle time, to minimize average tardiness, and to maximize machine utilization. A Pareto optimal solution, which is not inferior to any other feasible solutions in terms of all objectives, is generated combining the analytically optimal and conjunctive simulated scheduling approach. First, the machine-scheduling problem is modeled using the discrete event simulation approach and the problem is divided into simulation clock based lot selection sub-problems. Then, a Pareto optimal lot is selected using the compromise programming technique for multiobjective optimization at each decision instant in simulated time. With the help of a broad experimental design, this developed solution is then compared with common heuristic-dispatching rules such as SPT and EDD, which show better results for all the objectives over a wide range of problems. The developed scheduling method shows approximately 16.7% reduction in average cycle time, 25.6% reduction in average tardiness, and 21.6% improvement in machine utilization over the common dispatching rules, SPT and EDD.     

Parallel-machine scheduling of deteriorating jobs with potential machine disruptions

We consider parallel-machine scheduling of deteriorating jobs in a disruptive environment in which some of the machines will become unavailable due to potential disruptions. This means that a disruption to some of the machines may occur at a particular time, which will last for a period of time with a certain probability. If a job is disrupted during processing by a disrupted machine and it does not need (needs) to re-start after the machine becomes available again, it is called the resumable (non-resumable) case. By deteriorating jobs, we mean that the actual processing time of a job grows when it is scheduled for processing later because the machine efficiency deteriorates over time due to machine usage and aging. However, a repaired machine will return to its original state of efficiency. We consider two cases, namely performing maintenance immediately on the disrupted machine when a disruption occurs and not performing machine maintenance. In each case, the objective is to determine the optimal schedule to minimize the expected total completion time of the jobs in both non-resumable and resumable cases. We determine the computational complexity status of various cases of the problem, and provide pseudo-polynomial-time solution algorithms and fully polynomial-time approximation schemes for them, if viable.     

一类新型批处理机调度问题的理论分析

钢卷在冷轧生产中,为了改进其性能,需要在罩式炉进行退火,退火过程由加热、保温和降温三段组成,而这三段处理时间由于工艺上的要求不能归结为一个时间,这与传统批处理机调度有明显的差别.对新型批处理机的总加权完成时间最小化问题建立了非线性整数规划模型,开发了基于动态规划的启发式算法.通过理论分析,获得该算法的误差性能比为3.对于三段中的某一段板卷的处理时间相同的情况,证明了启发式算法的误差性能比是2,而且证明是紧界.对于三段中的某二段板卷的处理时间相同的情况,证明了启发式算法是最优算法.对启发式算法扩展到带有任意段的加工时间的一般情况进行了性能分析.     

Competitive analysis of online machine rental and online parallel machine scheduling problems with workload fence

In this paper, we introduce the concept of “workload fence" into online machine rental and machine scheduling problems. With the knowledge of workload fence, online algorithms acquire the information of a finite number of first released jobs in advance. The concept originates from the frozen time fence in the domain of master scheduling in materials management. The total processing time of the jobs foreseen, corresponding to a finite number of jobs, is called workload fence, which is irrelevant to the job sequence. The remaining jobs in the sequence, however, can only become known on their arrival. This work aims to reveal whether the knowledge of workload fence helps to boost the competitive performance of deterministic online algorithms. For the online machine rental problem, we prove that the competitiveness of online algorithms can be improved with a sufficiently large workload fence. We further propose a best online algorithm for the corresponding scenario. For online parallel machine scheduling with workload fence, we give a positive answer to the above question for the case where the workload fence is equal to the length of the longest job. We also show that the competitiveness of online algorithms may not be improved even with a workload fence strictly larger than the largest length of a job. The results help one manager to make a better decision regarding the tradeoff between the performance improvement of online algorithms and the cost caused to acquire the knowledge of workload fence.