Multi-agent scheduling on a single machine with max-form criteria

Cheng, T.C.E.; Ng, C. T.; Yuan, Jinjiang

doi:10.1016/j.ejor.2007.04.040

Cited by 150 publications

(56 citation statements)

References 13 publications

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“…These papers assume various combinations of scheduling measures and machine settings. The relevant reference list contains Baker and Smith (2003) (focused on a single machine and the criteria of makespan, maximum lateness and total weighted completion time), Agnetis et al (2004) (considered the same and additional measures, eg the number of tardy jobs and maximum regular functions, and studied multi-machine settings as well), Cheng et al (2006) (proved that the problem with minimum number of tardy jobs for each agent is strongly NP-hard, and introduced a polynomial time solution for the case of unit time jobs), Ng et al (2006) (studied minimum weighted completion time for one agent subject to an upper bound on the number of tardy jobs for the second agent), Cheng et al (2007) (studied total tardiness), Agnetis et al (2007) (focused on a multi-agent setting), Cheng et al (2008) (multi-agent problems with precedence constraints), Liu and Tang (2008) and Liu et al (2009) (two agent scheduling with deteriorating jobs), Agnetis et al (2009) (branch-andbound algorithms for minimum total weighted completion time of the first agent, subject to an upper bound on several measures of the second agent), Lee et al (2009) (introduced multi-agent scheduling with total weighted completion time, and provided fully polynomial approximation schemes), Mor and Mosheiov (2010) (two-agent scheduling with various earliness measures), Leung et al (2010) (twoagent scheduling with preemption and release dates), Wan et al (2010) (two-agent problems with controllable processing times), Liu et al (2010) (two-agent single-machine scheduling with position-dependent processing times), Cheng et al (2011) (minimum weighted completion time of the first agent subject to no tardy jobs of the second agent, with learning effect based on sum-of-processing times), Li and Yuan (2012) (two-agent scheduling with batching, where the total processing time of a batch is equal to the maximum processing time of the jobs in the batch), Mor and Mosheiov (2011) (two-agent batch scheduling assuming identical jobs and minimum total flowtime), Li and Hsu (2012) (minimizing total weighted completion time of both agents, subject to an upper bound on the makespan of both agents, with a learning effect), Gawiejnowicz et al (2011) (minimum total tardiness of the first agent subject to no tardy jobs of the second agent, with time-dependent proce...…”

Section: Introductionmentioning

confidence: 99%

Polynomial time solutions for scheduling problems on a proportionate flowshop with two competing agents

Mor

Mosheiov

2014

Journal of the Operational Research Society

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In scheduling problems with two competing agents, each one of the agents has his own set of jobs and his own objective function, but both share the same processor. The goal is to minimize the value of the objective function of one agent, subject to an upper bound on the value of the objective function of the second agent. In this paper we study two-agent scheduling problems on a proportionate flowshop. Three objective functions of the first agent are considered: minimum maximum cost of all the jobs, minimum total completion time, and minimum number of tardy jobs. For the second agent, an upper bound on the maximum allowable cost is assumed. We introduce efficient polynomial time solution algorithms for all cases.

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Section: Introductionmentioning

confidence: 99%

Polynomial time solutions for scheduling problems on a proportionate flowshop with two competing agents

Mor

Mosheiov

2014

Journal of the Operational Research Society

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“…Based on this property, it can be observed that the complexity of any MASP with LCC approach for two disjoint sets of jobs and makespan as one of the criteria is the same as the corresponding single criterion problem for the second criterion (Baker and Smith, 2003). This result can be generalized as follows: the complexity of any MASP with LCC approach for more than two disjoint sets of jobs and makespan criterion for J k is the same as the corresponding problem without the k-th set (Cheng et al, 2008).…”

Section: General Propertiesmentioning

confidence: 99%

“…Complexities for two sets of jobs are summarised in Table 2 Apart from the cases in Table 2, Agnetis et al (2007a) show that the general case 1||F l (max F Cheng et al (2008) show that the complexity of 1||F l (max (Baker and Smith, 2003). Moreover, this problem for K sets of jobs (K > 2) is polynomially solvable in O(n + K log K) (Cheng et al, 2008). However, the weighted version 1||F l (max w…”

Section: Lcc Approachmentioning

confidence: 99%

A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs: Multi-agent scheduling problems

González

Framiñán

2014

European Journal of Operational Research

117

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Most classical scheduling research assumes that the objectives sought are common to all jobs to be scheduled. However, many real-life applications can be modeled by considering different sets of jobs, each one with its own objective(s), and an increasing number of papers addressing these problems has appeared over the last few years. Since so far the area lacks a unified view, the studied problems have received different names (such as interfering jobs, multi-agent scheduling, mixed-criteria, etc), some authors do not seem to be aware of important contributions in related problems, and solution procedures are often developed without taking into account existing ones. Therefore, the topic is in need of a common framework that allows for a systematic recollection of existing contributions, as well as a clear definition of the main research avenues. In this paper we review multicriteria scheduling problems involving two or more sets of jobs and propose an unified framework providing a common definition, name and notation for these problems. Moreover, we systematically review and classify the existing contributions in terms of the complexity of the problems and the proposed solution procedures, discuss the main advances, and point out future research lines in the topic.

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“…In addition, Cheng et al (2006) study a two-agent problem on a single machine where the objective function of each agent is to minimize the total weighted number of tardy jobs. Also, Cheng et al (2008) study a single machine problem with multi-agent where the objective function is max-form. Liu and Tang (2008) considers a single machine scheduling problem with two-agent with linear deteriorated processing time of each job.…”

Section: Introductionmentioning

confidence: 99%

Heuristic algorithms for two-machine re-entrant flowshop scheduling problem with jobs of two classes

Jeong

Shim

2017

JAMDSM

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This paper considers a two-machine re-entrant flowshop scheduling problem in which there are two classes of jobs with different urgencies, i.e., urgent jobs and normal (not urgent) jobs. The objective of this problem is minimizing total tardiness of one class of urgent jobs and maximum completion times of the other class of normal jobs. To solve this problem, a lower bound and several heuristic algorithms for the problem are proposed. To evaluate the performance of developed algorithms, computational experiments are performed on randomly generated problems, and results are reported with analysis. The suggested algorithms show better performances compared with the ones used in real manufacturing systems in terms of solution quality and computation time. Jeong and Shim, Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.11, No.5 (2017) complete urgent jobs as early as possible since these jobs had very early due dates. In this problem, due dates of urgent jobs are set to the earliest possible completion times of the job on machine 2 (completion times of the job on machine 2 assuming that the job is processed through all machines without waiting). In this study, the objective of the problem is minimizing a weighted sum of total tardiness of urgent jobs and the maximum completion time of normal jobs.Re-entrant flowshop scheduling problems receive increasing attention in recent years. Graves et al. (1983) introduce a wafer fab in semi-conductor manufacturing system as a re-entrant flowshop and propose a simple scheduling algorithm for the re-entrant flowshop to minimize average throughput time while meeting a given production rate. Demirkol and Uzsoy (2000) suggest decomposition methods in a re-entrant flowshop for the objective of minimizing maximum lateness. Choi and Kim (2007) The problem in this study is one of the multi-objective flowshop problems since two types of measures are combined, i.e. weighted sum of total tardiness of urgent jobs and the maximum completion time of normal jobs. There have been various heuristic algorithms for multiple-objective flowshop problems including Rajendran and Ziegler (2004), Ravindran objective problems have two or more common objective functions for all jobs, this problem has a different objective function for jobs of a different class since jobs are classified into two classes according to their urgencies. Therefore, this problem is related to a multi-agent problem which is the special case of multi-objective problems. (Agnetis et al., 2004) Multi-agent problems consist of two or more agents (class or customers) and each agent has a different objective function for their jobs. That is, if we define each class of jobs as an agent, the problem in this paper can be regarded as a multiagent problem.Recently, multi-agent scheduling problems are also studied. Baker and Smith (2003) study weighted optimization problem for the multi-agent on single machine, the objectives including the maximum lateness, total weighted completion time and makespan. Agn...

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Multi-agent scheduling on a single machine with max-form criteria

Cited by 150 publications

References 13 publications

Polynomial time solutions for scheduling problems on a proportionate flowshop with two competing agents

Polynomial time solutions for scheduling problems on a proportionate flowshop with two competing agents

A common framework and taxonomy for multicriteria scheduling problems with interfering and competing jobs: Multi-agent scheduling problems

Heuristic algorithms for two-machine re-entrant flowshop scheduling problem with jobs of two classes

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