Effective heuristic for makespan minimization in parallel batch machines with non-identical capacities

Jia, Zhao; Li, Kai; Leung, Joseph Y.-T.

doi:10.1016/j.ijpe.2015.07.021

Cited by 46 publications

(11 citation statements)

References 48 publications

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“…More recently, several research groups have focused on the scheduling problems on parallel batch machines with different capacities and applications in many fields [30][31][32][33][34][35][36][37][38][39][40][41]. The special case of P s j , p − batch, K i C max , where all s j ≤ K 1 (i.e., all jobs can be assigned to any machine), is denoted as P s j ≤ K 1 , p − batch, K i C max .…”

Section: Literature Reviewmentioning

confidence: 99%

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A Novel Fast Parallel Batch Scheduling Algorithm for Solving the Independent Job Problem

Zhang

Song

et al. 2020

Applied Sciences

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With the rapid economic development, manufacturing enterprises are increasingly using an efficient workshop production scheduling system in an attempt to enhance their competitive position. The classical workshop production scheduling problem is far from the actual production situation, so it is difficult to apply it to production practice. In recent years, the research on machine scheduling has become a hot topic in the fields of manufacturing systems. This paper considers the batch processing machine (BPM) scheduling problem for scheduling independent jobs with arbitrary sizes. A novel fast parallel batch scheduling algorithm is put forward to minimize the makespan in this paper. Each of the machines with different capacities can only handle jobs with sizes less than the capacity of the machine. Multiple jobs can be processed as a batch simultaneously on one machine only if their total size does not exceed the machine capacity. The processing time of a batch is determined by the longest of all the jobs processed in the batch. A novel and fast 4.5-approximation algorithm is developed for the above scheduling problem. For the special case of all the jobs having the same processing times, a simple and fast 2-approximation algorithm is achieved. The experimental results show that fast algorithms further improve the competitive ratio. Compared to the optimal solutions generated by CPLEX, fast algorithms are capable of generating a feasible solution within a very short time. Fast algorithms have less computational costs.

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Section: Literature Reviewmentioning

confidence: 99%

“…Damodaran et al [32] proposed a PSO method for P s j , p − batch, K i C max . Jia et al [33] presented a heuristic and a metaheuristic for P s j , p − batch, K i C max . Wang and Leung [34] analyzed the problem P s j , p j = 1, p − batch, K i C max where each job has its own unit processing time.…”

Section: Literature Reviewmentioning

confidence: 99%

A Novel Fast Parallel Batch Scheduling Algorithm for Solving the Independent Job Problem

Zhang

Song

et al. 2020

Applied Sciences

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“…In the left part of the inequation (11) we have quantity of product q for order i , which may be released in batch x . This quantity is always less than available stock of necessary materials Apart from the constraint (11), in order to build tree nodes, it is necessary to take into account some constraints related to machine capacity. First, possibility of transfer from machine performing the previous operation to machine performing the following operation depends on current filling of these machines.…”

Section: Fig 1 Example Of Flexible Multiproduct Batch Linementioning

confidence: 99%

“…The GA method was successfully applied by [10] for multistage batch scheduling of big size with criteria max C or max F . In [11] the efficiency was demonstrated of the Max-Min Ant System (MMAS) algorithm for parallel unrelated machines scheduling and the criterion max…”

Section: Introductionmentioning

confidence: 99%

Bi-criteria scheduling for Multistage Multiproduct Batch Plants with Due Dates and Setups

Mauergauz¹

2016

IJIE

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This paper presents a method for multistage multiproduct batch scheduling based on two criteria simultaneously: relative setup cost criterion and average orders utility criterion. Batch size is determined at the first operation and will not change further. During scheduling process batches are automatically grouped by product types for cost decreasing. Storing between operations is unavailable. In this method, the concept of production intensity as a dynamic production process parameter is used. A software package allows scheduling for medium quantity of jobs. The result of software application is the set of non-dominant versions proposed to a user for making a final choice.

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“…Most of the existing results dealt with the problems with identical job sizes or batch capacities. Recently, several papers appeared which studied the problem with non-identical job sizes and batch capacities [9][10][11][12][13][14]. Xu and Bean [9] presented a genetic algorithm for problem cannot be approximated to within a ratio better than 2 unless P=NP, and then provided a 2-approximation algorithm for it.…”

Section: Introductionmentioning

confidence: 99%

A Linear Time Exact Algorithm for Scheduling Unit-processing-time-jobs with Sizes 1 or k

Xin¹,

Mu²,

Mou³

2017

Proceedings of the 2017 2nd International Conference on Materials Science, Machinery and Energy Engineering (MSMEE 2017)

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Abstract. The problem of scheduling jobs with sizes on batch machines is considered. Each machine can process several jobs as a batch simultaneously as long as the total size of these jobs does not exceed the capacity of the machine. The processing time of a batch is defined to be the longest processing time of the jobs in the batch. The goal is to minimize makespan, i.e., the maximum job completion time. It has been known to be strongly NP-hard. A linear time exact algorithm is presented for a special case where all the jobs have processing times 1 and sizes 1 or k (k is not fixed).

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Effective heuristic for makespan minimization in parallel batch machines with non-identical capacities

Cited by 46 publications

References 48 publications

A Novel Fast Parallel Batch Scheduling Algorithm for Solving the Independent Job Problem

A Novel Fast Parallel Batch Scheduling Algorithm for Solving the Independent Job Problem

Bi-criteria scheduling for Multistage Multiproduct Batch Plants with Due Dates and Setups

A Linear Time Exact Algorithm for Scheduling Unit-processing-time-jobs with Sizes 1 or k

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