A Longest Processing Time First Bin-Packing Algorithm for Makespan Minimizing Problem of Parallel Batch Processing Machines

2016 ◽  
Vol 14 (7) ◽  
pp. 119
Author(s):  
Sang-Un Lee
Keyword(s):  
Processing Time ◽  
Bin Packing ◽  
Batch Processing ◽  
Batch Processing Machines ◽  
Packing Algorithm

Optimal Semi-Online Algorithm for Scheduling on Two Parallel Batch Processing Machines

2014 ◽  
Vol 31 (05) ◽  
pp. 1450038 ◽  
Author(s):  
Ming Liu ◽  
Feifeng Zheng ◽  
Zhanguo Zhu ◽  
Chengbin Chu
Keyword(s):  
Processing Time ◽  
Online Algorithm ◽  
Machine Scheduling ◽  
Batch Processing ◽  
Batch Processing Machines ◽  
Uncertain Environment ◽  
Processing Machine ◽  
Processing Times ◽  
Batch Processing Machine ◽  
Over Time

Batch processing machine scheduling in uncertain environment attracts more and more attention in the last decade. This paper deals with semi-online scheduling on two parallel batch processing machines with non-decreasing processing time of job. Jobs arrive over time in the online paradigm, and the processing time of any batch is equal to the length of the last arrival job in the batch. We study the unbounded model where each processing batch may contain an unlimited number of jobs, and the objective is to minimize the makespan. Given any job Jj together with its following job Jj+1, it is assumed that their processing times satisfy pj+1 ≥ αpj where α ≥ 1 is a constant. That is, jobs arrive in a non-decreasing order of processing times. We mainly propose an optimal ϕ-competitive online algorithm where ϕ ≥ 1 is a solution of equation ϕ3 + (α-1)ϕ2 + (α2 - α - 1)ϕ - α2 = 0.

scholarly journals Efficient algorithms to minimize Makespan of the unrelated parallel Batch-processing machines scheduling problem with unequal job ready times

2021 ◽  
Author(s):  
yaser zarouk ◽  
javad rezaeian ◽  
iraj mahdavi ◽  
Masoud Yaghini
Keyword(s):  
Processing Speed ◽  
Mixed Integer Linear Programming ◽  
Processing Time ◽  
Original Problem ◽  
Batch Processing ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Batch Processing Machines ◽  
Ready Time

This paper considers the minimization of makespan in the unrelated parallel batch processing machines scheduling problem with considering non-identical job size and dynamic job ready time. The considered unrelated machines have different capacity and different processing speed. Each machine processes a number of the jobs as a batch at the same time so that the machine’s capacity is not exceeded. The batch processing time and the batch ready time are equal to the largest processing time and the largest ready time of jobs in the same batch, respectively. In this paper, a Mixed Integer Linear Programming (MILP) model, two categories of the heuristic procedures (six heuristics) and a meta-heuristic algorithm are proposed to solve the problem. A lower bound is also presented by relaxing of the original problem to evaluate the quality of the proposed algorithms. The computational experiments show the performance of the proposed algorithms under the considered measures.

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