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.

OPTIMAL SEMI-ONLINE ALGORITHM FOR SCHEDULING ON A BATCH PROCESSING MACHINE

2009 ◽  
Vol 01 (02) ◽  
pp. 219-226
Author(s):  
MING LIU ◽  
YINFENG XU ◽  
CHENGBIN CHU ◽  
LU WANG
Keyword(s):  
Processing Time ◽  
Online Algorithm ◽  
Optimal Algorithm ◽  
Batch Processing ◽  
Scheduling Problems ◽  
Constant Number ◽  
Processing Machine ◽  
Processing Times ◽  
Batch Processing Machine ◽  
Single Batch

We consider two semi-online scheduling problems on a single batch (processing) machine with jobs' nondecreasing processing times and jobs' nonincreasing processing times, respectively. Our objective is to minimize the makespan. A batch processing machine can handle up to B jobs simultaneously. We study an unbounded model where B = ∞. The jobs that are processed together construct a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Jobs arrive over time. Let pj denote the processing time of job Jj. Given job Jj and its following job Jj + 1, we assume that pj + 1 ≥ α pj, where α ≥ 1 is a constant number, for the first problem with jobs' nondecreasing processing times. For the second problem, we assume that pj + 1 ≤ α pj, where 0 < α < 1 is a constant number. We propose an optimal algorithm for both problems with a competitive ratio [Formula: see text] for the first problem and [Formula: see text] for the second problem.

OPTIMAL SEMI-ONLINE ALGORITHMS FOR m-BATCH-MACHINE FLOW SHOP SCHEDULING

2012 ◽  
Vol 04 (04) ◽  
pp. 1250051 ◽  
Author(s):  
MING LIU ◽  
CHENGBIN CHU
Keyword(s):  
Online Algorithms ◽  
Processing Time ◽  
Flow Shop ◽  
Optimal Algorithm ◽  
Flow Shop Scheduling ◽  
Shop Scheduling ◽  
Batch Machine ◽  
Processing Times ◽  
Batch Processing Machine ◽  
Over Time

This paper deals with semi-online scheduling on m-batch-machine flow shop. The objective is to minimize the makespan. A parallel batch processing machine can handle up to B jobs simultaneously. We study an unbounded model where B = ∞. The jobs that are processed together construct a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. The problem is online in the sense that jobs arrive over time. Let pi, j(i = 1,…,m) denote the processing time of job Jj on machines Mi, respectively. Let Jj+1 be the following job of Jj in a job instance. We study semi-online problem with jobs' nondecreasing processing times. We focus on the case where p1, j = ⋯ = pm, j for i = 1, …, m and pi, j+1 ≥ βpi, j (β ≥ 1). For this problem, we propose an optimal algorithm [Formula: see text] with a competitive ratio [Formula: see text].

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