Concise review of relaxations and approximation algorithms for nonidentical parallel-machine scheduling to minimize total weighted completion times

2008 ◽  
Vol 19 (4) ◽  
pp. 827-834 ◽  
Author(s):  
Li Kai ◽  
Yang Shanlin
Keyword(s):  
Approximation Algorithms ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Concise Review ◽  
Completion Times

scholarly journals Parallel-Machine Scheduling with DeJong’s Learning Effect, Delivery Times, Rate-Modifying Activity, and Resource Allocation

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Li Sun ◽  
Bin Wu ◽  
Lei Ning
Keyword(s):  
Resource Allocation ◽  
Learning Effect ◽  
Waiting Times ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Absolute Deviation ◽  
Delivery Times ◽  
Completion Times ◽  
Total Resource

We investigate parallel-machine scheduling with past-sequence-dependent (p-s-d) delivery times, DeJong’s learning effect, rate-modifying activity, and resource allocation. Each machine has a rate-modifying activity. We consider two versions of the problem to minimize the sum of the total completion times, the total absolute deviation of job completion times, and the total resource allocation and the sum of the total waiting times, the total absolute deviation of job waiting times, and the total resource allocation, respectively. The problems under our present model can be solved in polynomial time.

Online Scheduling on Two Parallel Identical Machines with a Non-Clairvoyant Disruption

2011 ◽  
Vol 88-89 ◽  
pp. 264-268
Author(s):  
Fei Feng Zheng ◽  
Hong Long Wei ◽  
Yin Feng Xu ◽  
Ming Liu
Keyword(s):  
Lower Bound ◽  
Unit Length ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Maximum Deviation ◽  
Identical Machines ◽  
Parallel Identical Machines ◽  
One Machine ◽  
Completion Times

This paper studies two parallel machine scheduling with a non-clairvoyantdisruption such that there happens one disruption on one machine at time 0 and its du-ration length can only be known at its end. As in [1], we introduce transportation timein the environment of disruption, aiming to minimize the maximum deviation of jobs'planned and actual completion times. We adopt online theory to describe the problemand focus on the case of unit length of job. We rst show that a greedily waiting strategyis 2-competitive. Our main result is a 3/2-competitive strategy BD which makes useof job transportation. We also prove a matching lower bound, implying that BD is anoptimal strategy.

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