scholarly journals Worst-Case Analysis of an Approximation Algorithm for Single Machine Scheduling Problem

2021 ◽  
Author(s):  
Natalia Grigoreva
Keyword(s):  
Approximation Algorithm ◽  
Single Machine ◽  
Case Analysis ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Worst Case Analysis ◽  
Scheduling Problem ◽  
Worst Case

scholarly journals Best Possible Approximation Algorithms for Single Machine Scheduling with Increasing Linear Maintenance Durations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xuefei Shi ◽  
Dehua Xu
Keyword(s):  
Approximation Algorithm ◽  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Point Of View ◽  
Scheduling Problem ◽  
Worst Case ◽  
Time Approximation ◽  
Polynomial Time Approximation Algorithm ◽  
Maintenance Activities

We consider a single machine scheduling problem with multiple maintenance activities, where the maintenance duration function is of the linear formft=a+btwitha≥0andb>1. We propose an approximation algorithm named FFD-LS2I with a worst-case bound of 2 for problem. We also show that there is no polynomial time approximation algorithm with a worst-case bound less than 2 for the problem withb≥0unlessP=NP, which implies that the FFD-LS2I algorithm is the best possible algorithm for the caseb>1and that the FFD-LS algorithm, which is proposed in the literature, is the best possible algorithm for the caseb≤1both from the worst-case bound point of view.

scholarly journals A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 61
Author(s):  
Wencheng Wang ◽  
Xiaofei Liu
Keyword(s):  
Approximation Algorithm ◽  
Single Machine ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Single Machine Scheduling ◽  
Release Time ◽  
Release Dates ◽  
Scheduling Problem ◽  
Release Times

In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a job is rejected. Each job has a release time and a processing time, and the job can not be processed before its release time. The objective of P|rj,reject|Cmax+π(R) is to minimize the makespan of the accepted jobs plus the penalty of the rejected jobs, where the penalty is determined by a submodular function. This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and submodular rejection penalties. In this paper, inspired by the primal-dual method, we present a combinatorial 2-approximation algorithm to P|rj,reject|Cmax+π(R). This ratio coincides with the best known ratio for the parallel-machine scheduling with submodular penalties and the single machine scheduling problem with release dates and submodular rejection penalties.

SINGLE MACHINE SCHEDULING WITH BATCH DELIVERY TO MULTIPLE CUSTOMERS IN A STAR-SHAPED NETWORK

2013 ◽  
Vol 30 (01) ◽  
pp. 1250048 ◽  
Author(s):  
LEIYANG WANG ◽  
ZHAOHUI LIU
Keyword(s):  
Approximation Algorithm ◽  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Limited Capacity ◽  
Batch Delivery ◽  
Single Vehicle

In this paper, we consider the scheduling problem in which the jobs are first processed on a single machine and then delivered in batches by a single vehicle with limited capacity to the respective customers located at the vertices of a star-shaped network. The goal is to minimize the makespan. We present a 3/2-approximation algorithm for the identical job size case and a 2-approximation algorithm for the non-identical job sizes case.

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