scholarly journals An improved approximation algorithm for single machine scheduling with job delivery

2011 ◽  
Vol 412 (3) ◽  
pp. 270-274 ◽  
Author(s):  
Peihai Liu ◽  
Xiwen Lu
Keyword(s):  
Approximation Algorithm ◽  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Job Delivery

scholarly journals A Primal-Dual Approximation Algorithm for Min-Sum Single-Machine Scheduling Problems

2017 ◽  
Vol 31 (2) ◽  
pp. 825-838 ◽  
Author(s):  
Maurice Cheung ◽  
Julián Mestre ◽  
David B. Shmoys ◽  
José Verschae
Keyword(s):  
Approximation Algorithm ◽  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Primal Dual ◽  
Machine Scheduling Problems

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.

scholarly journals Single machine scheduling with release dates and job delivery to minimize the makespan

2008 ◽  
Vol 393 (1-3) ◽  
pp. 102-108 ◽  
Author(s):  
Lingfa Lu ◽  
Jinjiang Yuan ◽  
Liqi Zhang
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Release Dates ◽  
Job Delivery

A 1.47-approximation algorithm for a preemptive single-machine scheduling problem

2000 ◽  
Vol 26 (4) ◽  
pp. 149-154 ◽  
Author(s):  
Michel X. Goemans ◽  
Joel M. Wein ◽  
David P. Williamson
Keyword(s):  
Approximation Algorithm ◽  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem

Single machine scheduling with job delivery to multiple customers

2017 ◽  
Vol 21 (3) ◽  
pp. 337-348 ◽  
Author(s):  
Jianming Dong ◽  
Xueshi Wang ◽  
Jueliang Hu ◽  
Guohui Lin
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Job Delivery

A PTAS for single-machine scheduling with release dates and job delivery to minimize makespan

2019 ◽  
Vol 53 (4) ◽  
pp. 1261-1266 ◽  
Author(s):  
Lingfa Lu ◽  
Liqi Zhang
Keyword(s):  
Single Machine ◽  
Approximation Scheme ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Release Dates ◽  
Polynomial Time Approximation Scheme ◽  
Round Trip ◽  
Time Approximation ◽  
Job Delivery ◽  
Capacitated Vehicle

We consider the single-machine scheduling problem with release dates and job delivery to minimize makespan. Preemption is not allowed in the processing of the jobs. All jobs are first processed on a single machine and then delivered by a capacitated vehicle to a single customer. The vehicle can deliver at most c ≥ 1 jobs in each shipment. The round-trip transportation time between the machine and customer is a constant T > 0. The problem was proved to be strongly NP-hard and a 3/2-approximation algorithm was presented in the literature. In this paper we provide a polynomial-time approximation scheme (PTAS) for the problem.

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