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

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 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.

SINGLE MACHINE SCHEDULING WITH JOB DELIVERY TO MINIMIZE MAKESPAN

2008 ◽  
Vol 25 (01) ◽  
pp. 1-10 ◽  
Author(s):  
LINGFA LU ◽  
JINJIANG YUAN
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Performance Ratio ◽  
Extended Version ◽  
Worst Case ◽  
Transportation Time ◽  
Transportation Times ◽  
Worst Case Performance Ratio ◽  
Job Delivery

In the single machine scheduling problem with job delivery to minimize makespan, jobs are processed on a single machine and delivered by a capacitated vehicle to their respective customers. We first consider the special case with a single customer, that is, all jobs have the same transportation time. Chang and Lee (2004) proved that this case is strongly NP-hard. They also provided a heuristic with the worst-case performance ratio [Formula: see text], and pointed out that no heuristic can have a worst-case performance ratio less than [Formula: see text] unless P = NP. In this paper, we provide a new heuristic which has the best possible worst-case performance ratio [Formula: see text]. We also consider an extended version in which the jobs have non-identical transportation times and the transportation time of a delivery batch is defined as the maximum transportation time of the jobs contained in it. We provide a heuristic with the worst-case performance ratio 2 for the extended version, and show that this bound is tight.

scholarly journals Price of fairness in two-agent single-machine scheduling problems

2019 ◽  
Vol 276 (1) ◽  
pp. 79-87 ◽  
Author(s):  
Alessandro Agnetis ◽  
Bo Chen ◽  
Gaia Nicosia ◽  
Andrea Pacifici
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Machine Scheduling Problems
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