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.

PARALLEL MACHINE SCHEDULING WITH JOB DELIVERY COORDINATION

2017 ◽  
Vol 58 (3-4) ◽  
pp. 306-313
Author(s):  
J. M. DONG ◽  
X. S. WANG ◽  
L. L. WANG ◽  
J. L. HU
Keyword(s):  
Parallel Machines ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Performance Ratio ◽  
Worst Case ◽  
Identical Machine ◽  
Worst Case Performance Ratio ◽  
Job Delivery ◽  
Identical Machine Scheduling

We analyse a parallel (identical) machine scheduling problem with job delivery to a single customer. For this problem, each job needs to be processed on $m$ parallel machines non-pre-emptively and then transported to a customer by one vehicle with a limited physical capacity. The optimization goal is to minimize the makespan, the time at which all the jobs are processed and delivered and the vehicle returns to the machine. We present an approximation algorithm with a tight worst-case performance ratio of $7/3-1/m$ for the general case, $m\geq 3$.

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.

scholarly journals Two Parallel Machines Scheduling with Two-Vehicle Job Delivery to Minimize Makespan

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Lisi Cao ◽  
Jianhong Hao ◽  
Dakui Jiang
Keyword(s):  
Parallel Machines ◽  
Parallel Machine Scheduling ◽  
Performance Ratio ◽  
Identical Parallel Machines ◽  
Worst Case ◽  
Worst Case Ratio ◽  
Parallel Machines Scheduling ◽  
Np Hard Problem ◽  
Worst Case Performance Ratio ◽  
Job Delivery

A problem of parallel machine scheduling with coordinated job deliveries is handled to minimize the makespan. Different jobs call for dissimilar sizes of storing space in the process of transportation. A range of jobs of one customer in the problem have priority to be processed on two identical parallel machines without preemption and then delivered to the customer by two vehicles in batches. For this NP-hard problem, we first prove that it is impossible to have a polynomial heuristic with a worst-case performance ratio bound less than 2 unless P = NP. Thereafter, we develop a polynomial heuristic for this problem, the worst-case ratio of which is bounded by 2.

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