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.

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, $m\geq 3$.

scholarly journals A parallel-machine scheduling with periodic constraints under uncertainty

2019 ◽  
Vol 11 (12) ◽  
pp. 168781401989243 ◽  
Author(s):  
Jiayu Shen ◽  
Yuanguo Zhu
Keyword(s):  
Parallel Machines ◽  
Parallel Machine Scheduling ◽  
Time Algorithm ◽  
Optimal Choice ◽  
Practical Reasons ◽  
Scheduling Problem ◽  
Worst Case ◽  
Uncertain Variables ◽  
Worst Case Ratio ◽  
Modified Algorithm

Most studies on scheduling problem have assumed that the machine is continuously available. However, the machine is likely to be unavailable for many practical reasons (e.g. breakdown and planned preventive maintenance). Once a machine is not available, the optimal scheme in the deterministic scenario may not be the optimal choice. To address the actual scenario, a scheduling problem with two identical parallel machines, one of which requires periodic maintenance, is considered in this article. For uncertainties in reality, the processing and maintenance time are considered as uncertain variables. A novel method to study the worst-case ratio in an uncertain scenario is proposed. It is shown that the worst-case ratio of the longest processing time algorithm is 3/2 at a high confidence level. Given theoretical analysis results, an modified algorithm is proposed. Finally, numerical experiments are used to verify the feasibility of the modified algorithm.

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.

An Optimal Preemptive Algorithm for the Single-Server Parallel-Machine Scheduling with Loading and Unloading Times

2014 ◽  
Vol 31 (05) ◽  
pp. 1450039 ◽  
Author(s):  
Yiwei Jiang ◽  
Huijuan Wang ◽  
Ping Zhou
Keyword(s):  
Parallel Machines ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Solution Algorithm ◽  
Single Server ◽  
Preemptive Scheduling ◽  
Scheduling Problem ◽  
Identical Parallel Machines ◽  
Loading And Unloading

We study a preemptive scheduling problem on two identical parallel machines that share a common server. Each job has to be loaded by the server before being processed on one of the machines and unloaded by the server after its processing. The loading and unloading times are both equal to one time unit. The goal is to minimize the makespan. We propose a O(n log n) solution algorithm for the preemptive variant of the problem.

Open-shop dense schedules: properties and worst-case performance ratio

2009 ◽  
Vol 15 (1) ◽  
pp. 3-11 ◽  
Author(s):  
Rongjun Chen ◽  
Wanzhen Huang ◽  
Zhongxian Men ◽  
Guochun Tang
Keyword(s):  
Open Shop ◽  
Performance Ratio ◽  
Worst Case ◽  
Worst Case Performance Ratio

scholarly journals Parallel Machine Scheduling with Batch Delivery to Two Customers

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Xueling Zhong ◽  
Dakui Jiang
Keyword(s):  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Variable Cost ◽  
Worst Case ◽  
Batch Delivery ◽  
Worst Case Ratio ◽  
Processing Facility ◽  
Production And Distribution ◽  
Distribution Cost

In some make-to-order supply chains, the manufacturer needs to process and deliver products for customers at different locations. To coordinate production and distribution operations at the detailed scheduling level, we study a parallel machine scheduling model with batch delivery to two customers by vehicle routing method. In this model, the supply chain consists of a processing facility withmparallel machines and two customers. A set of jobs containingn1jobs from customer 1 andn2jobs from customer 2 are first processed in the processing facility and then delivered to the customers directly without intermediate inventory. The problem is to find a joint schedule of production and distribution such that the tradeoff between maximum arrival time of the jobs and total distribution cost is minimized. The distribution cost of a delivery shipment consists of a fixed charge and a variable cost proportional to the total distance of the route taken by the shipment. We provide polynomial time heuristics with worst-case performance analysis for the problem. Ifm=2and(n1-b)(n2-b)<0, we propose a heuristic with worst-case ratio bound of 3/2, wherebis the capacity of the delivery shipment. Otherwise, the worst-case ratio bound of the heuristic we propose is2-2/(m+1).

Sign in / Sign up

Export Citation Format

Share Document