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 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.

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 ◽  
pp. 306
Author(s):  
Jianming Dong ◽  
Xueshi Wang ◽  
Liliang Wang ◽  
Jueliang Hu
Keyword(s):  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Job Delivery

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.

scholarly journals Two Parallel-Machine Scheduling Problems with Function Constraint

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Chia-Lun Hsu ◽  
Jan-Ray Liao
Keyword(s):  
Completion Time ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Total Completion Time ◽  
Scheduling Problems ◽  
Worst Case ◽  
Time Problem ◽  
Constraint Problem ◽  
Machine Scheduling Problems

The objective of this paper is to minimize both the makespan and the total completion time. Since parallel-machine scheduling which contains the function constraint problem has been a new issue, this paper explored two parallel-machine scheduling problems with function constraint, which refers to the situation that the two machines have a same function but one of the machines has another. We pointed out that the function constraint occurs not only in the manufacturing system but also in the service system. For the makespan problem, we demonstrated that it is NP-hard in the ordinary sense. In addition, we presented a polynomial time heuristic for this problem and have proved its worst-case ratio is not greater than 5/4. Furthermore, we simulated the performance of the algorithm through computational testing. The overall mean percent error of the heuristic is 0.0565%. The results revealed that the proposed algorithm is quite efficient. For the total completion time problem, we have proved that it can be solved in On4 time.

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).

scholarly journals Parallel Machine Scheduling with Nested Processing Set Restrictions and Job Delivery Times

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Shuguang Li
Keyword(s):  
Parallel Machines ◽  
Approximation Scheme ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
List Scheduling ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Delivery Times ◽  
Specific Subset ◽  
Job Delivery

The problem of scheduling jobs with delivery times on parallel machines is studied, where each job can only be processed on a specific subset of the machines called its processing set. Two distinct processing sets are either nested or disjoint; that is, they do not partially overlap. All jobs are available for processing at time 0. The goal is to minimize the time by which all jobs are delivered, which is equivalent to minimizing the maximum lateness from the optimization viewpoint. A list scheduling approach is analyzed and its approximation ratio of 2 is established. In addition, a polynomial time approximation scheme is derived.

Improved Approximation Algorithm for the Combination of Parallel Machine Scheduling and Vertex Cover

2017 ◽  
Vol 28 (08) ◽  
pp. 977-992 ◽  
Author(s):  
Wenyi Hong ◽  
Zhenbo Wang
Keyword(s):  
Approximation Algorithm ◽  
Parallel Machines ◽  
Vertex Cover ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Combination Problem ◽  
Vertex Cover Problem ◽  
Cover Problem

This paper studies the combination problem of parallel machine scheduling and the vertex cover problem. Wang and Cui developed a [Formula: see text]-approximation algorithm for this problem [13], where [Formula: see text] is the number of parallel machines. We reduce the approximation factors from [Formula: see text] to [Formula: see text] for [Formula: see text], from [Formula: see text] to [Formula: see text] for [Formula: see text], and to [Formula: see text] for [Formula: see text].

scholarly journals An Ant Optimization Model for Unrelated Parallel Machine Scheduling with Energy Consumption and Total Tardiness

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Peng Liang ◽  
Hai-dong Yang ◽  
Guo-sheng Liu ◽  
Jian-hua Guo
Keyword(s):  
Energy Consumption ◽  
Parallel Machines ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Taguchi Methods ◽  
Total Tardiness ◽  
Unrelated Parallel Machine ◽  
Heuristic Rule ◽  
Unrelated Parallel Machine Scheduling

This research considers an unrelated parallel machine scheduling problem with energy consumption and total tardiness. This problem is compounded by two challenges: differences of unrelated parallel machines energy consumption and interaction between job assignments and machine state operations. To begin with, we establish a mathematical model for this problem. Then an ant optimization algorithm based on ATC heuristic rule (ATC-ACO) is presented. Furthermore, optimal parameters of proposed algorithm are defined via Taguchi methods for generating test data. Finally, comparative experiments indicate the proposed ATC-ACO algorithm has better performance on minimizing energy consumption as well as total tardiness and the modified ATC heuristic rule is more effectively on reducing energy consumption.

PARALLEL MACHINE SCHEDULING WITH A SIMULTANEITY CONSTRAINT AND UNIT-LENGTH JOBS TO MINIMIZE THE MAKESPAN

2010 ◽  
Vol 27 (06) ◽  
pp. 669-676
Author(s):  
LIN LIN ◽  
YIXUN LIN ◽  
XIANWEI ZHOU ◽  
RUYAN FU
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
Unit Length ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Original Graph ◽  
Degree Of Vertex ◽  
Current Graph ◽  
Special Case

In this paper, we consider the parallel machine scheduling with a simultaneity constraint and unit-length jobs. The problem can be described as follows. There are given m parallel machines and a graph G, whose vertices represent jobs. Simultaneity constraint means that we can process a vertex job v if and only if there exists at least dG(v) idle machines, where dG(v) is the degree of vertex v in graph G. Once a vertex job is completed, we delete the vertex and its incident edges from the graph. The number of machines that a vertex job needing depends on its degree in current graph. Changes of graph result in changes of vertex degree. Here, we consider a special case that all jobs in the original graph are unit-length. Let pv denote the processing time of vertex job v, we define pv = 0 if d(v) = 0, and pv = 1, otherwise. The objective is to minimize the time by which each vertex job is completed, i.e., the time by which the graph becomes an empty graph. We show that this problem is strongly NP-hard and provide a [Formula: see text]-approximation algorithm.

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