scholarly journals 3/2-approximation algorithm for a single machine scheduling problem

2021 ◽  
Vol 17 (3) ◽  
pp. 240-253
Author(s):  
Natalia S. Grigoreva ◽  
Keyword(s):  
Approximation Algorithm ◽  
Optimization Problem ◽  
Single Machine Scheduling ◽  
Release Time ◽  
Scheduling Problem ◽  
Delivery Time ◽  
Scheduling Problems ◽  
Delivery Times ◽  
Jobshop Scheduling ◽  
Single Processor

The problem of minimizing the maximum delivery times while scheduling tasks on a single processor is a classical combinatorial optimization problem. Each task ui must be processed without interruption for t(ui) time units on the machine, which can process at most one task at time. Each task uw; has a release time r(ui), when the task is ready for processing, and a delivery time g(ui). Its delivery begins immediately after processing has been completed. The objective is to minimize the time, by which all jobs are delivered. In the Graham notation this problem is denoted by 1|rj,qi|Cmax, it has many applications and it is NP-hard in a strong sense. The problem is useful in solving owshop and jobshop scheduling problems. The goal of this article is to propose a new 3/2-approximation algorithm, which runs in O(n log n) times for scheduling problem 1|rj.qi|Cmax. An example is provided which shows that the bound of 3/2 is accurate. To compare the effectiveness of proposed algorithms, random generated problems of up to 5000 tasks were tested.

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 and due Date Assignment with Past-Sequence-Dependent Delivery Times and General Position-Dependent Processing Times

2014 ◽  
Vol 624 ◽  
pp. 675-680
Author(s):  
Yu Fang Zhao
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Due Date ◽  
Due Date Assignment ◽  
Processing Times ◽  
Delivery Times ◽  
Weighted Number ◽  
Tardy Jobs

We studied single machine scheduling problems in which the jobs need to be delivered to customers after processing. It is assumed that the delivery times are proportional to the length of the already processed jobs, and a job's processing time depended on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs and the cost of due date assignment. We analyzed these problems with two different due date assignment methods and conclude that the problems are polynomial time solvable.

scholarly journals An exact block algorithm for no-idle RPQ problem

2017 ◽  
Vol 27 (2) ◽  
pp. 323-330
Author(s):  
Jaroslaw Pempera
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Idle Time ◽  
Scheduling Problem ◽  
Delivery Time ◽  
Block Algorithm

Abstract In the work a single-machine scheduling problem is being considered, in which all tasks have a fixed availability (release) and delivery time. In the analyzed variant no-idle time is allowed on a machine. The purpose of optimization is to determine such order of tasks that minimizes the makespan, i.e. the time of execution of all the tasks. There is also a number of properties of the problem presented, in particular there are formulated block eliminating properties for no-idle constraint. There was an exact B&B algorithm based on the block properties proposed.

The Review of the Single Machine Scheduling Problem and its Solving Methods

2013 ◽  
Vol 411-414 ◽  
pp. 2081-2084 ◽  
Author(s):  
Ou Yang Quan ◽  
Hong Yun Xu
Keyword(s):  
Single Machine ◽  
Production Efficiency ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Efficiency And Effectiveness ◽  
History Of ◽  
Future Work ◽  
Difficult Subject

The research on the theory and method of single machine scheduling is a difficult subject, but it is very important for the companies to improve the production efficiency and effectiveness. The study on single machine scheduling problem has the history of 50 years, but there is still a gap between the classical scheduling theories and practical scheduling problems. According to this characteristic, the problems in practical scheduling area and the various factors need to be concerned are mentioned, and the main methods to solving the single machine scheduling problem and their applications are presented in details. Finally, the directions and suggestions of future work in single machine scheduling problem are summarized.

Minimizing Total Earliness and Total Tardiness on Single Machine with Release Dates

2011 ◽  
Vol 5 ◽  
pp. 30-43
Author(s):  
Elkanah Oyetunji ◽  
Ayodeji E. Oluleye
Keyword(s):  
Single Machine ◽  
Single Machine Scheduling ◽  
Total Tardiness ◽  
Release Dates ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Bicriteria Scheduling ◽  
Linear Composite ◽  
Effectiveness And Efficiency ◽  
Machine Scheduling Problems

This paper considers the bicriteria scheduling problem of minimizing the total earliness and the total tardiness on a single machine with release dates. In view of the fact that the problem has been characterized as NP-Hard, we propose two approximation algorithms (labeled as ETA1 and ETA2) for solving the problem. The proposed algorithms were compared with the MA heuristic selected from the literature. The two criteria (the total earliness and the total tardiness) were aggregated together into a linear composite objective function (LCOF). The performances of the algorithms were evaluated based on both effectiveness and efficiency. The algorithms were tested on a set of 1200 randomly generated single machine scheduling problems. Experimental results show that both the ETA1 and ETA2 algorithms outperformed (in terms of effectiveness and efficiency) the MA heuristic under all the considered problem sizes. Also, the ETA1 algorithm outperformed the ETA2 algorithm when the number of jobs (n) ranges between 20 and 500.

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