Scheduling Problem for Parallel Machines with Limited Processing Capacities

2011 ◽  
Vol 382 ◽  
pp. 110-113
Author(s):  
Jing Fan
Keyword(s):  
Approximation Algorithms ◽  
Objective Function ◽  
Completion Time ◽  
Parallel Machines ◽  
Industrial Engineering ◽  
Scheduling Problem ◽  
Np Hard ◽  
The Novel

In the actual industrial engineering, machines used for processing need to be checked periodically to ensure that they can work efficiently. Thus, the novel scheduling problem for parallel machines with limited capacities is worth to study. The objective function is to maximize the last completion time of jobs. We show the problem is NP-hard at least. Furthermore, two approximation algorithms are presented, and algorithms' performances are considered through the experiments with large amounts of data.

Scheduling Jobs on Dedicated Parallel Machines

2013 ◽  
Vol 433-435 ◽  
pp. 2363-2366 ◽  
Author(s):  
Sang Oh Shim ◽  
Seong Woo Choi
Keyword(s):  
Completion Time ◽  
Parallel Machines ◽  
Computation Time ◽  
Computational Experiments ◽  
Test Problems ◽  
Scheduling Problem ◽  
Suggested Algorithm ◽  
Reasonable Amount ◽  
Scheduling Method

This paper considers scheduling problem on dedicated parallel machines where several types of machines are grouped into one process. The dedicated machine is that a job with a specific recipe should be processed on the dedicated machine even though the job can be produced on any other machine originally. In this process, a setup is required when different jobs are done consecutively. To minimize the completion time of the last job, a scheduling method is developed. Computational experiments are performed on a number of test problems and results show that the suggested algorithm give good solutions in a reasonable amount of computation time.

ONLINE AND SEMI-ONLINE SCHEDULING ON CAPACITATED TWO-PARALLEL MACHINES

2011 ◽  
Vol 28 (02) ◽  
pp. 163-182
Author(s):  
AN ZHANG ◽  
YIWEI JIANG ◽  
ZHIYI TAN
Keyword(s):  
Lower Bound ◽  
Completion Time ◽  
Processing Time ◽  
Parallel Machines ◽  
Online Version ◽  
Special Period ◽  
Scheduling Problem ◽  
Subset Sum ◽  
Parallel Machines Scheduling ◽  
One Machine

In this paper, we investigate the capacitated two-parallel machines scheduling problem, where one machine is only available for a special period of time after which it can no longer process any job while the other machine is continuously available. Our objective is to minimize the completion time of the machine which is continuously available. The offline version of the problem is equivalent to the minimization version of the Subset-Sum problem. We first show the lower bound of the online version is infinite. We also consider the semi-online version with known the total job processing time in advance, for which both lower bound and semi-online algorithms are given.

Heuristic Algorithm for Solving Multi-Crane Scheduling in Steel Coil Warehouse

2014 ◽  
Vol 543-547 ◽  
pp. 1559-1562
Author(s):  
Xie Xie ◽  
Xiang Yu Kong ◽  
Yong Yue Zheng ◽  
Yan Ping Li
Keyword(s):  
Heuristic Algorithm ◽  
Completion Time ◽  
Scheduling Problem ◽  
Np Hard ◽  
Crane Scheduling ◽  
Steel Coil ◽  
Upper Level ◽  
Warehouse Operations

We consider a multi-crane scheduling problem commonly encountered in real warehouse operations in steel enterprises. Given some demanded coils, if a demanded coil is in upper level or in lower level without being blocked, it can be picked up directly to designated place; else, the blocking coils need to be picked up to another position first. Unlike previous literatures in which both operations have been considered to be scheduled separately, our problem schedules transportation operation and shuffling operation coordinately. The objective is to minimize the last demanded coil transported to its designated place which is consistent with the earliest possible completion time of one crane. We propose a heuristic algorithm for solving this demonstrated strongly NP-hard.

scholarly journals Practical comparison of approximation algorithms for scheduling problems

2004 ◽  
Vol 24 (2) ◽  
pp. 227-252
Author(s):  
Eduardo Candido Xavier ◽  
Flávio K. Miyazawa
Keyword(s):  
Experimental Study ◽  
Approximation Algorithms ◽  
Completion Time ◽  
Parallel Machines ◽  
Linear Formulation ◽  
The Other ◽  
Experimental Comparison ◽  
Scheduling Problems ◽  
Weighted Completion Time ◽  
Almost All

In this paper we consider an experimental study of approximation algorithms for scheduling problems in parallel machines minimizing the average weighted completion time. We implemented approximation algorithms for the following problems: P|r j|sigmaCj, P||sigmaw jCj, P|r j|sigmaw jCj, R||sigmaw jCj and R|r j|sigmaw jCj. We generated more than 1000 tests over more than 200 different instances and present some practical aspects of the implemented algorithms. We also made an experimental comparison on two lower bounds based on the formulations used by the algorithms. The first one is a semidefinite formulation for the problem R||sigmaw jCj and the other one is a linear formulation for the problem R|r j|sigmaw jCj. For all tests, the algorithms obtained very good results. We notice that algorithms using more refined techniques, when compared to algorithms with simple strategies, do not necessary lead to better results. We also present two heuristics, based on approximation algorithms, that generate solutions with better quality in almost all instances considered.

scholarly journals Top-k overlapping densest subgraphs: approximation algorithms and computational complexity

2020 ◽  
Author(s):  
Riccardo Dondi ◽  
Mohammad Mehdi Hosseinzadeh ◽  
Giancarlo Mauri ◽  
Italo Zoppis
Keyword(s):  
Computational Complexity ◽  
Approximation Algorithms ◽  
Approximation Algorithm ◽  
Objective Function ◽  
Graph Mining ◽  
Central Problem ◽  
Np Hard ◽  
Dense Subgraph ◽  
Dense Subgraphs ◽  
Approximation Factor

Abstract A central problem in graph mining is finding dense subgraphs, with several applications in different fields, a notable example being identifying communities. While a lot of effort has been put in the problem of finding a single dense subgraph, only recently the focus has been shifted to the problem of finding a set of densest subgraphs. An approach introduced to find possible overlapping subgraphs is the problem. Given an integer $$k \ge 1$$ k ≥ 1 and a parameter $$\lambda > 0$$ λ > 0 , the goal of this problem is to find a set of k dense subgraphs that may share some vertices. The objective function to be maximized takes into account the density of the subgraphs, the parameter $$\lambda $$ λ and the distance between each pair of subgraphs in the solution. The problem has been shown to admit a $$\frac{1}{10}$$ 1 10 -factor approximation algorithm. Furthermore, the computational complexity of the problem has been left open. In this paper, we present contributions concerning the approximability and the computational complexity of the problem. For the approximability, we present approximation algorithms that improve the approximation factor to $$\frac{1}{2}$$ 1 2 , when k is smaller than the number of vertices in the graph, and to $$\frac{2}{3}$$ 2 3 , when k is a constant. For the computational complexity, we show that the problem is NP-hard even when $$k=3$$ k = 3 .

A Batch Scheduling Problem with Two Agents

2015 ◽  
Vol 32 (06) ◽  
pp. 1550044 ◽  
Author(s):  
Byung-Cheon Choi ◽  
Myoung-Ju Park
Keyword(s):  
Approximation Algorithm ◽  
Optimality Conditions ◽  
Single Machine ◽  
Completion Time ◽  
Polynomial Algorithm ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Np Hard ◽  
Due Date ◽  
Processing Times

In this paper, we consider a two-agent batch scheduling problem on a single machine such that the processing times of agent 1 and the due date of agent 2 in the same batch are identical. The objective is to minimize the total completion time of agent 1 with a constraint on the maximum tardiness of agent 2. First, we propose the optimality conditions. Then, we show that the problem is strongly NP-hard. Finally, we prove the problem remains NP-hard even for the case with one batch of agent 2, and develop a pseudo-polynomial algorithm and an approximation algorithm for this case.

scholarly journals A two-agent one-machine multitasking scheduling problem solving by exact and metaheuristics

2021 ◽  
Author(s):  
Chin-Chia Wu ◽  
Ameni Azzouz ◽  
Jia-Yang Chen ◽  
Jianyou Xu ◽  
Wei-Lun Shen ◽  
...  
Keyword(s):  
Simulated Annealing ◽  
Completion Time ◽  
Simulated Annealing Algorithm ◽  
Optimal Schedule ◽  
Computational Studies ◽  
Scheduling Problem ◽  
Optimal Solutions ◽  
Large Size ◽  
Annealing Algorithm ◽  
One Machine

AbstractThis paper studies a single-machine multitasking scheduling problem together with two-agent consideration. The objective is to look for an optimal schedule to minimize the total tardiness of one agent subject to the total completion time of another agent has an upper bound. For this problem, a branch-and-bound method equipped with several dominant properties and a lower bound is exploited to search optimal solutions for small size jobs. Three metaheuristics, cloud simulated annealing algorithm, genetic algorithm, and simulated annealing algorithm, each with three improvement ways, are proposed to find the near-optimal solutions for large size jobs. The computational studies, experiments, are provided to evaluate the capabilities for the proposed algorithms. Finally, statistical analysis methods are applied to compare the performances of these algorithms.

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