Scheduling with Fuzzy Methods

Nowadays, manufacturing industries -- driven by fierce competition and rising customer requirements -- are forced to produce a broader range of individual products of rising quality at the same (or preferably lower) cost. Meeting these demands implies an even more complex production process and thus also an appropriately increasing request to its scheduling. Aggravatingly, vagueness of scheduling parameters -- such as times and conditions -- are often inherent in the production process. In addition, the search for an optimal schedule normally leads to very difficult problems (NP-hard problems in the complexity theoretical sense), which cannot be solved effciently. With the intent to minimize these problems, the introduced heuristic method combines standard scheduling methods with fuzzy methods to get a nearly optimal schedule within an appropriate time considering vagueness adequately

Hybrid Ant Colony Optimization For Fuzzy Unrelated Parallel Machine Scheduling Problems

This study extends the best hybrid ant colony optimization variant developed by Liao et al. (2014) for crisp unrelated parallel machine scheduling problems to solve fuzzy unrelated parallel machine scheduling problems in consideration of trapezoidal fuzzy processing times, trapezoidal fuzzy sequencing dependent setup times and trapezoidal fuzzy release times. The objective is to find the best schedule taking minimum fuzzy makespan in completing all jobs. In this study, fuzzy arithmetic is used to determine fuzzy completion times of jobs and defuzzification function is used to convert fuzzy numbers back to crisp numbers for ranking. Eight fuzzy ranking methods are tested to find the most feasible one to be employed in this study. The fuzzy arithmetic testing includes four different cases and each case with the following operations separately, i.e., addition, subtraction, multiplication and division, to investigate the spread of fuzziness as fuzzy numbers are subject to more and more number of operations. The effect of fuzzy ranking methods on hybrid ant colony optimization (hACO) is investigated. To prove the correctness of our methodology and coding, unrelated parallel machine scheduling with fuzzy numbers and crisp numbers are compared based on scheduling problems up to 15 machines and 200 jobs. Relative percentage deviation (RPD) is used to evaluate the performance of hACO in solving fuzzy unrelated parallel machine scheduling problems. A numerical study on large-scale scheduling problems up to 20 machines and 200 jobs is conducted to assess the performance of the hACO algorithm. For comparison, a discrete particle swarm optimization (dPSO) algorithm is implemented for fuzzy unrelated parallel machine scheduling problem as well. The results show that the hACO has better performance than dPSO not only in solution quality in terms of RPD value, but also in computational time

Reduction method based on a new fuzzy rough set in fuzzy information system and its applications to scheduling problems

AbstractIn this paper, we present the concept of fuzzy information granule based on a relatively weaker fuzzy similarity relation called fuzzy TL-similarity relation for the first time. Then, according to the fuzzy information granule, we define the lower and upper approximations of fuzzy sets and a corresponding new fuzzy rough set. Furthermore, we construct a kind of new fuzzy information system based on the fuzzy TL-similarity relation and study its reduction using the fuzzy rough set. At last, we apply the reduction method based on the defined fuzzy rough set in the above fuzzy information system to the reduction of the redundant multiple fuzzy rule in the scheduling problems, and numerical computational results show that the reduction method based on the new fuzzy rough set is more suitable for the reduction of multiple fuzzy rules in the scheduling problems compared with the reduction methods based on the existing fuzzy rough set

KEUNGGULAN PENERAPAN FUZZY PADA PENYELESAIAN PENJADWALAN PROYEK

Project scheduling is an activity to determine the duration of each activity on the project so that the project can be completed in an optimal time. Network flow in the application of graph theory is the theoretical basis used to complete the project schedule. Some methods that can be used to complete scheduling are Gantt, CPM (Critical Path Method), PERT method (Project Evaluation and Review Technique), and fuzzy application. This article will examine the advantages of applying fuzzy after project scheduling. In the PERT and CPM methods, there are forward computation, backward computation, and float or slack calculations, while scheduling using fuzzy calculations is carried out in one step, namely, the calculation starts from the 'start' node. and move to the 'end. In the application of fuzzy, the degree of membership is discussed to model uncertainty so that the value of the probability of reaching the target is represented in the form of a curve so that the tolerance for project completion can be determined if something unplanned occurs, such as changes in weather/rain or other constraints. The final result of the analysis of fuzzy calculations can be obtained as the most likely value, namely the value with the degree of membership equal to 1 to be the solution in the search for the fastest completion time of a project

A Fuzzy Nonlinear Programming Approach for Optimizing the Performance of a Four-Objective Fluctuation Smoothing Rule in a Wafer Fabrication Factory

In theory, a scheduling problem can be formulated as a mathematical programming problem. In practice, dispatching rules are considered to be a more practical method of scheduling. However, the combination of mathematical programming and fuzzy dispatching rule has rarely been discussed in the literature. In this study, a fuzzy nonlinear programming (FNLP) approach is proposed for optimizing the scheduling performance of a four-factor fluctuation smoothing rule in a wafer fabrication factory. The proposed methodology considers the uncertainty in the remaining cycle time of a job and optimizes a fuzzy four-factor fluctuation-smoothing rule to sequence the jobs in front of each machine. The fuzzy four-factor fluctuation-smoothing rule has five adjustable parameters, the optimization of which results in an FNLP problem. The FNLP problem can be converted into an equivalent nonlinear programming (NLP) problem to be solved. The performance of the proposed methodology has been evaluated with a series of production simulation experiments; these experiments provide sufficient evidence to support the advantages of the proposed method over some existing scheduling methods

A survey on gain-scheduled control and filtering for parameter-varying systems

Copyright © 2014 Guoliang Wei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This paper presents an overview of the recent developments in the gain-scheduled control and filtering problems for the parameter-varying systems. First of all, we recall several important algorithms suitable for gain-scheduling method including gain-scheduled proportional-integral derivative (PID) control, H 2, H ∞ and mixed H 2 / H ∞ gain-scheduling methods as well as fuzzy gain-scheduling techniques. Secondly, various important parameter-varying system models are reviewed, for which gain-scheduled control and filtering issues are usually dealt with. In particular, in view of the randomly occurring phenomena with time-varying probability distributions, some results of our recent work based on the probability-dependent gain-scheduling methods are reviewed. Furthermore, some latest progress in this area is discussed. Finally, conclusions are drawn and several potential future research directions are outlined.The National Natural Science Foundation of China under Grants 61074016, 61374039, 61304010, and 61329301; the Natural Science Foundation of Jiangsu Province of China under Grant BK20130766; the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning; the Program for New Century Excellent Talents in University under Grant NCET-11-1051, the Leverhulme Trust of the U.K., the Alexander von Humboldt Foundation of Germany

The Project Scheduling Problem with Non-Deterministic Activities Duration: A Literature Review

Purpose: The goal of this article is to provide an extensive literature review of the models and solution procedures proposed by many researchers interested on the Project Scheduling Problem with nondeterministic activities duration. Design/methodology/approach: This paper presents an exhaustive literature review, identifying the existing models where the activities duration were taken as uncertain or random parameters. In order to get published articles since 1996, was employed the Scopus database. The articles were selected on the basis of reviews of abstracts, methodologies, and conclusions. The results were classified according to following characteristics: year of publication, mathematical representation of the activities duration, solution techniques applied, and type of problem solved. Findings: Genetic Algorithms (GA) was pointed out as the main solution technique employed by researchers, and the Resource-Constrained Project Scheduling Problem (RCPSP) as the most studied type of problem. On the other hand, the application of new solution techniques, and the possibility of incorporating traditional methods into new PSP variants was presented as research trends. Originality/value: This literature review contents not only a descriptive analysis of the published articles but also a statistical information section in order to examine the state of the research activity carried out in relation to the Project Scheduling Problem with non-deterministic activities duration.Peer Reviewe

Fuzzy C-Mean And Genetic Algorithms Based Scheduling For Independent Jobs In Computational Grid

The concept of Grid computing is becoming the most important research area in the high performance computing. Under this concept, the jobs scheduling in Grid computing has more complicated problems to discover a diversity of available resources, select the appropriate applications and map to suitable resources. However, the major problem is the optimal job scheduling, which Grid nodes need to allocate the appropriate resources for each job. In this paper, we combine Fuzzy C-Mean and Genetic Algorithms which are popular algorithms, the Grid can be used for scheduling. Our model presents the method of the jobs classifications based mainly on Fuzzy C-Mean algorithm and mapping the jobs to the appropriate resources based mainly on Genetic algorithm. In the experiments, we used the workload historical information and put it into our simulator. We get the better result when compared to the traditional algorithms for scheduling policies. Finally, the paper also discusses approach of the jobs classifications and the optimization engine in Grid scheduling

A reusable iterative optimization software library to solve combinatorial problems with approximate reasoning

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available data may be uncertain, and compromises between antagonistic criteria may be necessary. We present a combination of approximate reasoning based constraints and iterative optimization based heuristics that help to model and solve such problems in a framework of C++ software libraries called StarFLIP++. While initially developed to schedule continuous caster units in steel plants, we present in this paper results from reusing the library components in a shift scheduling system for the workforce of an industrial production plant.Comment: 33 pages, 9 figures; for a project overview see http://www.dbai.tuwien.ac.at/proj/StarFLIP