42 research outputs found
Heuristic algorithm for a flexible flow shop problem minimizing total weighted completion time (WJCJ) with release dates (RJ), setup (SJK) constrains with proportional machines (QM) at stations
La programación de operaciones para un taller donde los trabajos poseen fechas de entrega, alistamiento y ponderación, buscando minimizar el tiempo de terminación ponderado no es un nuevo problema que se a trabajado a nivel investigativo, pero es un problema poco trabajado por ser un problema con una complejidad computacional alta, considerada de tipo NP-HARD, campo donde la mayoría de los casos las heurísticas dan soluciones no óptimas. Lo que se muestra en esta investigación es el desarrollo de una heurística que arroje una forma eficiente para programar los trabajos en un taller de máquinas en paralelo que tiene las condiciones antes mencionadas y busque minimizar el tiempo total ponderado en el sistema.Abstract: Scheduling on many stations and machines minimizing total weighted completion time (wjCj) as objective with released dates and setup’s constraints is not a new problem, but it is a low investigated because it has a computational complexity of NP-Hard and in most cases the heuristics are not optimal solutions Our objective in the problem is develop an heuristic to be applied through an algorithm that gives as output a sequence of jobs in
each station and machines having different velocities in each one and minimizing the principal objective total
weighted completion time
A PTAS for Minimizing Average Weighted Completion Time With Release Dates on Uniformly Related Machines
A classical scheduling problem is to find schedules that minimize average weighted completion time of jobs with release dates. When multiple machines are available, the machine environments may range from identical machines (the processing time required by a job is invariant across the machines) at one end, to unrelated machines (the processing time required by a job on any machine is an arbitrary function of the specific machine) at the other end of the spectrum. While the problem is strongly NP-hard even in the case of a single machine, constant factor approximation algorithms have been known for even the most general machine environment of unrelated machines. Recently, a polynomial-time approximation scheme (PTAS) was discovered for the case of identical parallel machines [1]. In contrast, it is known that this problem is MAX SNP-hard for unrelated machines [10]. An important open problem is to determine the approximability of the intermediate case of uniformly related machines where each machine i has a speed si and it takes p/si time to executing a job of processing size pIn this paper, we resolve this problem by obtaining a PTAS for the problem. This improves the earlier known ratio of (2 + ∈) for the problem
Two-agent scheduling in open shops subject to machine availability and eligibility constraints
Purpose: The aims of this article are to develop a new mathematical formulation and a new heuristic for the problem of preemptive two-agent scheduling in open shops subject to machine maintenance and eligibility constraints.
Design/methodology: Using the ideas of minimum cost flow network and constraint programming, a heuristic and a network based linear programming are proposed to solve the problem.
Findings: Computational experiments show that the heuristic generates a good quality schedule with a deviation of 0.25% on average from the optimum and the network based linear programming model can solve problems up to 110 jobs combined with 10 machines without considering the constraint that each operation can be processed on at most one machine at a time. In order to satisfy this constraint, a time consuming Constraint Programming is proposed. For n = 80 and m = 10, the average execution time for the combined models (linear programming model combined with Constraint programming) exceeds two hours. Therefore, the heuristic algorithm we developed is very efficient and is in need.
Practical implications: Its practical implication occurs in TFT-LCD and E-paper manufacturing wherein units go through a series of diagnostic tests that do not have to be performed in any specified order.
Originality/value: The main contribution of the article is to split the time horizon into many time intervals and use the dispatching rule for each time interval in the heuristic algorithm, and also to combine the minimum cost flow network with the Constraint Programming to solve the problem optimally.Peer Reviewe
A statistical comparison of metaheuristics for unrelated parallel machine scheduling problems with setup times
Manufacturing scheduling aims to optimize one or more performance measures by allocating a set of resources to a set of jobs or tasks over a given period of time. It is an area that considers a very important decision-making process for manufacturing and production systems. In this paper, the unrelated parallel machine scheduling problem with machine-dependent and job-sequence-dependent setup times is addressed. This problem involves the scheduling of tasks on unrelated machines with setup times in order to minimize the makespan. The genetic algorithm is used to solve small and large instances of this problem when processing and setup times are balanced (Balanced problems), when processing times are dominant (Dominant P problems), and when setup times are dominant (Dominant S problems). For small instances, most of the values achieved the optimal makespan value, and, when compared to the metaheuristic ant colony optimization (ACOII) algorithm referred to in the literature, it was found that there were no significant differences between the two methods. However, in terms of large instances, there were significant differences between the optimal makespan obtained by the two methods, revealing overall better performance by the genetic algorithm for Dominant S and Dominant P problems.FCT—Fundação para a Ciência e Tecnologia through the R&D Units Project Scope UIDB/00319/2020 and EXPL/EME-SIS/1224/2021 and PhD grant UI/BD/150936/2021
Parallel machine scheduling subject to machine availability constraints
Cataloged from PDF version of article.Within a planning horizon, machines may become unavailable due to
unexpected breakdowns or pre-scheduled activities. A realistic approach
in constructing the production schedule should explicitly take into
account such periods of unavailability. This study addresses the parallel
machine-scheduling problem subject to availability constraints on each
machine. The objectives of minimizing the total completion time and
minimizing the maximum completion time are studied. The problems
with both objectives are known to be NP-hard. We develop an exact
branch-and-bound procedure and propose three heuristic algorithms for
the total completion time problem. Similarly, we propose exact and
approximation algorithms also for the maximum completion time
problem. All proposed algorithms are tested through extensive
computational experimentation, and several insights are provided based
on computational results.Sevindik, KayaM.S
The Distributed and Assembly Scheduling Problem
Tesis por compendio[EN] Nowadays, manufacturing systems meet different new global challenges and
the existence of a collaborative manufacturing environment is essential to face
with. Distributed manufacturing and assembly systems are two manufacturing
systems which allow industries to deal with some of these challenges. This
thesis studies a production problem in which both distributed manufacturing
and assembly systems are considered. Although distributed manufacturing
systems and assembly systems are well-known problems and have been extensively
studied in the literature, to the best of our knowledge, considering
these two systems together as in this thesis is the first effort in the literature.
Due to the importance of scheduling optimization on production performance,
some different ways to optimize the scheduling of the considered problem are
discussed in this thesis.
The studied scheduling setting consists of two stages: A production and an
assembly stage. Various production centers make the first stage. Each of these
centers consists of several machines which are dedicated to manufacture jobs.
A single assembly machine is considered for the second stage. The produced
jobs are assembled on the assembly machine to form final products through a
defined assembly program.
In this thesis, two different problems regarding two different production
configurations for the production centers of the first stage are considered.
The first configuration is a flowshop that results in what we refer to as the
Distributed Assembly Permutation Flowshop Scheduling Problem (DAPFSP).
The second problem is referred to as the Distributed Parallel Machine and
Assembly Scheduling Problem (DPMASP), where unrelated parallel machines
configure the production centers. Makespan minimization of the product on the
assembly machine located in the assembly stage is considered as the objective
function for all considered problems.
In this thesis some extensions are considered for the studied problems
so as to bring them as close as possible to the reality of production shops.
In the DAPFSP, sequence dependent setup times are added for machines in
both production and assembly stages. Similarly, in the DPMASP, due to
technological constraints, some defined jobs can be processed only in certain
factories.
Mathematical models are presented as an exact solution for some of the
presented problems and two state-of-art solvers, CPLEX and GUROBI are
used to solve them. Since these solvers are not able to solve large sized
problems, we design and develop heuristic methods to solve the problems. In
addition to heuristics, some metaheuristics are also designed and proposed to
improve the solutions obtained by heuristics. Finally, for each proposed problem,
the performance of the proposed solution methods is compared through
extensive computational and comprehensive ANOVA statistical analysis.[ES] Los sistemas de producción se enfrentan a retos globales en los que el concepto
de fabricación colaborativa es crucial para poder tener éxito en el entorno
cambiante y complejo en el que nos encontramos. Una característica de los sistemas
productivos que puede ayudar a lograr este objetivo consiste en disponer
de una red de fabricación distribuida en la que los productos se fabriquen en
localizaciones diferentes y se vayan ensamblando para obtener el producto
final. En estos casos, disponer de modelos y herramientas para mejorar el
rendimiento de sistemas de producción distribuidos con ensamblajes es una
manera de asegurar la eficiencia de los mismos.
En esta tesis doctoral se estudian los sistemas de fabricación distribuidos
con operaciones de ensamblaje. Los sistemas distribuidos y los sistemas con
operaciones de ensamblaje han sido estudiados por separado en la literatura.
De hecho, no se han encontrado estudios de sistemas con ambas características
consideradas de forma conjunta.
Dada la complejidad de considerar conjuntamente ambos tipos de sistemas
a la hora de realizar la programación de la producción en los mismos, se ha
abordado su estudio considerando un modelo bietápico en la que en la primera
etapa se consideran las operaciones de producción y en la segunda se plantean
las operaciones de ensamblaje.
Dependiendo de la configuración de la primera etapa se han estudiado dos
variantes. En la primera variante se asume que la etapa de producción está
compuesta por sendos sistemas tipo flowshop en los que se fabrican los componentes
que se ensamblan en la segunda etapa (Distributed Assembly Permutation
Flowshop Scheduling Problem o DAPFSP). En la segunda variante
se considera un sistema de máquinas en paralelo no relacionadas (Distributed
Parallel Machine and Assembly Scheduling Problem o DPMASP). En ambas
variantes se optimiza la fecha de finalización del último trabajo secuenciado
(Cmax) y se contempla la posibilidad que existan tiempos de cambio (setup)
dependientes de la secuencia de trabajos fabricada. También, en el caso
DPMASP se estudia la posibilidad de prohibir o no el uso de determinadas
máquinas de la etapa de producción.
Se han desarrollado modelos matemáticos para resolver algunas de las
variantes anteriores. Estos modelos se han resuelto mediante los programas
CPLEX y GUROBI en aquellos casos que ha sido posible. Para las instancias
en los que el modelo matemático no ofrecía una solución al problema se han
desarrollado heurísticas y metaheurísticas para ello.
Todos los procedimientos anteriores han sido estudiados para determinar
el rendimiento de los diferentes algoritmos planteados. Para ello se ha realizado
un exhaustivo estudio computacional en el que se han aplicado técnicas
ANOVA.
Los resultados obtenidos en la tesis permiten avanzar en la comprensión
del comportamiento de los sistemas productivos distribuidos con ensamblajes,
definiendo algoritmos que permiten obtener buenas soluciones a este tipo de
problemas tan complejos que aparecen tantas veces en la realidad industrial.[CA] Els sistemes de producció s'enfronten a reptes globals en què el concepte de
fabricació col.laborativa és crucial per a poder tindre èxit en l'entorn canviant
i complex en què ens trobem. Una característica dels sistemes productius
que pot ajudar a aconseguir este objectiu consistix a disposar d'una xarxa de
fabricació distribuïda en la que els productes es fabriquen en localitzacions
diferents i es vagen acoblant per a obtindre el producte final. En estos casos,
disposar de models i ferramentes per a millorar el rendiment de sistemes de
producció distribuïts amb acoblaments és una manera d'assegurar l'eficiència
dels mateixos.
En esta tesi doctoral s'estudien els sistemes de fabricació distribuïts amb
operacions d'acoblament. Els sistemes distribuïts i els sistemes amb operacions
d'acoblament han sigut estudiats per separat en la literatura però, en allò
que es coneix, no s'han trobat estudis de sistemes amb ambdós característiques
conjuntament. Donada la complexitat de considerar conjuntament ambdós
tipus de sistemes a l'hora de realitzar la programació de la producció en els
mateixos, s'ha abordat el seu estudi considerant un model bietàpic en la que
en la primera etapa es consideren les operacions de producció i en la segona es
plantegen les operacions d'acoblament.
Depenent de la configuració de la primera etapa s'han estudiat dos variants.
En la primera variant s'assumix que l'etapa de producció està composta per
sengles sistemes tipus flowshop en els que es fabriquen els components que
s'acoblen en la segona etapa (Distributed Assembly Permutation Flowshop
Scheduling Problem o DAPFSP). En la segona variant es considera un sistema
de màquines en paral.lel no relacionades (Distributed Parallel Machine and
Assembly Scheduling Problem o DPMASP). En ambdós variants s'optimitza
la data de finalització de l'últim treball seqüenciat (Cmax) i es contempla la
possibilitat que existisquen temps de canvi (setup) dependents de la seqüència
de treballs fabricada. També, en el cas DPMASP s'estudia la possibilitat de
prohibir o no l'ús de determinades màquines de l'etapa de producció.
S'han desenvolupat models matemàtics per a resoldre algunes de les variants
anteriors. Estos models s'han resolt per mitjà dels programes CPLEX
i GUROBI en aquells casos que ha sigut possible. Per a les instàncies en
què el model matemàtic no oferia una solució al problema s'han desenrotllat
heurístiques i metaheurísticas per a això. Tots els procediments anteriors han
sigut estudiats per a determinar el rendiment dels diferents algoritmes plantejats.
Per a això s'ha realitzat un exhaustiu estudi computacional en què s'han
aplicat tècniques ANOVA.
Els resultats obtinguts en la tesi permeten avançar en la comprensió del
comportament dels sistemes productius distribuïts amb acoblaments, definint
algoritmes que permeten obtindre bones solucions a este tipus de problemes
tan complexos que apareixen tantes vegades en la realitat industrial.Hatami, S. (2016). The Distributed and Assembly Scheduling Problem [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/64072TESISCompendi
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Shop scheduling with availability constraints
Scheduling Theory studies planning and timetabling of various industrial and human activities and, therefore, is of constant scientific interest. Being a branch of Operational Research, Theory of Scheduling mostly deals with problems of practical interest which can be easily (from a mathematical point of view) solved by full enumeration and at the same time usually require enormous time to be solved optimally. Therefore, one attempts to develop algorithms for finding optimal or near optimal solutions of the problems under consideration in reasonable time. If the output of an algorithm is not always an optimal solution then the worst-case analysis of this algorithm is undertaken in order to estimate either a relative error or an absolute error that holds for any given instance of the problem.
Scheduling problems which are usually considered in the literature assume that the processing facilities are constantly available throughout the planning period. However, in practice, the processing facility, e.g. a machine, a labour, etc. can become non-available due to various reasons, e.g. breakdowns, lunch breaks, holidays, maintenance work, etc. All these facts stimulate research in the area of scheduling with non-availability constraints. This branch of Scheduling Theory has recently received a lot of attention and a considerable number of research papers have been published. This thesis is fully dedicated to scheduling with non-availability constraints under various assumptions on the structure of the processing system and on the types of non-availability intervals