Parallel Flow Shop Research Articles

Research on multi-objective optimal scheduling considering the balance of labor workload distribution.

In order to solve the problem of unbalanced workload of employees in parallel flow shop scheduling, a method of job standard balance is proposed to describe the work balance of employees. The minimum delay time of completion and the imbalance of employee work are taken as the two goals of the model. A bi-objective nonlinear integer programming model is proposed. NSGA-II-EDSP, NSGA-II-KES, and NSGA-II-QKES heuristic rule algorithms are designed to solve the problem. A number of computational experiments of different sizes are conducted, and compared with solutions generated by NSGA-II. The experimental results show the advantages of the proposed model and method, which error is reduced 14.56%, 15.16% and 15.67%.

An iterated greedy algorithm for the parallel blocking flow shop scheduling problem and sequence-dependent setup times

This paper deals with the problem of scheduling jobs in a parallel flow shop configuration under the blocking constraint, in which the setup time of machines depends not only on the job to be processed but also on the previously processed one, i.e., there are sequence-dependent setup times. The performance analysis of several iterated greedy algorithms with different initial solution procedures and local searches lets us define an efficient algorithm to minimize the maximum job completion time. Moreover, the computational evaluation showed the efficiency of searching in different neighborhood structures and noted the significant influence of the initial solution. However, contrary to other scheduling problems, starting with a high quality solution does not guarantee better performance of the algorithm.

A computational evaluation of constructive heuristics for the parallel blocking flow shop problem with sequence-dependent setup times

This paper deals with the problem of scheduling jobs in a parallel flow shop environment without buffers between machines and with sequence-dependent setup times in order to minimize the maximum completion time of jobs. The blocking constraint normally leads to an increase in the maximum completion time of jobs due to the blockage of machines, which can increase even more so when setup times are considerable. Hence, the heuristic to solve this problem must take into account these specificities in order to minimize the timeout of machines. Because the procedures designed to solve the parallel flow shop scheduling problem must deal not only with the sequencing of jobs but also with their allocation to the flow shops, 36 heuristics have been tested in this paper, of which 35 combine sequencing rules with allocation methods while the last one takes a different approach that is more related to the nature of this problem. The computational evaluation of the implemented heuristics showed good performance of the heuristic designed especially for the problem (RCP0) when the setup times are considerable. Furthermore, the evaluation has also allowed us to propose a combined heuristic that leads to good solutions in a short CPU time.

Two-stage open-shop scheduling with a two-machine flow shop as a stage: approximation algorithms and empirical experiments

We study a scheduling environment that finds many real-world manufacturing applications, in which there is a close connection between a hybrid multiprocessor open shop and multiple parallel identical flow shops. In this environment, there is an extended two-stage open shop, where in one stage we have a set of parallel identical machines, while in the other we have a two-machine flow shop. Our objective is to minimize the makespan, that is, the latest completion time of all jobs. We pursue approximation algorithms with provable performance, and we achieve a 2-approximation when the number of parallel identical machines is constant or is part of the input; we also design a 5/3-approximation for the special case where there is only one machine in the multiprocessor stage, which remains weakly NP-hard. Our empirical experiments show that both approximation algorithms perform much better in simulated instances; their average ratios over the proposed lower bound are around 1.5 and 1.2, respectively.

An iterated greedy algorithm for solving the total tardiness parallel blocking flow shop scheduling problem

This paper proposes an iterated greedy algorithm for scheduling jobs in F parallel flow shops (lines), each consisting of a series of m machines without storage capacity between machines. This constraint can provoke the blockage of machines if a job has finished its operation and the next machine is not available. The criterion considered is the minimization of the sum of tardiness of all the jobs to schedule, i.e., minimization of the total tardiness of jobs. Notice that the proposed method is also valid for solving the Distributed Permutation Blocking Flow Shop Scheduling Problem (DBFSP), which allows modelling the scheduling process in companies with more than one factory when each factory has an identical flow shop configuration. Firstly, several constructive procedures have been implemented and tested to provide an efficient solution in terms of quality and CPU time. This initial solution is later improved upon with an iterated greedy algorithm that includes a variable neighbourhood search for interchanging or reassigning jobs from the critical line to other lines. Next, two strategies have been tested for selecting the critical line; the one with a higher total tardiness of jobs and the one with a job that has the highest tardiness. The experimental design chooses the best combination of initial solution and critical line selection. Finally, we compare the performance of the proposed algorithm against other benchmark algorithms proposed for the DPFSP, which have been adapted to the problem being considered here since, to the best of our knowledge, this is the first attempt to solve either the Parallel Blocking Flow Shop problem or the Distributed Blocking Flow Shop problem with the goal of minimizing total tardiness. This comparison has allowed us to confirm the good performance of the proposed method.

A simheuristic algorithm to set up starting times in the stochastic parallel flowshop problem

This paper addresses the parallel flowshop scheduling problem with stochastic processing times, where a product composed of several components has to be finished at a particular moment. These components are processed in independent parallel factories, and each factory can be modeled as a permutation flowshop. The processing time of each operation at each factory is a random variable following a given probability distribution. The aim is to find the robust starting time of the operations at each factory in a way that all the components of the product are completed on a given deadline with a user-defined probability. A simheuristic algorithm is proposed in order to minimize each of the following key performance indicators: (i) the makespan in the deterministic version; and (ii) the expected makespan or a makespan percentile in the stochastic version. A set of computational experiments are carried out to illustrate the performance of the proposed methodology by comparing the outputs under different levels of stochasticity.

並列加工フローショップをもつ機械指定型・加工 : 組立スケジューリング問題の最適解法

並列加工フローショップをもつ機械指定型・加工 : 組立スケジューリング問題の最適解法

A NSGA-II based memetic algorithm for multiobjective parallel flowshop scheduling problem

In many real-world manufacturing applications, a number of parallel flowshops are often used to process the jobs. The scheduling problem in this parallel flowshop system has gained an increasing concern from the operational research community; however, multiple scheduling criteria are rarely considered simultaneously in the literature. In this paper, a special parallel flowshop scheduling (PFSS) problem that consists of two parallel non-identical shops, one with two consecutive machines and the other with only one machine, is investigated with two objective functions of minimizing the total flow time of jobs and the number of tardy jobs in the two-machine flowshop. A multiobjective evolutionary algorithm (MOEA) based memetic algorithm hybridizing the local search technique into the framework of NSGA-II, which is well known as the most popular MOEA, is proposed for addressing the investigated PFSS problem. A set of test instances are employed to examine the performance of the proposed algorithm in comparison with two peer MOEAs, which also adopt the similar algorithm mechanism of NSGA-II. Experimental results indicate the effectiveness and efficiency of the proposed NSGA-II based memetic algorithm in solving the multiobjective PFSS problem.

Comparative Simulation Study of Production Scheduling in the Hybrid and the Parallel Flow

AbstractScheduling is one of the most important decisions in production control. An approach is proposed for supporting users to solve scheduling problems, by choosing the combination of physical manufacturing system configuration and the material handling system settings. The approach considers two alternative manufacturing scheduling configurations in a two stage product oriented manufacturing system, exploring the hybrid flow shop (HFS) and the parallel flow shop (PFS) environments. For illustrating the application of the proposed approach an industrial case from the automotive components industry is studied. The main aim of this research to compare results of study of production scheduling in the hybrid and the parallel flow, taking into account the makespan minimization criterion. Thus the HFS and the PFS performance is compared and analyzed, mainly in terms of the makespan, as the transportation times vary. The study shows that the performance HFS is clearly better when the work stations’ processing times are unbalanced, either in nature or as a consequence of the addition of transport times just to one of the work station processing time but loses advantage, becoming worse than the performance of the PFS configuration when the work stations’ processing times are balanced, either in nature or as a consequence of the addition of transport times added on the work stations’ processing times. This means that physical layout configurations along with the way transport time are including the work stations’ processing times should be carefully taken into consideration due to its influence on the performance reached by both HFS and PFS configurations.

Efficient heuristics for the parallel blocking flow shop scheduling problem

We consider the NP-hard problem of scheduling n jobs in F identical parallel flow shops, each consisting of a series of m machines, and doing so with a blocking constraint. The applied criterion is to minimize the makespan, i.e., the maximum completion time of all the jobs in F flow shops (lines). The Parallel Flow Shop Scheduling Problem (PFSP) is conceptually similar to another problem known in the literature as the Distributed Permutation Flow Shop Scheduling Problem (DPFSP), which allows modeling the scheduling process in companies with more than one factory, each factory with a flow shop configuration. Therefore, the proposed methods can solve the scheduling problem under the blocking constraint in both situations, which, to the best of our knowledge, has not been studied previously. In this paper, we propose a mathematical model along with some constructive and improvement heuristics to solve the parallel blocking flow shop problem (PBFSP) and thus minimize the maximum completion time among lines. The proposed constructive procedures use two approaches that are totally different from those proposed in the literature. These methods are used as initial solution procedures of an iterated local search (ILS) and an iterated greedy algorithm (IGA), both of which are combined with a variable neighborhood search (VNS). The proposed constructive procedure and the improved methods take into account the characteristics of the problem. The computational evaluation demonstrates that both of them –especially the IGA– perform considerably better than those algorithms adapted from the DPFSP literature.

An FPTAS for the parallel two-stage flowshop problem

We consider the NP-hard m-parallel two-stage flowshop problem, abbreviated as the (m,2)-PFS problem, where we need to schedule n jobs to m parallel identical two-stage flowshops in order to minimize the makespan, i.e. the maximum completion time of all the jobs on the m flowshops. The (m,2)-PFS problem can be decomposed into two subproblems: to assign the n jobs to the m parallel flowshops, and for each flowshop to schedule the jobs assigned to the flowshop. We first present a pseudo-polynomial time dynamic programming algorithm to solve the (m,2)-PFS problem optimally, for any fixed m, based on an earlier idea for solving the (2,2)-PFS problem. Using the dynamic programming algorithm as a subroutine, we design a fully polynomial-time approximation scheme (FPTAS) for the (m,2)-PFS problem.

Proposição de algoritmo simulated annealing para programação em flow shops paralelos proporcionais com tempos de setup explícitos

Este trabalho aborda o problema de otimização da duração total da programação (makespan) em dois flow shops paralelos proporcionais com tempos de setup explícitos e independentes da sequência de tarefas. O problema de programação em flow shops paralelos é um caso específico do conhecido flow shop híbrido, caracterizado por sistemas produtivos multiestágio com mais de uma máquina operando em paralelo em cada estágio, e muito frequente em vários tipos de indústrias como química, eletrônica, automotiva, farmacêutica e alimentícia. Este trabalho objetivou propor seis algoritmos Simulated Annealing e seus respectivos esquemas de perturbação, além de um algoritmo para geração da sequência inicial, para solução do problema descrito. Este estudo pode ser classificado como “pesquisa aplicada” quanto à natureza, “pesquisa exploratória” quanto aos objetivos e “pesquisa experimental” quanto aos procedimentos, além da abordagem “quantitativa”. Os algoritmos propostos mostraram-se eficazes quanto a solução e eficientes computacionalmente. Os resultados da Análise de Variância (ANOVA) revelaram que não existe diferença significativa entre os esquemas de perturbação em termos do makespan. Sugere-se a utilização do esquema PS4, que faz o deslocamento de uma subsequência de tarefas, por ter fornecido a melhor porcentagem de sucesso. Verificou-se também que é significativa a diferença entre os resultados dos algoritmos para cada valor do fator de proporcionalidade dos tempos de processamento e de setup dos flow shops.

Parallel Machine Shop Scheduling Using Memetic Algorithm

Parallel machine shop scheduling problem can be stated as finding a schedule for a general task graph to execute on a customed flow so that the schedule length can be minimized. Parallel Flow Shop Scheduling with a case study has been . In this study we present an effective memetic algorithm to solve the problem. Also evaluating the performance of two algorithms (genetic algorithm and memetic algorithm) in terms of both the quality of the solutions produced and the efficiency. These results demonstrate that the memetic algorithm produces better and quality solutions and hence it is very efficient . KEY WORDS: Hybrid Flow Shop Scheduling, Multiprocessor, Memetic algorithm.

Research on a JIT scheduling problem in parallel motorcycle assembly lines considering actual situations

After the research of schedule problem of one kind of flexible motorcycle assembly lines, a kind of parallel conveyor belt flow shop schedule model using JIT (just-in-time) is given. The impacts of the different max process paces of different work pieces in different stations are considered. Besides, some actual situations, including unstable information and structural constrain, are also considered. Then a kind of improved artificial fish swarm algorithm based on polar coordinate coding is presented to optimise this schedule model. Lastly, this model is tested with the real data from two motorcycle assembly lines, and the result shows that the total production fee is reduced.

Approximation algorithms for the parallel flow shop problem

We consider the NP -hard problem of scheduling n jobs in m two-stage parallel flow shops so as to minimize the makespan. This problem decomposes into two subproblems: assigning the jobs to parallel flow shops; and scheduling the jobs assigned to the same flow shop by use of Johnson’s rule. For m = 2, we present a 3 2 -approximation algorithm, and for m = 3, we present a 12 7 -approximation algorithm. Both these algorithms run in O( n log n) time. These are the first approximation algorithms with fixed worst-case performance guarantees for the parallel flow shop problem.

Sequencing and scheduling of nonuniform flow pattern in parallel hybrid flow shop

This work is motivated by a practical need for operation scheduling for an automobile manufacturing industry involved with machining of different types of vibration dampers. This work aims to minimize the makespan time for relatively different types of vibration dampers with nonuniform flow pattern through a two-parallel inseparable hybrid flow shop. A mathematical model has been developed for simulation of the hybrid flow line performance. The simulation provides data relating to completion time, queue status, and machine utilization of various schedules. After analysis and evaluation of different possible schedules, simultaneous processing of two types of dampers is suggested. The model was evaluated for nonuniform flow pattern for any number of types of dampers for different sets, and a parallel solution based on completion time is suggested.

A Case Study on Integrated Production Planning and Scheduling in a Three-Stage Manufacturing System

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper presents an integrated optimization model of production planning and scheduling for a three-stage manufacturing system, which is composed of a forward chain of three kinds of workshops: a job shop, a parallel flow shop consisting of parallel production lines, and a single machine shop. As the products at the second stage are assembled from the parts produced in its upstream workshop, a complicated production process is involved. On the basis of the analysis of the batch production, a dynamic batch splitting and amalgamating algorithm is proposed. Then, a heuristic algorithm based on a genetic algorithm (known as the integrated optimization algorithm) is proposed for solving the problem. </para>

A genetic algorithm with sub-indexed partitioning genes and its application to production scheduling of parallel machines

Production scheduling seeks optimal combination of short manufacturing time, stable inventory, balanced human and machine utilization rate, and short average customer waiting time. Since the problem in general has been proven as NP-hard, we focus on suboptimal scheduling solutions for parallel flow shop machines where jobs are queued in a bottleneck stage. A Genetic Algorithm with Sub-indexed Partitioning genes (GASP) is proposed to allow more flexible job assignments to machines. Our fitness function considers tardiness, earliness, and utilization rate related variable costs to reflect real requirements. A premature convergence bounce is added to traditional genetic algorithms to increase permutation diversity. Finally, a production scheduling system for an electronic plant based on GASP is implemented and illustrated through real production data. The proposed GASP has demonstrated the following advantages: (1) the solutions from GASP are better and with smaller deviations than those from heuristic rules and genetic algorithms with identical partitioning genes; (2) the added premature convergence bounce helps obtain better solutions with smaller deviations; and (3) the consideration of variable costs in the fitness function helps achieve better performance indicators.

Parallel flowshop scheduling using Tabu search

Production scheduling problems in manufacturing systems with parallel machine flowshops are discussed. A mathematical programming model for combined part assignment and job scheduling is developed. The objective of solving the scheduling problem is to minimize a weighted sum of production cost and the cost incurred from late product delivery. The solution of the model is NP-hard. To solve the problem efficiently, a heuristic algorithm combining Tabu search and Johnson's method was proposed. Several numerical examples are presented to illustrate the developed model and the algorithm. Computational results from these example problems are very encouraging.

The series–parallel replacement problem

Traditional equipment replacement models focus on single machine problems. However, the capacity of many production facilities is defined by multiple, heterogeneous machines. In this situation, optimal replacement (and expansion) decisions must consider all machines and their integration simultaneously as they define system capacity and are therefore economically interdependent. We model a multiple machine replacement problem that is characterized as a parallel flow shop environment. Work flows through processes in a facility according to a predetermined processing order for the product(s). For a given process, numerous machines, which may differ according to type (different manufacturers), capacity, and/or age, operate in parallel. A series of these processes defines a line and in our analysis, a plant is comprised of multiple, parallel lines. In this preliminary investigation, we present an integer programming formulation to determine optimal purchase, salvage, utilization and storage decisions for each asset over a finite horizon. We illustrate that this model is difficult to solve. We provide valid inequalities to improve the lower bound provided by the linear programming relaxation and a dynamic programming approach to provide initial upper bounds.