A flexible artificial neural networkâfuzzy simulation algorithm for ...

Int J Adv Manuf Technol (2010) 50:699–715 DOI 10.1007/s00170-010-2533-6

ORIGINAL ARTICLE

A flexible artificial neural network–fuzzy simulation algorithm for scheduling a flow shop with multiple processors Ali Azadeh & Mohsen Moghaddam & Pegah Geranmayeh & Arash Naghavi

Received: 6 September 2009 / Accepted: 11 January 2010 / Published online: 17 February 2010 # Springer-Verlag London Limited 2010

Abstract One of the most popular approaches for scheduling manufacturing systems is dispatching rules. Different types of dispatching rules exist, but none of them is known to be globally the best. A flexible artificial neural network–fuzzy simulation (FANN–FS) algorithm is presented in this study for solving the multiattribute combinatorial dispatching (MACD) decision problem. Artificial neural networks (ANNs) are one of the commonly used metaheuristics and are a proven tool for solving complex optimization problems. Hence, multilayered neural network metamodels and a fuzzy simulation using the α-cuts method were trained to provide a complex MACD problem. Fuzzy simulation is used to solve complex optimization problems to deal with imprecision and uncertainty. The proposed flexible algorithm is capable of modeling nonlinear, stochastic, and uncertain problems. It uses ANN simulation for crisp input data and fuzzy simulation for imprecise and uncertain input data. The solution quality is illustrated by two case studies from a multilayer ceramic capacitor manufacturing plant. The manufacturing lead times produced by the FANN–FS model turned out to be superior to conventional simulation models. This is the first study that introduces an intelligent and flexible approach for handling imprecision and nonlinearity of scheduling problems in flow shops with multiple processors. Keywords Artificial neural network . Metamodeling . Flow shop scheduling . Fuzzy simulation . Multiattribute combinatorial dispatching . Optimization A. Azadeh (*) : M. Moghaddam : P. Geranmayeh : A. Naghavi Department of Industrial Engineering and Center of Excellence for Intelligent Based Experimental Mechanics, University College of Engineering, University of Tehran, Tehran, Iran e-mail: [email protected] e-mail: [email protected]

1 Introduction Flow shops with multiple processors (FSMP; i.e., a flexible flow line or hybrid flow shop) scheduling problem is applied for the sequencing of jobs in a flow shop with two or more identical machines. This type of manufacturing systems is relatively common and has a variety of applications including semiconductor and electronics manufacturing and petrochemical production [7, 36]. In any manufacturing system, dispatching rules are one of the most important performance factors. In general, whenever a machine becomes free, a job with the highest priority in the queue is selected to be processed on a machine or work center [37]. Numerous dispatching rules exist including shortest processing time (SPT) served first, longest processing time served first, earliest due date (EDD) served first, first in first out (FIFO), and last in first out [25], in which, FIFO is a commonly used dispatching rule in FSMP environments [32]. There is no dispatching rule to be globally better than any other. Their efficiency depends on the characteristics of the system, operating condition parameters, and the production objectives [25]. Selective applications of different dispatching rules at different processing stages in any FSMP improve the shop performance. This type of problem is a combinatorial dispatching decision [22]. There is a significant body of literature that aimed to propose a global dispatching rule and does not consider a combinatorial dispatching strategy that uses different dispatching rules for different stages [9, 19, 31]. Applying a sole dispatching rule to all stages of a FSMP system can cause an inferior control strategy and significant productivity losses. Two different types of dispatching approaches exist for scheduling a FSMP system [19]. The first type uses a single job attribute to decide the dispatching priority, such as SPT,

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EDD, etc. The second type uses more than one job attribute to decide the dispatching priority, such as the ratio of process time to time in system. The latter one is generally more effective in solving a dispatching problem [6]. A multiattribute combinatorial dispatching (MACD) decision algorithm allows the use of both multiple attributes and combinatorial dispatching rules to optimize system performance. Commonly seen performance measures are tardiness, flow time, and throughput [41]. Over the last two decades, different modeling methods based on fuzzy sets and artificial neural networks (ANNs) have become popular and have been used by many research fields and for a variety of engineering applications. Neural networks, fuzzy sets, and evolutionary computing regarded as the leading technologies of computational intelligence have expanded and enriched a field of system modeling quite immensely [29]. ANNs act as a tool for simulation metamodeling, which include a number of highly interconnected processing elements or nodes, and incorporate the ability to process information by a dynamic response of these nodes and their connections to external inputs [44]. An ANN performs any particular function as the human brain, which is a highly complex, nonlinear, and parallel information processing system with the capability of performing certain computations many times faster than the fastest digital computer in existence today [15]. ANNs are simulated neurons interconnected in similar manner as the human brain’s neurons. ANNs have the ability of improving its performance by learning from examples and learning underlying relationships from a collection of training examples instead of following a set of determined rules. ANNs require no detailed information about the system parameters. Instead, they learn the relationship between the input and output parameters as a result of training with previously recorded data, which leads to solve large and complex systems with many interrelated parameters. To deal with imprecision and uncertainty, concepts and techniques of probability theory are usually employed. In the 1960 s, meanings of the probability theory have been reconsidered and criticized when modeling practical problems, especially in artificial intelligence. Around the same time as the development of chaos theory to handle nonlinear dynamic systems in physics and mathematics, fuzzy set theory was developed by Zadeh [42]. Since then, it has been applied to the fields of operation research, management science, artificial intelligence and expert systems, control theory, simulation, statistics, and many other fields. In this study, knowing the parameter of each distribution only, our aim is to use a fuzzy simulation. Therefore, a triangular membership function is proved to be the best shape of membership functions. In this paper, we propose a flexible artificial neural network–fuzzy simulation (FANN–FS) algorithm based on

Int J Adv Manuf Technol (2010) 50:699–715

the network modeling using Visual SLAM to provide a robust solution for FSMP scheduling problem. Using the proposed flexible algorithm, we are able to solve the FSMP problem with both crisp and fuzzy input data. In order to model the network, Visual SLAM is used because of its structure based on network modeling, its ease to add or remove attributes of the system, and the suitability of it for the system manager to obtain statistical reports in order to make proper decisions in different conditions. The model outputs contain valuable information about machine utilization, idle time for each machine, the average queue length of jobs for each machine, and the average waiting time of jobs for each machine. Two case studies from a multilayer ceramic capacitor (MLCC) manufacturing plant are brought to illustrate the robustness and effectiveness of the proposed algorithm. The remainder of this paper is organized as follows: Section 2 is about the related literature. Section 3 presents the background information for the case study problem and the process-oriented simulation. In Section 4, the proposed FANN–FS algorithm and implementation of it in two case studies is presented. Section 5 provides the experimental results in two case studies. Conclusions and future research opportunities are presented in Section 6.

2 Literature review The related literature to this study can be divided into three main categories. The first is the category of conventional simulation methods for flow shop optimization problems. In this regard, Grangeon et al. [16] proposed a generic simulation model for hybrid flow shop where the job priorities at each machine stage were established dynamically. The main goal of their simulation study was to facilitate the performance evaluation of different priority rules for job dispatching. Allaoui and Artiba [2] presented a hybrid flow shop scheduling problem under maintenance constraints to optimize several objectives based on flow time and due date, considering setup, cleaning, and transportation times. The main objective of their study was to show how simulation and optimization can be integrated to tackle this practical nondeterministic polynomial (NP)-hard problem. Another study by Kuo et al. [22] attempted to provide a robust solution for a dispatching decision in order to have a “good” performance under different operating scenarios. They proposed a simulation case of a FSMP, specifically a MLCC manufacturing system. In this regard, multiple criteria decision-making methods in combination with Taguchi orthogonal array were used to find the most suitable dispatching rule for every workstation. The second category includes flow shop heuristics in FSMP scheduling studies, which has been less attended in the past research literature. Brah and Loo [8] evaluated the


performance of scheduling heuristics in a FSMP by investigating five better performing flow shop heuristics for their performances of makespan and mean flow time criteria. Wang and Zheng [40] proposed an effective hybrid heuristic for flow shop scheduling by incorporating the famous Nawaz–Enscore–Ham (NEH) heuristic into the random initialization of the GA to generate the initial population and applied multi-crossover operators to subpopulations divided from the original population. Thornton and Hunsucker [38] attempted to minimize the makespan in an FSMP with no intermediate storage (FSMP–NIS) and identical multiple processors at each stage by development of a new heuristic. Noorul Haq and Ramanan [28] used ANN that has the ability of acquiring sequencing knowledge in order to make the future sequencing decisions over time in flow shop problems. A hybrid algorithm based on particle swarm optimization (PSO) was presented by Liu et al. [23] for no-wait flow shop scheduling with the objective of minimizing makespan. They developed a novel encoding scheme based on random key representation, an efficient population initialization, an effective local search based on the NEH heuristic, and a local search based on simulated annealing with an adaptive metaLamarckian learning strategy to be incorporated into PSO to solve the problem. Ng et al. [27] proposed three heuristics (EDD, EEDD, and PGA) for the problem where it specifies which of the two adjacent jobs in flow shop scheduling problem precedes in an optimal solution. Ant Colony Optimization (ACO) method, as a powerful and well-known metaheuristic, was used by Alaykýran et al. [1] to solve hybrid flow shop problems with the objective of minimizing makespan, which makes the problem to be NP-hard. Huang et al. [18] presented a no-wait two-stage multiprocessor flow shop with setup time to minimize total completion time. They developed an integer programming model and an ACO method to test, analyze, and compare simulated data. Dulluri et al. [14] developed a priority-based heuristic based on the dynamic priorities of the customer work orders for minimizing the makespan for a turbine manufacturing industry. Another study by Venkataramana and Raghavan [39] proposed a mixed integer nonlinear program for jobs in parallel identical batch processors with incompatible job families to minimize the total weighted completion time using two heuristics whose performance was evaluated in the case of two and three batch processors. Azizi et al. [5] presented a generic framework to tackle combinatorial optimization problems, based on it, a new algorithm tailored for flow shop scheduling. The performance of their method was compared with other techniques including a conventional simulated annealing, a standard genetic algorithm, and a hybrid genetic algorithm. MouelhiChibani and Pierreval [25] proposed neural networks (NN) to select in real time, each time a resource becomes

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available the most suited dispatching rule, in which the NN parameters were determined through simulation optimization. The benefits of their study were illustrated through the example of a simplified flow shop manufacturing system. Davoudpour and Ashrafi [12] developed a greedy randomized adaptive search procedure version to deal with the hybrid flow shop scheduling problems with sequence-dependent setup time, known as the SDST hybrid flow shops. The third category is related to the simulation studies in the past research literature. In this regard, Kazerooni et al. [20] investigated the operational problems of FMSs through simulation and evaluated different combinations of scheduling rules by a fuzzy integrated decision-making support system. Azadeh et al. [4] used a computer simulation model for a car industry using a just-in-time production system. Azadeh et al. [3] used a computer simulation for finding optimal solution of an assembly line in a shop floor. Nejati [26] modeled a computer simulation of a press shop of a car manufacturing. Grangeon et al. [16] proposed a generic simulation model for a hybrid flow shop where the job priorities at each machine are established dynamically. They used GPSSS (GPSS under Simulation) language. Cochran and Chen [11] developed a fuzzy set approach for multicriteria selection of object-oriented simulation software in order to analyze the production system. They used fuzzy set theory and algebraic operations of fuzzy numbers to characterize simulation software so that the strength and weakness of each alternative can be compared. Olson and Wu [30] demonstrated how simulation can be used to reflect fuzzy inputs, which allows more complete probabilistic interpretation of model results. Zhang et al. [43] proposed an approach to evaluate and optimize dispatching rules by integrating the simulation and response surface methodology. They considered a dynamic bottleneck dispatching policy in their problem, in which bottlenecks were detected in a time-consuming process, and therefore, adaptive dispatching decisions were made based on the real-time conditions. Another study by Puig et al. [34] proposed a new approach to simulation of discrete linear time-invariant dynamic systems with parameters and initial conditions described by fuzzy numbers. The proposed approach solved the problem of fuzzy simulation by determining at each iteration a nested family of intervals, corresponding to different levels of certainty (α-cuts), that enclosed the possible system states using optimization. Chen and Wang [10] presented a nonlinear scheduling rule incorporating a fuzzy–neural remaining cycle time estimator to improve scheduling performance in a semiconductor manufacturing factory. They used a look-ahead selforganization map-fuzzy back-propagation network approach to estimate the remaining cycle time of each job. Then, the release time and remaining cycle time of each job were both normalized to balance their importance in the fluctuation

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smoothing rule, and finally, the normalized release times were divided by the normalized remaining cycle time to obtain the slack. Based on this motivation, in this study, a FANN–FS algorithm—as a combination of heuristics, fuzzy logic, and simulation methods—is presented in order to solve a MACD decision problem in a FSMP environment. In this regard, Liu et al. [24] proposed an effective hybrid algorithm based on particle swarm optimization simulation for permutation flow shop scheduling problem with the limited buffers between consecutive machines to minimize the maximum completion time. Rayward-Smith and Rebaine [35] analyzed the problem of minimizing the overall completion time for the two machine flow shop problem, in which two heuristic algorithms were presented to solve this problem along with their worst-case analyses. In general, the main objective of simulation metamodeling has been to provide robust, fast decision support aids to enhance the overall effectiveness of decision-making processes [15]. To the best of our knowledge, this is the first study which represents a flexible algorithm based on ANN and fuzzy simulation to deal with a FSMP optimization problem.

3 Case studies 3.1 System description In this study, a problem from Yang et al. [41] is extracted and enhanced. The process of MLCC manufacturing begins from Fig. 1 Generic MLCC manufacturing process


ceramic powder preparation and ends with reel taping. A generic MLCC manufacturing process is illustrated in Figs. 1 and 2 which is of a leading MLCC manufacturing company located in Tainan, Taiwan. The present study models the case study problem in nine stages in a typical disconnected flow line from stacking to testing stages (Fig. 1). The stages before the stacking stage are for the preparation of raw material and are not considered in the present study. In this case, one of the key work-in-process management strategies is dispatching decision which affects the system performance. The scheduling decision determines the product mix to be released into the line and influences the workload of the line and the location of the bottlenecks. The MLCC manufacturing process is an FSMP problem because all products have same manufacturing stages and are subject to the constraints of process precedence. This problem is much more complicated than a conventional FSMP problem because of having several stages (more than ten) in its process, in which two stages of the process (i.e., binder burnout and sintering) are batch processing processors adding more complexity to the problem. The product mix is determined by both material type and product size, the combination of which decides the setup requirements. The MLCC problem contains nine stages from stacking to testing. Stage 7 (dipping/curing) has two disjointed segments and is separated into two substages (7a and 7b). So, there are in general ten stages in the MLCC problem. This FSMP problem allows for the use of different dispatching decisions among the ten sequential stages, in addition to the use of a multiattribute dispatching rule.

Int J Adv Manuf Technol (2010) 50:699–715 Fig. 2 An example of MLCC

703 Electrode Ceramic Dielectric Layer

Termination Edge

Termination Edge

3.2 Process-oriented simulation In this study, Visual SLAM language is used to build the model and simulate the system. The computer model is a fully object-oriented model. The reason for employing simulation approach is the high number of stages and blocks (nine and ten, respectively) that represents queues and resources, respectively. We begin by defining the system and its components. The system is a set of permanent and temporary entities taking into consideration the entities’ attributes and relationships between them. This set is directed to achieve a specified objective. Permanent entities, such as machines and manpower in a manufacturing system, are named as a server. Temporary entities are incorporated into the system represented within the simulation model. They pass and then leave the system. The attributes of each entity are considered as an entity characteristic required for identifying the temporary entities. Examples of entity characteristic are arrival time, part number, and processing time of the system with each temporary entity. Different simulation languages are available in the literature and market. Visual SLAM is the simulation language used in this paper for solving the flow shop problem. The structure of this language is based on network modeling. Therefore, adding or removing some elements in different sections of the model is easy [33]. In the presented problem based on the network model, the materials and machines are considered as entities and servers, respectively. Descriptions of network components are taken from Pritsker and O’Reilly [33]. Drake and Smith [13] introduced a framework for online simulation systems in operational planning, scheduling, and control of manufacturing systems. They identified five basic concepts for software design of an online simulation system and solved an example simulator. In this procedure, there is a budgetary limitation in this shop. Hence, the main goal of simulator is to facilitate the

performance evaluation of different priority rules for job dispatching, concerning the mean flow time and make span as well as other performance criteria like average resource utilization, average queue length, etc. 3.3 Case study 1: FSMP problem with crisp input data The required data for modeling the FSMP problem including stage names, number of machines in each stage, setup time, machine failure information, and processing time are collected in Tables 1, 2, and 3 in detail. The historical production data are downloaded from the company’s shop floor control system for the collection purpose. The setup times, mean time between failures (MTBF), and mean time to repair (MTTR) are stochastic data analyzed by commercial curve fitting software, ExpertFit. The resulting distributions for each tool type are validated by both Chi-square and Kolmogorov– Smirnov tests for their goodness of fit. The variance for the raw process time is negligible. Thus, all of the process time data are deterministic as shown in Tables 2 and 3. It should be noted that some data have been modified to respect the confidential proprietary information from the company. The process time for the stages in Table 2 is dependent on material type, regardless of product size. The process time for the stages in Table 3 is independent of product type. Note that the unit of measure is minute per lot for the data in the above tables. The notation for product size and material types is a convention of the case study company. There are 24 product types as a combination of six material types and four product sizes. The minimal processing unit is a “lot,” and also, lot size is product specific. Because of a batch processing requirement for the binder burnout and sintering stages, a batch size of six lots is assigned for experimental purposes. In what follows, each customer order represents one batch. The proposed methodology solves the MACD problem for MLCC manufacturing by

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Table 1 Machine data Machine no.

Stage name

Number of machines

Setup time (min)

MTBFa (min)

MTTRb (minutes)

1 2 3 4 5 6 7a 7b

Stacking Pressing Cutting Binder burnout Sintering Tumbling Dipping Curing

17 1 4 16 2 8 4 4

Uniform (27, 33)c 0 Uniform (25, 33)d 0 Constant (1,440)c 0 Uniform (29, 35)d Constant (1,440)c

Exp 0 Exp 0 0 Exp Exp Exp

Exp 0 Exp 0 0 Exp Exp Exp

8 9

Plating Testing

1 12

Uniform (1, 2)c,d Uniform (20, 29)d

Exp (72) Exp (2)

a

Mean time between failures

b

Mean time to repair

c

Setup needed for the material change

d

Setup needed for the size change

minimizing the tardiness that is one of the key performance indices of the case study. 3.4 Case study 2: FSMP problem with fuzzy inputs In this case, we have used fuzzy inputs for solving the FSMP problem. The only difference between required data in this case and case study 1 is that we have considered different process times for each product type in tumbling, plating, and testing stages, while there are equal process times for each product type in ANN simulation problem. The required data for modeling the FSMP problem machines data, material-type-dependent process time data, product type-dependent process time data, and single process time data are collected in Tables 4, 5, 6, and 7 in detail. The historical production data are downloaded from the company’s shop floor control system. The setup times, MTBF, and MTTR are stochastic data analyzed by ExpertFit. The resulting distributions for each tool type are validated by both Chi-square and Kolmogorov–Smirnov tests for their goodness of fit. Table 2 Material-typedependent process time data (minutes)

Stage name

Stage Stage Stage Stage Stage Stage Stage

1 2 3 4 6 8 9

tacking pressing cutting binder burnout tumbling plating testing

(30) (2)

(54) (25) (35)

(5) (0.17)

(15) (3) (2)

Exp (7) Exp (0.17)

4 The flexible ANN–Fuzzy simulation algorithm In this study, we propose a FANN–FS algorithm to deal with the FSMP scheduling problem. The proposed algorithm is a combination of ANN and fuzzy logic with conventional simulation to cover all types of input data including fuzzy and crisp data (Fig. 3). In the proposed FANN–FS algorithm, according to the upside illustration, we should firstly collect and then analyze the nature of input data. There are different types of data such as crisp or fuzzy that may be involved in any real FSMP problem and should be determined before consideration in the problem. After determining the nature of input data, if they are crisp, the conventional simulation method and then the integrated ANN computer simulation method should be developed. Otherwise, the fuzzy simulation method should be taken into account. In both conditions, after developing the methods, the results should be verified and validated according to some criteria discussed in the following sections. Therefore, if the results are valid, the proposed methods can be implemented.

Material types K12000

K3400

K3000

K90

K60

K30

823.6 22.05 344.88 3,434.17 399.17 336 836.58

446.58 39.05 147 2,714.17 361.9 336 560.58

296.73 39.05 147 3,434.17 374.67 336 560.58

694.8 44.05 220.2 2,534.17 555.83 296 674.58

555.85 44.05 176.16 2,114.17 525 336 752.58

393 39.03 132 2,714.17 690 336 752.58


705

Table 3 Single process time data (minutes) Stage 5 sintering

Stage 7a dipping

Stage 7b curing

in the available literature [17, 33]. A brief description of each one is provided as follows.

1593

105.02

62.28

4.1.1 Implementation of the training algorithm

Otherwise, new data should be collected, and the algorithm should be started again. 4.1 Development of the ANN models The simulation software package Visual SLAM is used to create the set of examples necessary to train and test the prototype networks. In the proposed study, only feed forward, multilayered, fully connected networks are considered. The models are trained through the back-error-propagation learning algorithm. MATLAB is used as the development shell for this study. The simulated FSMP consists of the use of nine stages to manufacture MLCC. Material arrivals are modeled according to a uniform distribution. Simulation runs are executed for 480 TU. Output statistics for 900 different and randomly selected job shop situations are collected from 20 independent replications. The first 800 problems are used for training and testing the ANNs during the design step, while the other 100 scenarios are reserved for validation purposes. The simulation analysis consists of estimating the average flow times when orders follow different machine sequences. All other parameters, even stochastic, are kept unchanged throughout the simulation runs. ANNs with one hidden layer (Fig. 4) are pursued in this study, although some tests on two-hidden layer networks are also performed. Data representation is a critical issue that directly affects the architecture of ANN results. The number of input neurons requires representing any given material type. Several codification rules are developed and tested in this study following conventional guidelines given

The general procedure applied to each sequence codification schemes (SCS) in order to develop the ANN models is as follows: 1) The training and testing data order is randomized by shuffling the training and testing facts several times with ZRandom. ZRandom uses the Mersenne Twister algorithm to generate pseudorandom numbers, as one of the best algorithms available. Mersenne Twister is a very fast algorithm and has a cycle period of 219,937 −1. 2) An initial setting for the maximum number of learning epochs is set to 10,000. The “Training Tolerance Tuning” option is used since its results are proved to be better than those of a fixed tolerance. All final experiments are initiated with a training tolerance of 0.18. The tuning is set to be automatically reduced by a factor of 0.9 any time that the percentage of good facts reached at least 85%. The reduction limit is set at 0.02, mostly, to ensure that the training will not terminate prior to reaching the maximum number of runs. Testing tolerance is kept fixed in 0.2. 3) The network architectures are initialized following a pre-established methodology. Input layers are dependent on material type. Output layers are provided with ten nodes in all instances. Only one hidden layer, with ten nodes, is employed. As long as training failed, one node is added to the hidden layer. Some experiments are later performed with two hidden layers. 4) The MATLAB option “Testing While Training” is set “on.” The idea is to test any run for which at least 75% of the training facts are correct. A second condition is

Table 4 Machine data Machine no.

Stage name

Number of machines

Setup time (min)

MTBF (min)

MTTR (min)

1 2 3 4 5 6 7a 7b 8 9

Stacking Pressing Cutting Binder burnout Sintering Tumbling Dipping Curing Plating Testing

17 1 4 16 2 8 4 4 1 12

Uniform (27, 33)a 0 Uniform (25, 33)b 0 Const (1,440)a 0 Uniform (29, 35)b Const (1,440)a Uniform (1, 2)a,b Uniform (20, 29)b

Exp 0 Exp 0 0 Exp Exp Exp Exp Exp

Exp 0 Exp 0 0 Exp Exp Exp Exp Exp

a

Setup needed for the material change

b

Setup needed for the size change

(30) (2)

(54) (25) (35) (72) (2)

(5) (0.17)

(15) (3) (2) (7) (0.17)

706


Table 5 Material-typedependent process time data (minutes)

Stage name

Stage Stage Stage Stage

5)

6)

7)

8)

1 2 3 4

Material types

stacking pressing cutting binder burnout

K12000

K3400

K3000

K90

K60

K30

823.6 22.05 344.88 3,434.17

446.58 39.05 147 2,714.17

296.73 39.05 147 3,434.17

694.8 44.05 220.2 2,534.17

555.85 44.05 176.16 2,114.17

393 39.03 132 2,714.17

added to stop the training if the number of good testing facts reaches at least 90%. At the end of each epoch, the current network is evaluated on the testing set, and their results are written to a file. The advantage of this approach, known as best-net-testing, is that the selected network is not the one that learns most of the training facts, rather the one that performs better on new data, i.e., the one that generalized better. A smoothing factor, or momentum, is defined. This is a variable that adds a delta to the error correction, which is in the direction of the last run’s overall error adjustment. This helps the network move in only one direction. Using a momentum of zero would imply that the past direction of the error is irrelevant, what might considerably slow the training process. In this study, the value of 0.9 is utilized for the smoothing factor. A changing learning rate is used during training. This is set to linearly change between 0.1 (i.e., 100% of the training facts are correct) and 1.0 (i.e., 100% of the training facts are incorrect). Unipolar Sigmoid transfer functions are finally defined. For this type of functions, there is a common problem

Table 6 Product-typedependent process time data (minutes)

Stage name

Stage 6 tumbling 0402 0603 0805 1005 Stage 8 plating 0402 0603 0805 1005 Stage 9 testing 0402 0603 0805 1005

reported in the literature known as undershooting, which consists of the systematical underestimation of the output values. To avoid this problem, a range between 10% below the minimum training and testing values and 10% above the maximum one is used. In this study, the scaling range is increased by 10% beyond the maximum and minimum values. 4.1.2 ANN train and test The number of output neurons in all generated architectures is ten, one for the average waiting time of each stage. The number of input neurons is directly determined by the material type. A major consideration is to determine the optimum number of neurons in the hidden layer. The followed approach is to start with networks with a small number of hidden neurons and to continue adding hidden neurons as needed. In some instances, an ANN may test well before it has gotten all of the training facts correct. It should be considered that a network that performs well on new data is frequently much better than a network that is able to learn the 100% of the training data. The capability provided by MATLAB of “testing while training” is continuously utilized. In this way,

Material types K12000

K3400

K3000

K90

K60

K30

399.17

361.90

374.67

555.84

525.00

690.00

489.17 541.82 579.17

459.17 543.67 603.67

450.00 450.00 483.67

689.17 753.83 818.83

689.17 772.50 872.50

749.17 772.50 832.50

336.00 276.00 296.00 316.00

336.00 306.00 256.00 276.00

336.00 306.00 256.00 276.00

296.00 316.00 286.00 366.00

336.00 306.00 296.00 316.00

336.00 306.00 296.00 316.00

836.00 512.58 332.58 242.58

560.58 338.58 242.58 216.58

560.58 338.58 242.58 216.58

674.58 458.54 302.58 242.58

752.58 392.58 272.58 212.58

752.58 392.58 272.58 212.58


707

Table 7 Single process time data (minutes) Stage 5 sintering

Stage 7a dipping

Stage 7b curing

1593

105.02

62.28

after each run over the whole training set, a previously separated set of facts is executed, and the number of “good” and “bad” facts are computed and saved. The learning rate is set as linearly variable between 0.1 and 1.0, for 100% good and 100% bad training facts, respectively. Sigmoid is the selected transfer function. Training tolerance is tuned during training. All final experiments initiate with a training tolerance of 0.18. The tuning is set to be automatically reduced by a factor of 0.9 any time that the percentage of good facts reached at least 85%. The reduction limit is set at 0.02, mostly, to ensure that the training will not terminate prior to reaching the maximum number of runs. Testing tolerance is kept fixed in 0.2. A smoothing factor, or momentum, is defined. The average number of epochs or iterations needed for successfully training the constructed neural networks is 320. After completion of the specified number of training runs, a chart depicting the number of good facts and the Fig. 3 The proposed flexible ANN–Fuzzy simulation algorithm

root mean squared (RMS) error as a function of the epoch will be generated. Inspection of the mentioned chart make possible to select the network with the smallest testing RMS. Once the best network for each SCS is obtained, further attempts to improve their performances are made. They include the addition of noise to the training data and the pruning of small connections. Some trials are also performed with two hidden layers. After completion of the experiments, the two networks with best testing performance are selected for validation (Table 8). 4.2 Fuzzy simulation network models In this section, we explain how fuzzy numbers for parameters in probability density functions (probability mass functions, the discrete case) are obtained from a set of confidence intervals. Consider X as a random variable with probability density function f(x, θ) for single parameter θ. It is easy to generalize our method to the case where θ is a vector of parameters. Assume that θ is unknown, and it must be estimated from a random sample (X1,..., Xn). Let Y=u (X1,..., Xn) be a statistic for estimating θ. Given the values of these random variables Xi ≤xi, 1≤i≤n, a point » estimate q ¼ y ¼ uðx1 ; :::; xn Þ is obtained for θ. We would

708


Fig. 4 General ANN architecture for the FSMP problem

Average Wait Time

Input

Output Depending

Depending on

on Stage

Input Layer

never expect this point estimate to exactly equal θ, so we often also compute a (1−β)100% confidence interval for θ. We are using β here since α, usually employed for confidence interval, is reserved for α-cuts of fuzzy numbers. In this confidence interval, one usually sets β equal to 0.10, 0.05, or 0.01. We propose to find the (1−β)100% confidence interval for all 0.01≤β≤1. Starting at 0.01 is arbitrary, and we can begin at 0.001 or 0.005. Denote these confidence intervals as [θ1(β), θ2(β)] for 0.01≤β≤1. Add to this the interval [θ*, θ*] for the 0% confidence interval for θ. Then we have (1−β)100% confidence interval for θ for 0.01≤β≤1. Now place these confidence intervals one on top of the other to produce a triangular-shaped fuzzy number q whose α-cuts are the confidence intervals. We have q½a ¼ ½q1 ðaÞ; q2 ðaÞ for 0.01≤α≤1. All that is needed is to finish the “bottom” of q to make it a complete fuzzy number. We will simply drop the graph of q straight down to complete its α-cuts, q½a ¼ ½q1 ð0:01Þ; q 2 ð0:01Þ for 0.01≤α≤1. In this way, we are using more information in q than just a point estimate, or just a single interval estimate. In this study, we use triangular fuzzy numbers for the fuzzy values of uncertain parameters in probability density (mass) functions. In the FSMP, MTBF and MTTR of each stage (Table 1) are exponential distributions. In the following section, we present the fuzzification procedure of the exponential distribution.

Table 8 Selected ANN models (ANN 1 and ANN 2) ANN

Layers configuration

Range

Noise in training

Hidden Layer

4.2.1 Fuzzy service rate for FSMP problem Let μ be the expected value of service rate for a busy server in the number of service completions per time unit. Then 1/ μ is the expected value of service time. The exponential probability density of the time interval between successive service completions is ð1=mÞ expðt=mÞ

1 2

Hidden

Output

6 6

30 19

10 10

(0, 1) (−1, +1)

0.50% –

ð1Þ

Let (X1,..., Xn) be a random sample from this exponential density function. Then the maximum likelihood estimator for μ is X , the mean of the random sample (crisp data set). We know that the probability density for X is gamma with mean μ and variance μ2/n. If n is sufficiently large, we can use the normal approximation to determine approximate confidence intervals for μ. Now consider Z¼

pffiffiffih i n X m =m

ð2Þ

which is approximately normally distributed with zero mean and unit variance, provided n is sufficiently large. The graph in Fig. 5 is for the Chi-square distribution which is a special case of the gamma distribution. So we now assume that n≥100 and use the normal approximation to the gamma. An approximate (1−β)100% confidence interval for μ is obtained from h i P z b < Z < z b ¼ 1 b 2

Input

Output Layer

2

ð3Þ

After solving for μ, we have: P½LðbÞ < m < RðbÞ ¼ 1 b

ð4Þ


709

Then, if 1 u ¼ expðxÞ, we have x=−ln(u). Thus, generating the random numbers u ∈[0,1], exp(1) will be generated. We generate six upper and lower boundaries for each distribution, each referred to different α-cuts set as follows: 0.001, 0.2, 0.4, 0.6, 0.8, and 1. Table 9 illustrates the generated upper and lower bound for each distribution. Having generated the fuzzy parameters for each exponential distribution, we can simulate the FSMP problem each time with the upper or lower interval of different α-cuts.

Fig. 5 Fuzzy arrival rate l with X ¼ 25

5 Experimental results where hpffiffiffi i nX LðbÞ ¼ h pffiffiffii zb þ n

ð5Þ

2

and hpffiffiffi i nX i RðbÞ ¼ hpffiffiffi n zb

ð6Þ

2

Therefore, an approximate (1−β)100% confidence interval for μ is hpffiffiffi i 3 2 hpffiffiffi i nX nX 4h i h i5 ; pffiffiffi pffiffiffi zb þ n n zb 2

ð7Þ

2

Now we can introduce the fuzzy exponential distribution. How we compute fuzzy probabilities with these fuzzy distributions is discussed as follows. These fuzzy probability distributions may be used to model random branching or arrival/service times. The exponential E(l) has density of f(x, l)=l exp(−lx). The mean and variance of E(l) is 1/l and 1/l2, respectively. In summary, the basis of this method algorithm is to generate the exponential distribution: f ðxÞ ¼

l expðlxÞ x 0 0 otherwise

( FðxÞ ¼

1 expðlxÞ

x0

0

otherwise

ð8Þ

ð9Þ

Tables 1, 2, 3, 4, 5, 6, and 7 show data required for the FSMP problem with six material and ten resources in order to test the model with crisp and fuzzy inputs, respectively. Machines’ priorities and processing times for each stage are input data to the model. Data entering is carried out by suitable control statements to be analyzed. Tables 10 and 11, respectively, present the control statements for the ANN and fuzzy simulation models, in which these statements are analyzed. By analyzing the output of model materials, sequencing on each machine will be determined. The variable material type is equal to allowable variable in Visual SLAM. The array statements make a table with seven rows for ANN simulation (Table 10) and a table with 16 rows for fuzzy simulation (Table 11). The required information about the material-type-dependent processing times and stages sequencing have to be read from this table. Each array statement determines one table row that represents the process time of each stage. Material types are determined by six columns of this row. This material has nine stages that must be processed by machines of stages. The processing time of materials on stages is determined for the model by array statements. Columns’ number is the same as the material number. This statement is entered in the control file by the comment statement and is ineffective in model. After determining the control statements, the simulation model will be ready to run. It should be mentioned that the conventional simulation has been run for both ANN and fuzzy network models to yield outputs of conventional simulation for verification and validation of the proposed models. The simulation output shows information given in the nodes of the model, such as the average queue length, the average waiting time, average utilization, and average availability of resources for each machine. Tables 12 and 13, respectively, illustrate the results of conventional and ANN simulation models (case study 1) and conventional and fuzzy simulation models (case study 2) for the FSMP problem. Figures 6 and 7, respectively, illustrate schematic comparison between the performance of conventional

710


Table 9 Upper and lower bounds for each distribution α-Cuts

exp(30) (MTBF stage 1) exp(2) (MTBF stage 9 & MTTR stage 7b) exp(54) (MTBF stage 6) exp(25) (MTBF stage 7a) exp(35) (MTBF stage 7b) exp(72) (MTBF stage 8) exp(5) (MTTR stage 1) exp(0.17) (MTTR stage 3) exp(15) (MTTR stage 6) exp(3) (MTTR stage 7a) exp(7) (MTTR stage 8)

0.001

0.2

0.4

0.6

0.8

1

Lower Upper Lower Upper Lower

17.28903 47.25692 1.396803 4.120875 31.28733

18.35406 27.53268 1.765044 2.581888 38.4594

17.5704 22.52913 2.005451 2.535246 44.27029

28.14908 32.28004 1.552385 1.778769 44.57928

27.74032 29.69274 1.741102 1.85879 48.28094

28.63285 28.63285 1.754581 1.754581 39.1282

Upper Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper

104.0047 11.0922 34.21804 18.21869 50.77277 39.25295 96.58658 1.862284 4.910415 0.085315 0.238683 6.215834 22.76242 1.376465 5.498069 3.084888 9.613161

54.95229 21.40532 30.91389 27.80682 39.82879 62.91936 91.49711 3.865719 5.568891 0.131087 0.175334 13.1754 19.16901 2.318464 3.682371 6.939421 9.67748

55.05765 19.25412 23.98222 32.3071 43.36606 51.01652 66.63632 4.049127 4.932085 0.112458 0.141107 14.2208 18.78739 3.005653 3.903037 7.612796 9.409038

54.80072 28.13447 32.28096 34.4523 40.85308 76.70447 91.86295 4.615594 5.261413 0.160799 0.182442 13.34452 15.23179 3.706087 4.313012 5.575317 6.353671

51.98191 20.9071 22.37111 34.75412 37.24174 58.12547 62.1119 4.474967 4.792875 0.137744 0.146919 15.01121 15.98112 2.772631 2.947107 7.164551 7.623097

39.1282 28.79274 28.79274 27.61654 27.61654 64.32399 64.32399 4.611687 4.611687 0.190297 0.190297 14.06969 14.06969 2.932903 2.932903 8.697746 8.697746

simulation in contrast with ANN and fuzzy simulation approaches in terms of machine utilization, as a crucial performance criterion within any manufacturing system. Comparison of the results shows that, by using ANN and fuzzy simulation instead of conventional simulation, in general, we have improvements for all ten resources in average queue length, the average waiting time, average utilization, and average availability of resources for each machine. The paired t test is used to verify the effectiveness Table 10 Control statements for ANN simulation

of the proposed FANN–FS algorithm. The paired t test compares the means of two variables, computes the difference between the two variables for each case, and tests to see if the average difference is significantly different from zero. At confidence level α=0.05, the paired t test performed on classification accuracy rate showed that the proposed ANN and fuzzy approaches are better than conventional simulation for solving the FSMP problem as shown in Table 14.

GEN, “Azadeh and Moghaddam.”,“FSMP”,08/04/20,1,YES,YES,100; LIMITS,,,,1; EQUIVALENCE,{{materialtype,ATRIB[1]}}; ARRAY,1,6,{823.6,446.58,296.73,694.8,555.85,393}; ARRAY,2,6,{22.05,39.05,39.05,44.05,44.05,39.03}; ARRAY,3,6,{344.88,147,147,220.2,176.16,132}; ARRAY,4,6,{3434.17,2714.17,3434.17,2534.17,2114.17,2714.17}; ARRAY,5,6,{399.17,361.9,374.67,555.83,525,690}; ARRAY,6,6,{336,336,336,296,336,336}; ARRAY,7,9,{836.58,560.58,560.58,674.58,752.58,752.58}; NET; FIN;


711

Table 11 Control statements for fuzzy simulation

6 Conclusions and future research opportunities

GEN, “Azadeh and Moghaddam”,“FSMP”,08/04/20,YES,YES; LIMITS,82,,,40,2; EQUIVALENCE,{{PRODUCT,LTRIB[1]},{MATERIAL,LTRIB[2]}, {SETUP1,ATRIB[25]},{SETUP3,ATRIB[26]},{SETUP71, ATRIB[27]},{SETUP72,ATRIB[28]},{SETUP8,ATRIB[29]}, {SETUP9,ATRIB[30]}};

In this paper, we presented a flexible ANN–fuzzy simulation algorithm to solve a MACD problem in an FSMP environment. It has combined the stochastically modeling capability of discrete-event simulation and the intelligent search neural networks to solve the problem with crisp input data. Also, an α-cuts method was used to collect structured data and then construct a fuzzy simulation network that was solved to find the optimal production time. The effectiveness and efficiency of the proposed methodology has been illustrated by the case study from a leading MLCC manufacturing plant. Computational results showed that the flexible ANN–fuzzy simulation algorithm is an efficient tool for solving FSMP problems with minimizing the makespan with crisp or fuzzy nature of input data, especially for large-scale problems. The user has to rebuild the model based on the number of stages and machines given in the problem. The results obtained from the outputs of the models help managers to evaluate the performance of the system by knowing the average queue length, the average waiting time, average utilization, and average availability of resources for each machine. As mentioned, the proposed flexible algorithm is capable of modeling nonlinear, stochastic, and uncertain problems. It uses ANN simulation for crisp input data and fuzzy simulation for imprecise and uncertain input data. The solution quality was illustrated by two case studies from a MLCC manufacturing plant. The manufacturing lead times produced by the flexible ANN–fuzzy simulation model turned out to be superior to conventional simulation models. This is the first study that introduces an intelligent and flexible approach for handling imprecision and nonlinearity of scheduling problems in flow shops with multiple processors.

INTLC,{{XX[1],7},{XX[71],7},{XX[72],7},{XX[8],7}, {XX[9],7},{XX[3],7}}; ARRAY,1,6,{823.60,446.58,296.73,694.80,555.85,393.00}; ARRAY,2,6,{22.05,39.05,39.05,44.05,44.05,39.03}; ARRAY,3,6,{344.88,147.00,147.00,220.20,176.16,132.00}; ARRAY,4,6,{3434.17,2714.17,3434.17,2534.17,2114.17,2714.17}; ARRAY,5,6,{399.17,361.90,374.67,555.83,525.00,690.00}; ARRAY,6,6,{489.17,459.17,450.00,689.17,689.17,749.17}; ARRAY,7,6,{541.82,543.67,450.00,753.83,772.50,772.50}; ARRAY,8,6,{579.17,603.67,483.67,818.83,872.50,832.50}; ARRAY,9,6,{336.00,336.00,336.00,296.00,336.00,336.00}; ARRAY,10,6,{276.00,306.00,306.00,316.00,306.00,306.00}; ARRAY,11,6,{296.00,256.00,256.00,286.00,296.00,296.00}; ARRAY,12,6,{316.00,276.00,276.00,366.00,316.00,316.00}; ARRAY,13,6,{836.58,560.58,560.58,674.58,752.58,752.58}; ARRAY,14,6,{512.58,338.58,338.58,458.58,392.58,392.58}; ARRAY,15,6,{332.58,242.58,242.25,302.58,272.58,272.58}; ARRAY,16,8,{242.58,216.58,216.58,242.58,212.58,212.58}; NET; FIN;

In significance level of 0.05 and freedom degree of 9, we have t0.025;9 =2.262. Thus, it is concluded that we have considerable improvements in average utilization and average availability of resources by using ANN–fuzzy simulation method instead of conventional simulation.

Table 12 Results of conventional and ANN simulation models Resources

1. 2. 3. 4. 5. 6.

Stacking Pressing Cutting Binder burnout Sintering Tumbling

7a. Dipping 7b. Curing 8. Plating 9. Testing

Ave. queue length

Ave. waiting time

Ave. utilization

Ave. availability

Conventional simulation

ANN simulation


ANN simulation


ANN simulation


ANN simulation

0.000 0.011 0.000 0.000 1.478 0.198

0.000 0.000 0.000 0.000 0.026 0.003

0.000 2.766 0.000 0.000 2,561.386 63.234

0.000 0.721 0.000 0.000 416.227 7.599

2.287 0.152 0.890 1.641 1.595 1.482

2.350 0.160 0. 930 1.760 1.910 1.850

16.765 0.984 3.907 15.824 1.809 7.815

14.713 0.848 3.110 14.359 0.405 6.518

0.104 20.315 0.945 0.000

0.016 5. 72 0.173 0.000

34.531 6,821.431 488.328 0.000

42.601 1,509.128 456.811 0.000

0.410 2.954 0.626 1.339

0. 520 3.690 1.250 2.620

3.948 3.431 0.875 11.738

3.590 1.046 0.374 10.661

712


Table 13 Results of conventional and fuzzy simulation models Resources

1. Stacking 2. Pressing 3. Cutting 4. Binder burnout 5. Sintering 6. Tumbling 7a. Dipping 7b. Curing 8. Plating 9. Testing

Ave. queue length

Ave. waiting time

Ave. utilization


Fuzzy simulation


Fuzzy simulation


Fuzzy simulation


Fuzzy simulation

0.003 0.004 0.002 0.000 0.001 0.002 0.000 0.000 0.059 0.000

0.014 0.019 0.008 0.000 0.005 0.010 0.000 0.000 0.262 0.000

99.932 129.879 54.803 0.000 220.803 73.793 0.000 0.000 1,834.659 0.000

99.932 128.854 55.003 0.000 218.434 71.666 0.000 0.000 1,811.177 0.000

0.160 0.001 0.085 0.015 0.009 0.235 0.111 0.056 0.099 0.091

0.220 0.005 0.122 0.069 0.038 0.317 0.130 0.056 0.113 0.132

16.84 0.999 3.915 15.985 1.991 7.765 3.889 3.944 0.901 11.909

16.780 0.995 3.878 15.931 1.962 7.683 3.870 3.944 0.887 11.868

Fig. 6 Machine utilization with conventional and ANN simulation

Fig. 7 Machine utilization with conventional and fuzzy simulation

Ave. availability


713

Table 14 Paired t test comparison between conventional simulation and ANN–fuzzy simulation at confidence interval α=0.05 Method

Ave. queue length t value

Ave. waiting time t value

Ave. utilization t value

Ave. availability t value

Conventional vs ANN Simulation Conventional vs Fuzzy Simulation

1.14033 1.24244

1.37271 1.24764

2.84183 4.11505

5.00377 4.11504

We have proved ANNs to be a viable tool for stochastic simulation metamodeling. Also, the fuzzy simulation was proved to be a good approach for noncrisp simulation. The expected simulation output from both ANN and fuzzy models turned out to be as valid as the data generated from the conventional simulation approach. However, it is superior to conventional simulation because it is capable of modeling complex multiple processor problems where simulation either fails or consumes much more efforts and time. Despite the noise introduced by the stochastic nature of the interarrival and processing times, the ANN-based simulations were able to fairly capture the underlying relationship between stages’ machine sequences and their resulting average waiting time. From the practical application standpoint, the developed models offer significant advantages regarding time consumption and simplicity to evaluate new FSMP situations. The software operation is considerably fast when compared against conventional simulation approaches. This feature can

become more relevant as the model is expanded and enlarged. In addition, ANN models, properly embedded in manufacturing decision support systems, may greatly contribute to the simplification of sequencing and scheduling decision-making processes. A new hybrid or any metaheuristic method can be proposed to solve very large-sized problems for further studies. The flexible ANN–fuzzy simulation approach is also compared with some of the current studies and methods in manufacturing systems. Its features are compared with previous models to show its advantages over previous models (Table 15). The proposed flexible approach is capable of dealing both data complexity and ambiguity due to fuzzy logic and ANN mechanisms. Also, it can preprocess (train) and postprocess (test) the given data to provide higher precision. In addition, it dominates all recent studies and is capable of dealing with complexity, ambiguity, and uncertainty.

Table 15 The features of the flexible ANN–Fuzzy simulation approach vs other methods Method

The FANN– FS approach ANN simulation Fuzzy simulation Conventional simulation Genetic algorithm simulation Cochran and Chen [11] Azizi et al. [5] Kuo et al. [22] Kuo et al. [21]

Feature Multiple Data complexity Data Intelligent Fuzzy data High precision inputs and nonlinearity uncertainty modeling and modeling: and reliability and noncrisp forecasting dealing data set ambiguity

Flexibility: Data preprocessing conventional, and postprocessing fuzzy, or ANN simulation

√

√

√

√

√

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√

√

√

√ √

√

√ √

√

√

√

√

√

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714 Acknowledgement The authors are grateful for the valuable comments and suggestion from the respected reviewers. Their valuable comments and suggestions have enhanced the strength and significance of our paper.

References 1. Alaykýran K, Engin O, Döyen A (2007) Using ant colony optimization to solve hybrid flow shop scheduling problems. Int J Adv Manuf Technol 35(5–6):541–550 2. Allaoui H, Artiba A (2004) Integrating simulation and optimization to schedule a hybrid flow shop with maintenance constraints. Comput Ind Eng 47(4):431–450 3. Azadeh MA, Karimizad K, Shakeri SH (2000) Using computer simulation in a heavy electromotors assembly line unit. J Faculty Engineering 34(2):127–139 4. Azadeh MA, Bidokhti B, Sakkaki SMR (2005) Design of practical optimum JIT systems by integration of computer simulation and analysis of variance. Comput Ind Eng 49(4):504– 519 5. Azizi N, Liang M, Zolfaghari S (2009) Hybrid simulated annealing in flow shop scheduling: a diversification and intensification approach. Int J Ind Systems Eng 4(3):326–348 6. Barman S (1997) Simple priority rule combinations: an approach to improve both flow time and tardiness. Int J Prod Res 35 (10):2857–2870 7. Botta-Genoulaz V (2000) Hybrid flow shop scheduling with precedence constrains and time lags to minimize maximum lateness. Int J Prod Econ 64(1–3):101–111 8. Brah SA, Loo LL (1999) Heuristics for scheduling in a flow shop with multiple processors. Eur J Oper Res 113(1):113–122 9. Chang YL, Sueyoshi T, Sullivan RS (1996) Ranking dispatching rules by data envelopment analysis in a job shop environment. IIE Trans 28(8):631–642 10. Chen T, Wang YC (2009) A nonlinear scheduling rule incorporating fuzzy-neural remaining cycle time estimator for scheduling a semiconductor manufacturing factory—a simulation study. Int J Adv Manuf Technol 45(1–2):110–121 11. Cochran JK, Chen HN (2005) Fuzzy multi-criteria selection of object-oriented simulation software for production system analysis. Comput Oper Res 32(1):153–168 12. Davoudpour H, Ashrafi M (2009) Solving multi-objective SDST flexible flow shop using GRASP algorithm. Int J Adv Manuf Technol 44(7–8):737–747 13. Drake GR, Smith JS (1996) Simulation system for real-time planning; scheduling and control. Proceedings of the 28th conference on winter simulation Coronado California United States 14. Dulluri S, Mahesh V, Rao CSP (2008) A heuristic for prioritybased scheduling in a turbine manufacturing job-shop. Int J Ind Systems Eng 3(6):625–643 15. Fonseca DJ, Navaresse DO, Moynihan GP (2003) Simulation meta-modeling through artificial neural networks. Eng Appl Artif Intell 16(3):177–183 16. Grangeon N, Tanguy A, Chernev N (1999) Generic simulation model for hybrid flow shop. Comput Ind Eng 137(1–2):207– 210 17. Haykin S (1999) Neural networks. Prentice Hall, New Jersey 18. Huang RH, Yang CL, Huang YC (2008) No-wait two-stage multiprocessor flow shop scheduling with unit setup. Int J Adv Manuf Technol 44(9–10):921–927

Int J Adv Manuf Technol (2010) 50:699–715 19. Jayamohan MS, Rajendran C (2000) A comparative analysis of different approaches to scheduling in flexible flow shops. Prod Plan Control 11(6):572–580 20. Kazerooni A, Chan FTS, Abhary K (1997) A fuzzy integrated decision-making support system for scheduling of FMS using simulation. Comput-Integr Manuf Syst 10(1):27–34 21. Kuo Y, Taho Y, Peters BA, Chang I (2007) Simulation metamodel development using uniform design and neural networks for automated material handling systems in semiconductor wafer fabrication. Simul Modeling Pract Theory 15(8):1002–1015 22. Kuo Y, Yang T, Cho C, Tseng YC (2008) Using simulation and multi-criteria methods to provide robust solutions to dispatching problems in a flow shop with multiple processors. Math Comput Simul 78(1):40–56 23. Liu B, Wang L, Jin YH (2006) An effective hybrid particle swarm optimization for no-wait flow shop scheduling. Int J Adv Manuf Technol 31(9–10):1001–1011 24. Liu B, Wang L, Jin YH (2008) An effective hybrid PSO-based algorithm for flow shop scheduling with limited buffers. Comput Oper Res 35(9):2791–2806 25. Mouelhi-Chibani W, Pierreval H (2009) Training a neural network to select dispatching rules in real time. Comput Ind Eng. doi:10.1016/j.cie.2009.03.008 26. Nejati M (1998) Press shop modeling in automobile manufacturer industry by computer simulation. MS Eng Thesis (in Persian) Faculty of Engineering University of Tehran, Tehran, Iran 27. Ng CT, Allahverdi A, Al-Anzi FS, Cheng TCE (2007) The threemachine flow shop scheduling problem to minimize maximum lateness with separate setup times. Int J Oper Research 2(2):135– 155 28. Noorul Haq A, Ramanan TR (2005) A bicriterian flow shop scheduling using artificial neural network. Int J Adv Manuf Technol 30(11–12):1132–1138 29. Oh SK, Pedrycz W, Roh SB (2009) Hybrid fuzzy set-based polynomial neural networks and their development with the aid of genetic optimization and information granulation. Appl Soft Computing 9(3):1068–1089 30. Olson DL, Wu D (2006) Simulation of fuzzy multiattribute models for grey relationships. Eur J Oper Res 175(1):111–120 31. Petroni A, Rizzi A (2002) A fuzzy logic based methodology to rank shop floor dispatch rules. Int J Prod Econ 76(1):99–108 32. Pinedo M (1995) Scheduling: theory, algorithms, and systems. Prentice Hall, New Jersey 33. Pritsker AAB, O’Reilly JJ (1999) Simulation with Visual SLAM and AweSim. Wiley, New York 34. Puig V, Saludes J, Quevedo J (2008) Simulation of discrete linear time-invariant fuzzy dynamic systems. Fuzzy Sets Syst 159 (7):787–803 35. Rayward-Smith VJ, Rebaine D (2008) Analysis of heuristics for the UET two-machine flow shop problem with time delays. Comput Oper Res 35(10):3298–3310 36. Santos DL, Hunsucker JL, Deal DE (1996) An evaluation of sequencing heuristics in flow shops with multiple processors. Comput Ind Eng 30(4):681–692 37. Tay JC, Ho NB (2008) Evolving dispatching rules using genetic programming for solving multi-objective flexible job-shop problems. Comput Ind Eng 54(3):453–473 38. Thornton HW, Hunsucker JL (2004) A new heuristic for minimal makespan in flow shops with multiple processors and no intermediate storage. Eur J Oper Res 152(1):96–114 39. Venkataramana M, Raghavan NRS (2009) Scheduling parallel batch processors with incompatible job families to minimize weighted completion time. Int J Ind Systems Engineering 4(1):76–93

Int J Adv Manuf Technol (2010) 50:699–715 40. Wang L, Zheng D (2003) An effective hybrid heuristic for flow shop scheduling. Int J Adv Manuf Technol 21(1):38– 44 41. Yang T, Kuo Y, Cho C (2007) A genetic algorithms simulation approach for the multi-attribute combinatorial dispatching decision problem. Eur J Oper Res 176(3):1859–1873 42. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

715 43. Zhang H, Jiang Z, Guo C (2008) Simulation-based optimization of dispatching rules for semiconductor wafer fabrication system scheduling by the response surface methodology. Int J Adv Manuf Technol 41(1–2):110–121 44. Zobel CW, Keeling KB (2008) Neural network-based simulation meta-models for predicting probability distributions. Comput Ind Eng 54(4):879–888

A flexible artificial neural networkâfuzzy simulation algorithm for ...

A flexible artificial neural networkâfuzzy simulation algorithm for ...

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