INT. J. COMPUTER INTEGRATED MANUFACTURING, APRIL–MAY 2004, VOL. 17, NO. 3, 195–211
Artificial neural networks for design of manufacturing systems and selection of priority rules T. C¸AKAR and I. CIL Abstract. Simulation is one of the most effective methods in the Design of Manufacturing Systems (MS). Typical reasons for simulation of a manufacturing system includes evaluating the capacity and equipment utilization, identifying bottlenecks in the system, comparing the performance of alternative designs. Simulation is often coupled with Artificial Intelligence (AI) techniques to provide an efficient decision making framework. In this study, Artificial Neural Networks (ANN) are used for the design of a manufacturing system. Four different priority rules are used: EDD, SPT, CR and FCFS. As a result four different design alternatives are obtained from trained ANN. Performance measures of a manufacturing system are given to the ANN which then gives a design alternative. The design alternatives are evaluated in terms of performance measures and then the best design alternative is selected from four different alternatives.
1. Introduction In the literature there are a few approaches related to resource assignment problems. The mathematical programming techniques require large amounts of data, and solutions obtained from them are not as good as the results obtained from Artificial Neural Networks (ANNs) (Chryssolouris et al. 1990, Sarin and Chen 1986). Using random sampling instead also involves many alternatives. Visiting many alternatives is time-consuming, not logical and impossible, especially in large manufacturing systems. In this kind of situation, the main goal is to obtain a near optimum solution in a very short time. It is observed that the use of Artificial Intelligence (AI) techniques is very helpful (Vujosevic et al. 1994, C¸akar 1996).
Authors: Sakarya University Engineering Faculty, Industrial Engineering Department, 54040 Esentepe – Adapazari, Turkey. E-mail:
[email protected],
[email protected]
However, there is one point that should not be misunderstood. The use of simulation on its own provides a wide range of solutions and wastes valuable time. However if simulation is used effectively with Artificial Intelligence techniques, it will reach the right results much quicker. Artificial Intelligence techniques help simulation processes to look for a solution. It is very important to recognize that simulation is an inevitable tool for the design of manufacturing systems, but in a simulation process there is no need to train. Training a backpropagation neural network (BPNN) is a long process but it is very fast in providing results. In order to reach a good solution it may be necessary to carry out many tests. Instead, it is preferred to spend more time training, but not to do so many tests. This research described in this paper follows a similar path. In the literature, much research has been conducted using expert systems, ANNs, or both. Chryssolouris et al. (1990) estimated the number of machines in a work centre using ANNs, given the system performance measures like mean flow time, mean tardiness, maximum completion time, machine utilization rate in each work centre as input to the ANN system. As opposed to the simulation process, the configuration is not known in advance and it is the output of the ANN (Chryssolouris et al. 1990). However, no matter how good the parameters chosen, the solution algorithm was inadequate to find the desired solution. They observed that only one single ANN is inadequate. In order to reduce the risk of making an error and to have many solution alternatives, more than one ANN is trained. If the ANN solution is far away from the desired performance, then this erroneous configuration is refed to the system one more time to produce a better solution. Therefore, the approach here is to change direction. However, the shop floor has to operate under management policies. To change the direction outside
International Journal of Computer Integrated Manufacturing ISSN 0951-192X print/ISSN 1362-3052 online # 2004 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/09511920310001607078
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of managerial policies cannot be allowed. In brief, the target given by management should be met. On the other hand, the priority rules also should be considered. In this study, all the above-mentioned factors are considered and a new ANN system is proposed (C¸akar 1997, C¸akar et al. 1998a, 1998b). Scheduling in Manufacturing Systems (MS) has been particularly difficult. More especially, priority rules which should be used in MS are very important to obtain desired performance measures, because every priority rule can change the performance measures of the MS. Priority rules can affect the design of MS (Askin and Standridge 1993, Hutchison et al. 1991). There are no fundamental weaknesses in the MS design and developing operating strategies for work scheduling and job sequencing (Basnet and Mize 1995). The shortest processing time (SPT) dispatching rule has been the best performer more frequently over any other, although no single dispatching rule clearly dominates for all criteria. It is known that the difference in performance between various dispatching rules disappears as alternative machine options increase in a job shop environment (French 1982, Pinedo 1995).
2. Artificial intelligence applications in manufacturing 2.1. Neural network applications in manufacturing There exists a quantitative approach to this problem. Various mathematical programming formulations have been reported. These formulations in general require large amounts of data, which would be difficult and expensive to collect in a real facility. Simpler mathematical programming formulations, which avoid this pitfall, have also been developed (Chryssolouris et al. 1990). The proposed research provides this means by employing, in conjunction with simulation, the artificial intelligence tool of neural networks. The role of neural networks is the inverse of the simulator function. Given a set of desired performance measures, the neural network outputs a suitable MS design, namely, this output is based on the results of training simulation runs. In the proposed approach the suitability of a manufacturing system design is measured solely by the proximity of the system’s actual performance. It is important to express desired performance in terms of some combination of measures that cannot be optimized simply (Udo 1992). AI techniques provide capabilities for improving the efficiency of problemsolving in the MS design process (C¸akar et al. 1996). ANNs are most often applied to manufacturing problems. A neural network represents an associative memory that serves either as an optimizer or a classifier
and is applied to solve combinatorial optimization problems (Verduin et al. 1990, Wang and Takefuji 1996). Foo and Takefuji (1988) extended their previous work by formulating the scheduling problem as a set of integer linear equations, creating an integer linear programming Hopfield neural network. The energy function is represented by the sum of the starting times of all jobs. This function is minimized while making sure the constraints are not violated, all jobs are processed in a specified order, the right process sequence is followed and no machine processes two jobs simultaneously. However, there is no guarantee of an optimal solution; only small problems are solved and the requirement for amplifiers and resistive connections increases as a high degree polynomial. Zhou et al. (1991) proposed a linear programming Hopfield neural network to circumvent some shortfalls of the local convergence of an Integer linear programming Hopfield neural network used by Foo and Takefuji (1988). They avoid the use of a quadratic energy function by implementing a linear function instead. This prevents the need for a conventional integer linear programming method, which incorporates numerous control variables. However there is no guarantee of an optimal solution for a larger problem. Zhang et al. (1991) proposed a similar method using a Hopfield network to that of Foo and Takefuji (1988). They classify jobs into various priority categories, depending on their importance. The energy equation is formulated in such a way that it minimizes the sum of the finishing times of all the jobs. An additional term is introduced in the energy equation that allows high priority jobs to be processed first, while the constraint equation prevents the early processing of low priority jobs. However, this method is again limited to small problems and there is a tendency for the system to converge on non-optimal solutions. Chang and Nam (1993) implemented a linear programming Hopfield neural network, which tries to converge on the global optimum. The system works on the same principle as that of Foo and Takefuji (1988) except that it avoids the need for integer constraints by introducing slack variables. However, only small problems are solved and there is no guarantee of finding an optimal solution. Sabuncuoglu and Gurgun (1996) developed a modified 3D Hopfield model for a single machine mean tardiness problem and the minimum makespan job-shop scheduling problem. Rabelo and Alptekin (1989) provided one of the earliest studies in the neural scheduling. Although this system is able to get lower tardiness values than six dispatch heuristics, the neural
ANNs for design of manufacturing systems network does not perform any real scheduling, but purely ranks priority rules and determines coefficients. Potwin et al. (1992) employed a back propagation neural network (BPNN) for a dynamic vehicle dispatching problem. The model is only trained from the perspective of an expert system and no guarantee of optimality is provided. The method can be described as a data retrieval situation, as in the system developed by Jain (1995). Sastri and Malave (1991) applied two neural network models, a Bayesian classifier and a Back propagation neural network, to calculate the expected operation cost per period and the optimum control policy. Cedimoglu (1993) applied a BPNN approach to produce better sequences of jobs to be processed and the results show that the neural model generally outperforms several dispatch rules for various criteria. Keymeulen and De Gerlache (1993) proposed a dual BPNN for the rescheduling of an airline crew which is trained from the judgement of an expert system. Sim et al. (1994) claim that expert systems are not able to provide better results as they act basically as simple decision tables. A hybrid neural network and expert system simulation model is proposed to solve the dynamic job-shop problem and overcome this problem. Sixteen BPNNs are embedded in an expert system. Kim et al. (1995) proposed combining the BPNN paradigm with the apparent tardiness cost (ATC) rule. Jain and Meeran (1998) used a modified BPNN structure. It is able to deal with much larger and more complex problems than any previous method If training is unsuccessful, additional user-defined parameters are incorporated to take the error function from a local into a global optimum. The model is trained on optimum data rather than relying on the guesses of experts. The robustness of the model allows data to be taken directly to and from the shop-floor without requiring additional filtering and modifications. Schedules can be retrieved very quickly for a known job-shop and the modified approach employs a novel input– output structure to encode large problems in such a way that the requirement of neurons grows linearly with problem size. However, test examples are successful only when they do not vary by more than 20% from any training examples. Although this requirement strikes at the heart of the generalization capability of BPNNs it should be noted that this is one of the first systems that has used a modified BPNN model to solve job-shop scheduling problems using input–output mappings. A simple mapping of the input–output is made which, as expected, does not solve the universal scheduling problem. Wang and Yih (1997) used neural networks to select a control strategy for automated storage and retrieval
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systems. Wang and Yih’s control system is able to deal with changes in system configuration and multiple performance requirements. The AI technique has been applied broadly in many production areas because it gives fast and acceptable solutions, although it does not guarantee optimal solutions. The main idea behind the applications of AI to scheduling problems is that each scheduling system is unique to the given environment and therefore a wide variety of technical knowledge and expertise should be taken into account in solving the scheduling problems (Fox and Smith 1984, Yih 1990). Philipoom et al. (1994) developed a back propagation (BP) model to assign the due dates of parts in a job shop, Min et al. (1998) use a competitive neural network approach to multi-objective FMS scheduling, Vaithyanathan and Ignizio (1992) investigated the use of neural networks for solving certain types of large-scale, resource-constrained scheduling problems. Arizona et al. (1992) solved a scheduling problem for minimizing the total actual flow time by using the Gaussian machine model, which is one of the stochastic neural network models, timetable scheduling by Yu (1990), real time scheduling by Liang et al. (1992), real time assembly scheduling by Chen (1992) and multiple job scheduling by Lo and Bavarian (1993) and all applications of Neural Networks in scheduling which have been studied by many researchers. Since the scheduling problem is one of immense importance, it is certain that considerable effort will continue in applying neural networks in scheduling. Zhang and Huang (1995) presented a state-of-the-art survey of neural network applications in manufacturing. The application of neural networks in group technology has been studied by many researchers. Kaparthi and Suresh (1991) proposed a neural system for shape-based classification and coding rotational parts. The use of neural networks for part family formation has also been studied by a couple of researchers (Kao and Moon 1990, Moon and Chi 1992). In their approach, a three-layer feed-forward neural network is trained with the back propagation algorithm. Each input of the unit of the network presents a part feature and each output unit presents a part family. An operator plays the role of a teacher to the network by presenting each part in terms of features, and by identifying which family a part belongs to. Another Group Technology problem is machine part cell formation. Neural network approaches have been used to reduce computational complexity. Dagli and Huggahalli (1991) applied ART-1 for machine cell formation. The result obtained compared favourably with popular algorithms proposed in the literature, such as the ROC2 algorithm provided by
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King and Nakornchai (1982). The application of neural network approaches in the design of cellular manufacturing systems, which involves the machinepart family formation problem, has been studied by Malave and Ramachandran (1991) and Lee et al. (1992) A product design process can be modelled as a mapping from a function space to a structure space to a physical space (Kumara and Kamarthi 1991). An experienced human designer is usually aware of the structures that satisfy a particular set of functions. In his/her memory the designer may have stored the representations of a number of physical devices. By association, the designer can selectively retrieve those designs. Neural networks are very well suited for modelling the human associative memory. Hence, researchers are interested in applying neural networks in the product design process. Retrieval of old designs that meet current requirements on geometrical and/or technical information is a problem often encountered in batch manufacturing. Venugopal and Narendran (1992) modelled the design retrieval system as a human associative memory and applied a Hopfield neural network model to develop a design retrieval system. The use of neural networks for design data retrieval was also studied by Kamarthi et al. (1990). Instead of a Hopfield net, a feed-forward neural network trained with the back propagation algorithm is used. The neural network approach is able to provide correct output even when the input is inexact or incomplete and hence is useful for retrieval of design data. Coyne and Postmus (1990) explored the application of neural networks to simple spatial reasoning in computer-aided design. Kumara and Ham (1990) and Kumara and Kamarthi (1991) suggested an associative memory base modelling procedure for conceptual design. Arai and Iwata (1990) applied a four-layer neural network to connect lower level items to upper level ones in the design specification step of the conceptual design phase. Kim et al. (1992) adopted the neural network approach for engineering drawing with geometrical constraints. Dhingra and Rao (1992) examined a new conceptual framework for solving design optimization problems based on the neural computer paradigm. Among the research of neural networks in engineering design, the work done by Chovan and Waldron (1991) is quite interesting. The authors proposed a cognitive model of the transformation from perceived form to function based on findings from a behavioural study of expert mechanical designers when they were reading two-dimensional mechanical drawings. The model is simulated using the ART network and is
exercised and compared with findings from the behavioural study. Chen and Yan (1991) also applied neural network computing techniques in the design of an assembly planning system. Babic (1999) gives an axiomatic design methodology for flexible manufacturing systems.
2.2. Expert system applications in manufacturing Expert systems have found many applications in planning and scheduling systems. To date, numerous papers have been published on this subject. Kumara et al. (1986) briefly discussed the expert system concepts and techniques and presented a list of their applications in process planning and job-shop scheduling. Parunak (1987) outlined the distributed artificial intelligence approach and its applications to factory scheduling and control. De and Whinston (1986) studied the problems of natural language understanding, plan understanding and integrated understanding, which are of benefit to the decision-making process in manufacturing systems. Kusiak and Chen (1988) discussed research and applications of expert systems in production planning and scheduling. Relationships between expert system and operational research approaches are presented. Bruno et al. (1986) developed an expert scheduling system for scheduling parts in a flexible machining environment. The parts are grouped into batches, each batch containing 100 to 200 parts. In order to generate a release time for each batch a dynamic priority scheme is used. Erschler and Esquirol (1986) presented a jobshop scheduling system that uses a constraint-based analysis. This system makes resources (machines) constantly available and finishes jobs before the required due dates. The system was applied to solve a scheduling problem involving machines and operations only. The start time of operations and constraints that use common list resources are considered as important aspects of the problem. The constraint-based analysis approach is to generate a precedence relationship from conflicting resources. Consequently, only two types of rules were established in the knowledge base: timeupdating rules and sequencing rules to generate precedence among operations. An expert scheduling system similar to the above was presented by Bensana et al. (1986). The job-shop scheduling system integrates the constraint-based analysis module with the rulebased decision support module. O’Conner (1984) developed a rule-based expert system. The system is used for scheduling customer orders and it has the capability of classifying difficult orders into two categories: material shortage category and credit line
ANNs for design of manufacturing systems insufficiency category. It generates a loading strategy dealing with difficult orders. Subramanyam and Askin (1986) discussed an approach for scheduling FMS on a daily basis for two shifts to meet the weekly production requirement. The FMS is described by three object statuses such as: system status, machine status and job status. The system and machine status can be assigned one of the following three attribute values: heavily loaded, moderately loaded or under loaded. Similarly, the jobs waiting in the queues for machining can be assigned attribute values: critically late, moderately late and normal. A three-level hierarchical decision structure for the expert system was developed. Ben Arieh (1986) developed an expert scheduling system. The system schedules a production cell feeding an assembly station. Fellenstein et al. (1985) developed an expert system for solving a capacity planning problem for a manufacturing tester. Shaw and Whinston (1985) studied the planning and control system in cellular flexible manufacturing system. Shen and Chang (1986) developed an expert scheduling system using frames to present product status and the problem solving process. Two real-time scheduling algorithms were developed. The IF-THEN rules and algorithms are presented by frames. Shaw and Whinston (1986) presented an AI (Artificial Intelligence) approach for solving a planning problem that can be decomposed into a number of subproblems. They used the following criteria to solve the problem: maximizing the parallel usage of machines and avoiding harmful interactions among sub-problems. C¸akar (1991) developed a priority rule selecting expert system. The system defines a priority rule using some performance measures of the system. ISIS is a hierarchical job-shop scheduling model developed by Mark Fox using AI technology. In the design of the approximate reasoning-based scheduling model, the structure of ISIS is taken as a framework in order to provide a structural basis for a comparison of performance of the two models. ISIS represents the scheduling environment through constraints. Constraints are interrelated and linked to the components of the scheduling model using a variety of relationships. The method of constraint-directed search is used to generate schedules (Fox 1983, 1986, Fox and Smith 1984). Pereira (1996) developed an expert system to minimize the production time of disturbance elements in civil construction; it also aims to offer support to technicians involved in the decision-making process and to production administrators. Dutta (1990) studied a knowledge-based rescheduling expert system that was adapted to the flexible manufacturing environment. Tayanlthi et al. (1992) proposed a knowledge-based simulation system to analyse and handle disturbances in
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a flexible manufacturing environment. Recently, Belz and Mertens (1996) studied the production rescheduling system, combining an expert system with a simulation technique. When random disturbances occur, a number of disposal programs will be generated by the expert system. These programs will be simulated and marked according to a set of evaluation criteria. Finally, the best program will be selected according to the marks by policy-makers and the original production schedule will be modified on the basis of the program selected. Heikkila and Heikki (1998) proposed a modular control system for a flexible manufacturing cell based on a microcomputer and a local area network. May and Varga (1996) modelled day-to-day scheduling decisions made at a manufacturing facility using an intelligent decision support system. Li (1999) developed a hybrid knowledge-based system for production rescheduling. The study shows knowledge base methods applied to production rescheduling are a valuable approach for manufacturers to manage production disturbances and deliver customer orders on time.
2.3. Applications of simulated annealing and tabu search algorithms in manufacturing Common local search heuristics include simulated annealing, tabu search and genetic algorithms. Simulated annealing was developed by Kirkpatrick et al. (1983) and Cerny (1985). Matsuo et al. (1988), Van Learhoven et al. (1992) and Aarts et al. (1994) applied the technique to solve the job-shop scheduling problem. Tabu search can be traced to a paper by Glover (1977) and has been used in job shop scheduling by Taillard (1994) and Barnes and Chambers (1991).
2.4. Genetic algorithm applications in manufacturing Holand (1975) developed the idea of genetic algorithms. Some examples of the application of genetic algorithms to job-shop scheduling are Davis (1985), Whitley et al. (1989), Storer et al. (1992), Fox and MacMahon (1990), Lawton (1992), Della Croce et al. (1992), Nakano and Yamada (1993), Gupta et al. (1993) and Bean (1994). Storer et al. (1992) presented a general overview of the search space for scheduling problems. Herrmann et al. (1995) applied genetic algorithms to a job-shop environment for semiconductor test operations with significant performance improvement. These common searches have been called ‘smart-and-lucky searches’ by Herrmann and Lee (1993), since they must be smart enough to escape
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from most local optima; they must be lucky, however, in order to find global optimum. Local search approaches like tabu search and simulated annealing and genetic algorithms hybridized with local search procedures have yielded very good results in classical job-shop scheduling problems (Mattfeld 1996). Candido et al. (1998) developed a robust procedure to solve job shop scheduling problems with a large number of realistic constraints, such as jobs with several sub-assembly levels, an alternative processing plan for parts and alternative resources for operation requirement of multiple resources to process an operation, resources calendars, batch overlap and sequence dependent set-ups. In addition, the approach considers multi-objective evaluation functions. The system uses modified schedule generation algorithms to obtain a set of initial solutions. Each initial solution is enhanced by a local improvement procedure. A hybrid genetic algorithm, which incorporates a local hill climbing procedure, is then applied to the set of local optimum schedules. Lee et al. (1997) developed an approach to automate job-shop scheduling systems by combining both job release policy (when to release and which job to be released into the shop floor) and a dispatching rule. Rao et al. (1999) developed a design methodology and a genetic algorithm based approach for the redesign of a manufacturing system for a small steel pre-fabricated building manufacturer. Through the application of cellular principles, they discussed the application of the design methodology that takes a top-down approach to determine system needs and a bottom-up integrated design approach to develop the configurations of the manufacturing system. Mahmoodi et al. (1990) addressed part release in a cellular manufacturing environment. Irastorza and Deane (1974) and Shimoyashiro et al. (1984) studied loading and balancing in a job-shop. Baker (1984), Melnyk et al. (1991) and Ragatz and Mabert (1988) studied order release and concluded that order release does make a significant impact on dispatching performance.
3. RULES-3 inductive learning system In recent years, there has been a growing amount of research into inductive learning. In its broadest sense, induction (or inductive inference) is a method of moving from the particular to the general – from specific examples to general rules. Induction can be considered as the process of generalizing a procedural description from presented or observed examples (Quinlann 1988, Forsyth 1989, Hancox et al. 1990).
These examples may be specified by an expert as a good tutorial set, or may come from some neutral source such as an archive. The induction process will attempt to find a method of classifying an example expressed as a function of the attributes which explains the training examples and which may also be used to classify previously unseen cases. RULES-3 (Pham and Aksoy 1995) is a simple algorithm for extracting a set of classification rules from a collection of examples for objects belonging to one of a number of known classes. An object must be described in terms of a fixed set of attributes, each with its own range of possible values which could be nominal or numerical. For example, attribute ‘length’ might have nominal values {short, medium, long} or numerical values in the range { 7 10, 10}. An attribute-value pair constitutes a condition in a rule. If the number of attributes is Na, a rule may contain between one and Na conditions. Only conjunction of conditions is permitted in a rule and therefore the attributes must all be different if the rule comprises more than one condition. RULES-3 extracts rules by considering one example at a time. It forms an array consisting of all attribute-value pairs associated with the object in that example, the total number of elements in the array being equal to the number of attributes of the object. The rule-forming procedure may require at most Na iterations per example. In the first iteration, rules may be produced with one element from the array. Each element is examined in turn to see if, for the complete example collection, it appears only in objects belonging to one class. If so, a candidate rule is obtained with that element as the condition. In either case, the next element is taken and the examination repeated until all elements in the array have been considered. At this stage, if no rules have been formed, the second iteration begins with two elements of the array being examined at a time. Rules formed in the second iteration therefore have two conditions. The procedure continues until an iteration when one or more candidate rules can be extracted or the maximum number of iterations for the example is reached. In the latter case, the example itself is adopted as the rule. If more than one candidate rule is formed for an example, the rule which classifies the highest number of examples is selected and is used to classify objects in the collection of examples. Examples of which objects are classified by the selected rule are removed from the collection. The next example remaining in the collection is then taken and rule extraction is carried out for that example. This procedure continues until there are no examples left in the collection and all objects have been classified. This algorithm can be summarized as follows:
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ANNs for design of manufacturing systems Step 1.
Step 2. Step Step Step Step
3. 4. 5. 6.
Step 7.
Step 8.
Step 9. Step 10. Step 11.
Define ranges for the attributes which have numerical values and assign labels to those ranges. Set the minimum number of conditions (Ncmin) for each rule. Take an unclassified example. Nc = Ncmin –1. If Nc 5 Na then Nc = Nc + 1. Take all values or labels contained in the example. Form objects which are combinations of Nc values or labels taken from the values or labels obtained in step 6. If at least one of the objects belongs to a unique class then form rules with those objects; ELSE go to step 5. Select the rule that classifies the highest number of examples. Remove examples classified by the selected rule. If there are no more unclassified examples then STOP; ELSE go to step 3
i Input layer indice
j Hidden layer indice
Wij
Wjk OUT1
I1
I2
OUT2
B
Artificial neural networks are the mathematical models that present the biological process of the human brain. In an artificial neural network, there are three main components: neurons, interconnection, learning rules. The back propagation can map a nonlinear process. It is a feed-forward network with one or more hidden layers. The elementary architecture of the back propagation network has three layers. There are no constraints about the number of hidden layers. Back propagation is a systematic method for training multi-layer artificial neural networks. It has a mathematical foundation that is strong if not highly practical. The general structure of the back propagation neural network is given in figure 1.
WBk
WBj
Input Layer
B Hidden Layer
Output Layer
Figure 1. General structure of the back propagation neural network.
after that NET values are applied to activation function so OUT values are obtained. Similarly, the outs of hidden units are considered as input of the next hidden NEW layer units or output layer units. WBjNEW and WBk values present biases. NETk ¼
X
OUTk ¼
4. Back propagation algorithm
k Output layer indice
NEW Ik Wjk þ WBk
1 1 þe NETk
ð3Þ ð4Þ
4.2. Error propagation from output layer to the last hidden layer The outputs of a neural network model are obtained from the output layer units. The difference between target values and actual values is considered as system error, the obtained error values are propagated back to connection weights. This process is applied using the following equations: dk ¼ ð@f ðNETk Þ=@NETk ÞðTARGETk OUTk Þ
ð5Þ
dk ¼ OUTk ð1 OUTk ÞðTARGETk OUTk Þ
ð6Þ
DWkj ðn þ 1Þ ¼ Zdk OUTk þ a½DWkj ðnÞ
ð7Þ
WkjNEW ¼ WkjOLD þ DWkj ðn þ 1Þ
ð8Þ
4.1. Forward pass process in back propagation neural network NET values are computed by multiplying inputs and related weights. For units of hidden layer NET is computed as: X NETj ¼ Ii Wij þ WBjNEW ð1Þ OUTj ¼
1 1 þe NETj
ð2Þ
TARGETk presents desired output value. Z is learning rate, a is momentum coefficient, f(NETk) presents activation function. n presents iteration number. DW is change of related weight. This term is added to the old weight of the related connection to obtain the new one.
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4.3. Error propagation from hidden layer to the input layer
level is achieved, i.e. the differences between TARGET and OUT are minimized.
This process is similar to the previous one, but this time since there is no certain error, dj is computed using dk. It can be shown from equations (9) and (10). dj ð@f ðNETj =@NETj Þ
X
dj ¼ OUTj ð1 OUTj Þ
dk Wkj ;
X
dk Wkj ;
5. The proposed study
ð9Þ
The prototype system consists of four work centres, each having five machines. Six different parts are provided in batches in the shop. The number of parts, inter-arrival times of parts and processing times are given in table 1. The inter-arrival times are exponential and a total of 200 parts are to be processed. Due dates are based on the Total Work Content (TWK) method, which is defined as TWKi = ai + k 6 TPTi; where TPTi is Total Processing Time of the ith part, and k = 5. The BP (Back Propagation) algorithm was used to train the network for good performance as a supervised learning algorithm. The problems need a structured relationship between a group of inputs and outputs, hence it can be seen very clearly that BP is the best algorithm in this kind of problem. The inputs to the BPNN (Back Propagation Neural Network) are mean flow time, mean tardiness, maximum completion time, machine utilization rate in each centre and percentage of the late parts. The output of the system is the number of machines in each work centre. Figure 2 illustrates the structure of the BPNN system. The hidden layer contains 30 neurons. In this study, the shop is simulated for four different priority rules, EDD, SPT, FCFS and CR, making up four different training sets. Using these training sets, four BPNNs are trained for four priority rules. Each BPNN was tested using 125 unseen examples and the success of each network was obtained accordingly. In order to show the superiority of the BPNN over classical methods, a linear regression model was used. To compare the effectiveness of the BPNN system, the same test sets were used in regression. It was observed that as the number of variables is increased, the regression model performs better, although not as good as the BPNN system. The results are given in table 2, along with those of BPNNs. Non-linear regression
ð10Þ
DWji ðn þ 1Þ ¼ Zdj OUTj þ a½DWji ðnÞ;
ð11Þ
WjiNEW ¼ WjiOLD þ DWji ðn þ 1Þ:
ð12Þ
4.4. Recalculation of bias values The bias effects the activation function in order to force the learning process, therefore the speed of the learning process increases. Biases are recomputed as follows: for the biases of the output layer: DWBk ðn þ 1Þ ¼ Zdk þa½DWBk ðnÞ
ð13Þ
NEW OLD WBk ¼ WBk þ DWBk ðn þ 1Þ
ð14Þ
for the biases of hidden layer: DWBj ðn þ 1Þ ¼ Zdj þa½DWBj ðnÞ;
ð15Þ
WBjNEW ¼ WBjOLD þ DWBj ðn þ 1Þ:
ð16Þ
Training of the neural network model, as may be understood from the previous process, is carried out in two steps. The first step is called forward pass, which is composed of calculation for NET and OUT values. The second step is called backward pass, which is composed of error propagation through connection weights. This iterative process is repeated until a satisfactory learning
Table 1. Data information for parts to be processed.
Jobs J1 J2 J3 J4 J5 J6
Number of processed parts
Inter-arrival times
WC-1
WC-2
WC-3
WC-4
17 50 30 17 43 43
20 10 15 18 10 12
25 30 20 – 30 –
10 20 25 – 25 –
25 10 – 15 20 40
5 – – 25 15 10
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ANNs for design of manufacturing systems models are also included in the test. However, they do not perform as good as linear regression models (Denton 1995, Kuo and Reitsch 1996). The same data were used to train and test the RULES-3 induction algorithm. The test results and comparisons are given in table 2. Different quantization levels were defined for each attribute and the best set of rules was selected and employed. The aim of using RULES-3 was to test whether an expert system is suitable to use for the same task or not. The results showed that BPNN gives a better performance. It is easy to achieve the results using BPNN rather than Genetic Algorithms, because Genetic Algorithms require many simulations and much research to
WC-1
WC-2
WC-3
WC-4
achieve a result. The reason why four priority rules were used to train four different BPNNs was that these rules directly affect the performance measures. Each rule gives a different performance value for the same shop. These rules have different characteristics. For example, SPT rule reduces mean flow time while on the other side the EDD rule reduces mean tardiness. Therefore, they are considered in order to obtain the desired performance measures. In this study, the purpose of using priority rules is different from their classical purpose. They are used to find the equilibrium states of the performance measures rather than to minimize the performance measures. Another purpose of using four different BPNNs is that they can provide erroneous solutions. If any one of the BPNNs provides an undesired solution, then the erroneous BPNN is corrected by employing the BPNN that obtains the desired performance measures.
6. Suggested system In table 2, the characteristics of the BPNNs used are given. In this table, it is also reported that the success of BPNNs is very high, about 90%. Since the BPNNs are trained under different priority rules, they are consistent with each other. The system works as follows: F
T
Cmax
mu-1
mu-2
mu-3
mu-4
.
% nT
Figure 2. The structure of the BPNN used.
TRAINED NETWORKS P E R F O R M A N C E
EDD
SPT CR
FCFS
First, each of the expected performance measures from the system to be designed are applied to BPNN.
CRITERIA ERROR C O M P U T I N G
CRITERION - 1 .
CRITERION -2 . .
CRITERION . -3 . .
CRITERION-4
MEASURES
SIMULATION PROCESS
Figure 3. The system of manufacturing system design and determination of priority rule.
MANUFACTURING SYSTEM DESIGN AND PRIORITY RULE
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Trained networks Learning rate Momentum coefficient Iteration number Activation function Sample size in training set Learned sample in training set Number of test data to test trained network Network achievement rate Regression achievement rate RULES-3 Inductive Learning System
. .
SPT
EDD
CR
FCFS
0.40 0.70 4.000.000 Sigmoid 50 50 125 96.8% 12.0% 60%
0.40 0.70 4.200.000 Sigmoid 50 50 125 90.4% 24.0% 60%
0.44 0.66 5.000.000 Sigmoid 50 50 125 97.6% 44.0% 60%
0.40 0.70 4.500.000 Sigmoid 50 50 125 98.0% 26.4% 60%
As a result, the system will generate four different manufacturing system designs along the priority rules. These four different configurations obtained are tested with error analysis; therefore, the best design and priority rule are identified.
The performance measures given to BPNN as inputs are interrelated and proportional. They have their own equilibrium, which changes with the priority rule used. Since the performance measures reflect a firm’s operational strategy, the priority rules used are very important. BPNNs trained with certain performance measures may react strangely when a different performance measure is given. To prevent this, an auto-control mechanism should be built in. For this reason, BPNNs are trained for each priority rule so that they can work consistently. This also provides a synergy to the system. Assume that four different manufacturing system designs generated from BPNNs are simulated. In order to chose the best system the one which gives the smallest error is preferred. This will automatically avoid the alternative that has a very big error being considered. In this system, the important issue is not to minimize or maximize the value of performance measures, but to perform the performance criteria used to develop operational strategies consistent with the firm’s policies. There is no need to return from criteria to performance measures, because the system does not propose to change performance measures, merely to achieve the desired performance measures. When the performance criteria for the obtained solution are input to the system there will be no difference, because the system will produce the same solution. So, there is no need to do this. The detailed scheme of the system is illustrated in figure 3.
6.1. Performance criteria One of the elements of the system is to obtain the best answer. The criteria used for this purpose are given as follows. Criterion 1. Analyse all solutions. If there is any alternative to be corrected, consider other criteria to correct it, make all four alternatives available for evaluation and then choose the one with the least error. Criterion 2. If an alternative exists which has a big gap between machine usage rates, either increase or decrease the number of machines in that work cell by one. If this does not cause any change in other performance measures and the machine usage rate is at the desired level use this configuration otherwise use the original one. Criterion 3. If one of the alternatives is far different in terms of performance measures, employ this alternative with the configuration producing the least error. If the result is improved, then consider it. Criterion 4. If the error rates are so close, choose the performance measure whose value is the minimum (C¸akar 1997). On examination of the criteria, the following aims can be seen: .
.
Amongst the BPNNs’ alternative solutions, if any alternative solution don’t reach the desired performance measures, apply another BPNN’s available solution to obtain another useful alternative. If there is a difference between the machine usage rates, the number of machines should be increased or decreased to produce a better solution.
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Among the alternative solutions, the one with a minimum error rate should be chosen.
Thereafter, an error analysis should be carried out. It is not necessary to return to the beginning to give new performance measures to the trained networks, as doing so would merely incur the same operation being performed and time being wasted. However, the best alternative solution’s performance measures can be given to the system again and once this operation is carried out the system will produce the same solution.
6.2. Implementation For the proposed system, a software was developed in the language ‘Pascal’ and linked with the SIMAN. The software for this proposed system lists all the performance measures on the monitor and allows the user to enter their values. Based on the values entered, it provides four different solutions based on four different priority rules, using the BPNNs trained. In order to illustrate how it works, consider the following example: F = 419, T = 340, Cmax = 1625, mu 7 1 = 0.78, mu 7 2 = 0.52, mu 7 3 = 0.45, mu 7 4 = 0.98 and nT = 0.5, where mu-i is machine utilization rate of work centre i. Given the above values to the BPNN system, the program first generates the following design alternatives and priority rules in table 3.
Table 3.
1. 2. 3. 4.
Design Design Design Design
Next, considering the design suggested according to the performance criteria, the system tries to improve these alternatives. In the second design (with EDD), when considering the number of machines at work centre 1, it is clear that the machine usage rate is higher than the desired level. To overcome this extra usage, the number of machines is increased by one, from 2 to 3. After simulating this configuration, better results are obtained. On the other hand, when the third design is analysed, the machine usage rate at the second work centre is less than the desired level. To increase this rate, the number of machines is decreased from 5 to 4. When the system is re-simulated, better results are obtained compared with the previous ones. In the last design, the machine usage rate at the second work centre is observed and found to be higher than the desired level. Similarly, when the number of machines at this work centre increases from 2 to 3, an improvement is observed. After this analysis, four new and better system designs are obtained. The results from these four new designs are given in table 4. When the error rates for F, T and Cmax are defined as the ratio of the absolute difference between desired and obtained performance values divided by the desired performance value for machine usage rate and the percentage of the parts delayed, the error is defined as the absolute value of the difference from the desired performance level. In this modified version, the second (EDD), third (CR) and the last design (FCFS) solutions contain less error, and it should be noted that the number of machines for the first three designs become identical. If the designs generated are analysed according to performance values and the error percentages they possess, the information in tables 5 and 6 is obtained.
Design suggestions from the BPNNs.
WC-1
WC-2
WC-3
WC-4
Priority rules
3 2 3 3
4 4 5 2
5 5 5 5
1 1 1 1
SPT EDD CR FCFS
Table 4. New modified system design solutions.
1. 2. 3. 4.
Design Design Design Design
WC-1
WC-2
WC-3
WC-4
Priority rules
3 3 3 3
4 4 4 3
5 5 5 5
1 1 1 1
SPT EDD CR FCFS
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When machine utilization rate is considered, a change of number of the machines at some work centre is needed. Then, after performance criteria are applied to the suggested design alternatives, new modified design alternatives are obtained. When the output suggested by the system after applying performance criteria is analysed, the results in tables 7 and 8 are obtained.
According to the results shown in table 8, SPT, EDD and CR alternative designs have the same shop floor configuration. Although the FCFS alternative is different, it is close to other alternative designs. Therefore, the shop configurations of other designs should be applied to the FCFS design. After the application of the other configurations, it can be seen that the 3 4 5 1 alternative will perform better than the 3 3 5 1
Table 5. Performance measures and error rates of the raw design solutions Outputs of BPNNs and error analysis SPT Performance measures are given to trained networks
F T cmax MU1 MU2 MU3 MU4 NT
419 340 1625 0.78 0.52 0.45 0.98 0.50
3
4
EDD 5
Value
1 Error
419 340 1625 0.78 0.52 0.45 0.98 0.50
0.0% 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Table 6. Alternatives 1. 2. 3. 4.
2
4
CR
5
1
3
5
FCFS 5
1
3
3
5
Value
Error
Value
Error
Value
Error
605 467 1980 0.96 0.43 0.37 0.80 0.75
30.8% 27.3 17.9 18.0 9.0 0.0 0.0 25.0
601 373 1625 0.78 0.42 0.45 0.98 0.76
30.0% 8.9 0.0 0.0 10.0 0.0 0.0 26.0
601 373 1625 0.78 0.70 0.45 0.98 0.76
30.0% 8.9 0.0 0.0 18.0 0.0 0.0 26.0
The error indicators for the raw design solutions.
F-T-C errors (%)
Errors of MU and nt
Mean error (%)
0.0 25.33 12.96 12.96
0.0 10.04 7.2 8.8
0.0 16.0 9.36 10.36
Alternative Alternative Alternative Alternative
1
Table 7. Performance measures and error rates of the modified design solutions. Outputs of BPNNs and error analysis SPT Performance measures are given to trained networks
F T Cmax MU1 MU2 MU3 MU4 nT
419 340 1625 0.78 0.52 0.45 0.98 0.50
3 Value 419 340 1625 0.78 0.52 0.45 0.98 0.50
4
EDD 5
1 Error 0.0% 0.0 0.0 0.0 0.0 0.0 0.0 0.0
3
4
5
CR 1
3
4
FCFS 5
1
3
3
5
1
Value
Error
Value
Error
Value
Error
467 307 1625 0.78 0.52 0.45 0.98 0.67
10.3% 10.6 0.0 0.0 0.0 0.0 0.0 17
601 373 1625 0.78 0.52 0.45 0.98 0.76
30.0% 8.9 0.0 0.0 0.0 0.0 0.0 26
601 373 1625 0.78 0.70 0.45 0.98 0.76
30.0% 8.9 0.0 0.0 18.0 0.0 0.0 26
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ANNs for design of manufacturing systems alternative. When the final results suggested by the system are analysed, the results in tables 9 and 10 are obtained. When the results are analysed, it is concluded that the alternative with the least error is the 3 4 5 1 SPT alternative design. Accordingly, the number of machines and the priority rule that should be followed are identified. In this illustrative example, every shop configuration is similar. However, different configurations could be obtained. The main issue here is to apply different design alternatives each other before the final results are obtained. In this manner, many design alternatives can be generated and the more design alternatives that are generated, the better solution can be found.
Table 8. Alternatives 1. 2. 3. 4.
7. Conclusions A neural network is an efficient tool used in the modelling of highly nonlinear relations. For this reason, neural networks contains a very large application field in the design of manufacturing systems and the solution of manufacturing problems. Manufacturing system design by simulation is a trial and error process that is highly iterative and hence time-consuming. The proposed study is the inverse of the simulation study. In other words, in this system, given a set of desired performance measures, the neural network outputs a suitable manufacturing system design configuration. This system reaches a conclusion quicker than simulation approaches, it does not mean that the simulation
The error indicators for the modified design solutions.
F-T-C Errors (%)
Errors of MU and nt
Mean error (%)
0.0 6.96 12.96 12.96
0.0 3.4 5.20 8.80
0.0 4.73 8.11 10.36
Alternative Alternative Alternative Alternative
Table 9.
Performance measures and error rates of the final design solutions. Outputs of BPNNs and error analysis SPT
Performance measures are given to trained networks
F T cmax MU1 MU2 MU3 MU4 nT
419 340 1625 0.78 0.52 0.45 0.98 0.50
3
4
Value
EDD 5
1 Error
419 340 1625 0.78 0.52 0.45 0.98 0.50
0.0% 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Table 10. Alternatives 1. 2. 3. 4.
Alternative Alternative Alternative Alternative
3
4
5
CR 1
3
4
FCFS 5
1
3
4
5
1
Value
Error
Value
Error
Value
Error
467 307 1625 0.78 0.52 0.45 0.98 0.67
10.3% 10.6 0.0 0.0 0.0 0.0 0.0 17.0
601 373 1625 0.78 0.52 0.45 0.98 0.76
30.0% 8.9 0.0 0.0 0.0 0.0 0.0 26.0
550 332 1625 0.78 0.52 0.45 0.98 0.80
23.8% 2.35 0.0 0.0 0.0 0.0 0.0 30.0
The error indicators for the final design solutions.
F-T-C Errors (%)
Errors of MU and nt
Mean error (%)
0.0 6.96 12.96 8.71
0.0 3.4 5.20 6.0
0.0 4.73 8.11 7.01
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process is discarded, but the simulation process is used effectively with the Artificial Intelligence technique. The suggested system reaches the solution faster but the training time is longer. The proposed system also determines which priority rules can be used in the evaluation and these priority rules directly contribute to system performance measures. On the other hand the proposed solution can be considered as a composite system, having four trained BPNNs, where the risk of obtaining an unacceptable solution will decrease, since more than one trained BPNN has been used in parallel.
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