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International Journal of Production
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A GA-based method to reduce material
handling: the case of TFT-LCD array
Fabs in Taiwan
Shian-Shyong Tseng ac , Fengming M. Chang b , Yian-Shu Chu a & Pi-Ju Chi a
a
Department of Computer Science , National Chiao Tung University , Hsinchu, Taiwan
b
Department of Information Management , National Taitung Junior College , Taitung, Taiwan
c
Department of Information Science and Applications , Asia University , Taichung, Taiwan
Published online: 09 Feb 2011.
To cite this article: Shian-Shyong Tseng , Fengming M. Chang , Yian-Shu Chu & Pi-Ju Chi (2011) A GA-based method to reduce material handling: the case of TFT-LCD array Fabs in Taiwan, International Journal of Production Research, 49:22, 6691-6711
To link to this article: http://dx.doi.org/10.1080/00207543.2010.495086
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Vol. 49, No. 22, 15 November 2011, 6691–6711
A GA-based method to reduce material handling: the case of
TFT-LCD array Fabs in Taiwan
Shian-Shyong Tsengac*, Fengming M. Changb
, Yian-Shu Chuaand Pi-Ju Chia
a
Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan;
b
Department of Information Management, National Taitung Junior College, Taitung, Taiwan;
c
Department of Information Science and Applications, Asia University, Taichung, Taiwan (Received 7 July 2009; final version received 23 April 2010)
This study proposes a genetic algorithm (GA)-based Material Handling Strategy Function (MHSF) method to increase the productivity of a TFT-LCD array fabrication to improve the traditional FIFO method in TFT-LCD fabrication by the reduction of the material handling for a Rail Guided Vehicle (RGV), because costs of material handling count up to about 50% of production costs. In this article, the MHSF is provided to help material handling commands choice, where a novel GA approach is used to adapt the weights of affecting factors in the function. Finally, to evaluate the performance of the proposed method, experiments using the data from a major TFT-LCD manufacturing plant in Taiwan have been carried out, and the results indicate that it can indeed reduce fabrication time and increase productivity.
Keywords: Material Handling Strategy Function, TFT-LCD, RGV, material handling, array process, productivity
1. Introduction
The way to decrease activities of material handling, waiting time, and material storage, are important issues to increasing productivity. In manufacturing, the largest percent of product cost is related to material handling (Yang et al. 2005). Material handling cannot add product value but does waste costs. Reducing lead times and costs become important factors for material handling in a Flexible Manufacturing System (FMS) (Kulak 2005). Material handling accounts for 30–75% of the total manufacturing cost, but a good design of a material handling system can reduce a plant’s costs by 15–30% (Kulak 2005). An automatic guided vehicle (AGV), including the rail guided vehicle (RGV) discussed in this study, is a way to reduce the cost of material handling. An AGV can be a buffer to decrease storage activities (Wu and Zhou 2007), and an efficient policy of AGV can decrease waiting time and material handling time. Hence, this study aimed to better the policy of RGV material handling by proposing a genetic algorithm-based Material Handling Strategy Function (MHSF) to decrease material handling time. Raw data from a major Thin Film Transistor Liquid Crystal Display (TFT-LCD) factory are offered as an example for MHSF.
TFT-LCD manufacturing is an important industry in Taiwan (Park et al. 2003, Hung 2006, Pan et al. 2007). It has become an important technology because it is widely used in *Corresponding author. Email: [email protected]
ISSN 0020–7543 print/ISSN 1366–588X online ß 2011 Taylor & Francis
http://dx.doi.org/10.1080/00207543.2010.495086 http://www.tandfonline.com
electric devices, such as cell phones, PDAs, computers, and TVs (Lu and Tsai 2004, Tsai and Hung 2005, Tsai et al. 2007, Huang et al. 2009). With a piece of glass substrate, TFT is a switch to control light and shade of each pixel on the LCD to reach color purposes. The fabrication of a TFT-LCD mainly consists of three processes: array, cell, and module processes (Lin et al. 2006). The array process, including the sub-processes of depot, photo, etch, and strip of glass substrates, creates TFT circuit. Several machines are put in an area for the array process and each machine in the array process can perform only one production operation. Each array process may need to perform the same operation more than once as a normal FMS does. Therefore, a lot of material handling work occurs among these machines in the array fabrication. As for the cell process, it only puts machines into a production line by combining colour filter and TFT panel, pouring liquid crystal into the panel, and cutting the LCD panel into the final product size without using any extra material handling facilities. The module process adds driver IC (integrated circuit) into the LCD panel and prepares to ship the final products only. Because machines for the array process are costly, high productivity in the array process can reduce fabrication cost, and a material handling strategy can influence the effectiveness of productivity. Therefore, how to design the array process is the key issue for all TFT-LCD manufacturers.
2. Preliminaries
In this study, GA-based MHSF is applied in the material handling strategy to increase the TFT-LCD fabrication performance. In this section, related works about material handling efficiencies, GA, and TFT-LCD fabrication performances are reviewed.
2.1 Material handling system
A material handling system which is used to transport parts, WIPs, and products within machines or storehouses plays an important role in a manufacturing system (Gabbert and Brown 1998, Dongmin et al. 2006). AGVs and RGVs which can load, unload, and transport materials automatically are the most often used facilities for material handling to save costs in a manufacturing system (Heragu 1997, Jawahar et al. 1998, Malmborg 2003, Berman et al. 2003, Wu and Zhou 2005). Gabbert and Brown (1998) pointed out that material handling and its relative overhead account for about 55% of product cost. Also, Asef-Vaziri et al. (2008) mentioned that 20–50% of the total production costs are for material handling. Therefore, it is very important to have an efficient method to reduce the cost of the material handling system. One previous research in 1994, by Lee et al. proposed a system modeled by Petri Nets to integrate AGV models for material handling and models for part processing into a single coherent model to reduce labor cost in a flexible manufacturing system (FMS) (Lee et al. 1994). In 2004, Wakabayashi et al. developed a high speed automated material handling system to shorten cycle time by one half or less with new concepts, hardware improvements, and new operation methods in a wafer process for the 300-mm fab (Wakabayashi et al. 2004). Later, Wu et al. (2007) showed that a robot or an AGV can be both a material handling device and a buffer. In their study, a resource-oriented Petri Nets (ROPN) was modeled and a new policy was proposed by treating robots as both material handling devices and buffers. At the same time, Nazzal et al. (2007) proposed an analytical approach to assess the expected time of an
automated material handling system for lots ready to move in a wafer fab, while Asef-Vaziri et al. (2008) invented an optimal model for the integrated design of the material flow path and the location of the pickup and delivery stations to reduce the material handling cost. Recently, Ventura et al. (2009) provided a dynamic programming algorithm to locate the idle AGV position and find out the optimal dwell point to minimise the maximum response time to improve the efficiency of an AGV system. In brief, AGV and RGV can decrease material handling cost, and a suitable strategy for AGV, and RGV can improve productivity.
2.2 Genetic algorithms
GA which was proposed by Holland (1975) is based on the natural evolution concept. It has been successfully applied in many NP-hard problems in many different areas (Miller et al. 1993). In GA, a chromosome represents a possible solution. With genetic operations, new generations are created. This process repeats again and again until the new generation solution cannot improve results. The genetic operations include encoding, evaluation (fitness), crossover, and mutation. An encoding transforms problems into binary digits to represent chromosomes in GA. The evaluation tests the fitness of the solution. The crossover and mutation are used to create new generations that are different from their parents (Miller et al. 1993). GA has often been used for FMS schedule or material handling strategy generation (Jawahar et al. 1998). For example, Jawahar et al. proposed a genetic algorithm based method to generate dynamic schedules in FMS (Jawahar et al. 1998). In addition, Liu et al. (2007) presented a genetic approach to a garment handling system strategy in 2007. Our study also applies GA using decimal fraction encoding chromosomes to generate material handling strategies in a TFT-LCD factory aimed at increasing fabrication productivity. In this study, due to seeking a group of suitable weights which are between 0 and 1 for our MHSF solution, decimal fraction encoding chromosomes are proposed and applied.
2.3 TFT-LCD
Although the process of production operations for a work-in-process (WIP) is fixed, the WIP may be moved in and out of the same machine more than once. Mainly, the material handling device used in a TFT-LCD factory is an RGV. In order to maximise the benefit of material handling, WIPs are grouped by a unit of ‘‘lot’’ containing 20 glass substrates to be fabricated and moved. Additionally, a factory may be divided into several working areas according to the different features of machines as shown in Figure 1. For example, there are nine machines, a stocker, and a material handling device in a working area as illustrated in Figure 2, where four machines are with the same machine type Ma and three machines are with the same machine type Mb.
For a given area, a lot may be moved in and out more than once, but each production process is not necessarily the same. For example in the working areas given in Figure 1, a kind of LCD production is moved through Area A five times:
Start ! S ! Að1Þ ! Bð1Þ ! Cð1Þ ! Að2Þ ! Bð2Þ ! Eð1Þ ! Að3Þ !Bð3Þ ! Cð2Þ ! ! Að4Þ ! ! Að5Þ ! ! End Where A(n) indicates the nth production process in Area A.
When a lot finishes a fabrication process in an area, it is moved to a stocker in the next area by a RGV. There are two rules for this lot in the next area:
. If the target machine for the next operation is idle, then the lot must be sent to this idle machine directly.
. Otherwise, the lot must be sent to the stocker for waiting.
Within a process of a lot, when an operation in a machine is finished, the following rules are applied:
. The lot should stay at the current machine and wait for the next machine available after finishing an operation if no other lot is waiting for the current machine. . The lot should be sent directly to the next desired machine if the machine is idle. . For all lots waiting for a specific machine in the stocker, the lot will be chosen by
the longest waiting time first rule, when the machine is available. Figure 1. Six working areas in a TFT-LCD array manufactory.
Figure 2. Nine machines, a stocker, and a RGV in a working area.
It should be noted here that all the movements of the lots are made according to the material handling commands, where a material handling command consists of the current position of a lot and the machine where the lot will be sent to. A RGV performs a material handling command by moving to the position of the lot, taking the lot to the RGV, carrying the lot to object position, and taking the lot to the object machine. It may take about 20–40 s to perform a material handling command, depending on the distance between the positions of RGV and machine.
As the RGV can only perform one material handling command listed in a command table at a time, how to choose a suitable material handling command from the table to maximise the system productivity or minimise the fabrication time becomes an interesting and challenging issue. Suppose two commands (1) Ma2!Mc1 and (2) Ma3!Stocker
can be chosen in the TFT-LCD fabrication, then Figures 3(a) and (b) illustrate different moving routes corresponding to the command order of (1) ! (2) and (2) ! (1), respectively. Hence, different command conditions may affect moving route and system productivity.
The command performance time RMt is a time period from the creation to the completion of a material handling command. It consists of two parts, one is the waiting time CWt, and the other is the real material handling time CMt.
2.4 TFT-LCD fabrication productivity
Since a variety of new generation production processes of TFT-LCD have been developed quickly in recent years (Park et al. 2003), how to increase the productivity of a TFT-LCD company becomes an important issue. To solve the above issue, some studies have improved the efficiency of the TFT-LCD industry. For example, Jeong et al. developed a scheduling system for a TFT-LCD assembly process to minimise the mean flow time and maximise the production progressiveness (Park et al. 2003). Shin and Leon (2004) improved the scheduling problem for the module process to improve the TFT-LCD manufacturing productivity. Toba (2005) presented a WIP estimation flow control method to solve the problem of controlling the maximum number of waiting lots in a limited buffer capacity in 2005. In the method, three features were used, including dividing the whole schedule into small lot schedules, reducing redundant blocking time, and WIP assessment for contiguous limited buffer scheduling. Afterwards, Lin et al. (2006) proposed a hierarchical planning and scheduling framework for a TFT-LCD assembly-to-order Figure 3. Different moving routes and system productivities due to different command orders.
production chain, which mainly concentrates on the scheduling for the array, cell, and module processes in the TFT-LCD production. In addition, Huang pointed out the following four factors which influence Taiwan’s TFT-LCD industry strategy in the competitive environment (Lin et al. 2006): government policy, human resources, capital investment, and bridging institution. Also Shin and Kang (2010) proposed a rework-based dispatching algorithm to improve the productivity for module process in TFT-LCD manufacture. Also, Chen et al. (2008) proffered a statistical process control (SPC) method to evaluate the LCD industry performance, while Hsieh (2008) proposed a method incorporating fuzzy adaptive resonance theory and a stepwise regression approach for the clustering analysis on the abnormal position defect status in TFT-LCD process to increase the production performance. Recently, Wang et al. (2008) analysed the RFID enabled supply chain in the TFT-LCD industry to decrease inventory cost. Their study indeed lowers the production cost from the view point of inventory.
3. Proposed method
In this section, the proposed GA-based MHSF method with an explanation for the real array fabrication processes in the factory is described. It consists of two novel approaches, one is the MHSF, and the other is an adapted GA method to find the optimal set of values of MHSF for material handling commands.
3.1 Simulator
As the manufacturing environment is very complex in the TFT-LCD array fabrication, many unexpected conditions may affect the system, and some experiment results cannot be gained easily. In order to evaluate the proposed method well, we use a simulator to simulate the fabrication process. In our simulation model, a lot is generated first, goes to area S for an initialisation process, and then goes into area A for fabrication. After finishing its fabrication process in area A, the lot goes to another area for the next process. After a period of time, this lot is coming back to area A again. All the conditions are given for the simulator, including the number of lots for fabrication every day, the number of production machines, time to operate a lot by each machine, the TFT-LCD fabrication process, and time intervals between two subsequent arrival times of a lot back and forth to area A which are gained from the real company records. Some other attributes are also given, such as the types of machines, distances between each machine, RGV speed, time for bringing a lot in to a RGV or out from a RGV, and time for the internal material handling within a stocker. Figure 4 represents the fabrication process from the viewpoint of area A. Stay in area S for s mins. for example, s = 20 Fabrication process in area non-A for (10+15) mins = 25 mins Generate n lots every day Simulate the fabrication process in area A Simulate the fabrication process in area A Fabrication process in area non-A for
20 mins
Generation S A(1) C (1) B(1) A(2) D(1) ...
Figure 4. The fabrication process from the viewpoint of area A.
For example, assume there are a total of two machines in area S and there are six lots to be processed by them. It takes 10 min to process two new lots in the generation process; 20 min are needed for every two lots in the initialisation process in area S as shown in Figure 4. Based upon the FIFO rule, these six lots begin their fabrication process in area A and their leaving time is shown in Table 1, where each lot is sent to area A twice. Since each lot takes at least 20 min the first time and at least 10 min the second time in area A, the real process time for each lot in area A is greater than or equal to above 20 or 10 min after adding the waiting time. Table 2 records the lots to be processed in area A during every 10 min, where LiðAðj ÞÞ means the jth time of lot i in area A. Figure 5 illustrates the time series by a Gantt chart.
Figure 5. The Gantt chart for six lots fabrication. Table 1. The leaving time of six lots in area A.
Lot Generation Area non A (20 min in S) Leaving time of Að1Þ Area non A (10 min in Cð1Þ, 15 min in Bð1Þ) Leaving time of Að2Þ L1 00:10 00:30 00:50 01:15 01:27 L2 00:10 00:30 00:52 01:17 01:29 L3 00:20 00:40 01:01 01:26 01:43 L4 00:20 00:40 01:06 01:31 01:46 L5 00:30 00:50 01:17 01:42 02:02 L6 00:30 00:50 01:20 01:45 02:10
Table 2. The lots to be processed in area A during each time period.
Time period Processes in area A
01:00–01:10 L3ðAð1ÞÞ, L4ðAð1ÞÞ, L5ðAð1ÞÞ, L6ðAð1ÞÞ 01:10–01:20 L1ðAð2ÞÞ, L2ðAð2ÞÞ, L5ðAð1ÞÞ, L6ðAð1ÞÞ
01:20–01:30 L1ðAð2ÞÞ, L2ðAð2ÞÞ, L3ðAð2ÞÞ, L4ðAð2ÞÞ, L6ðAð1ÞÞ 01:30–01:40 L3ðAð2ÞÞ, L4ðAð2ÞÞ, L5ðAð2ÞÞ
01:40–01:50 L4ðAð2ÞÞ, L5ðAð2ÞÞ, L6ðAð2ÞÞ
01:50–02:00 L5ðAð2ÞÞ, L6ðAð2ÞÞ
For a single lot i, let the jth process time in area A be Rtij, where i is the lot number. Hence the total fabrication time in area A for lot i shall be Rti¼Rti1þRti2þ . As illustrated in Figure 6, the amount of blue areas is the total fabrication time for lot 1 in area A.
In addition, fabrication time for a lot in area A each time Rtij includes machine operation time RPtj, waiting time RWtij, and material handling time RMtij. Therefore,
Rtij¼RPtjþRWtijþRMt i j
For every lot, the machine operation time RPtj are the same. The waiting time RWtij
can be divided into waiting for material handling time RWmhtij and waiting for machine
time RWmatij. Therefore, the variable fabrication time for a lot in area A each time R0tijis
defined as:
R0ti
j¼RWmhtijþRWmatijþRMtij:
3.2 Material handling strategy function f (MHSF)
As we have known, factors to affect productivity include the utility rates of machines, RGV, and stocker. A high utility rate of machines can reach high productivity. Low utility rates of either RGV or stocker can also have a high productivity. Therefore, high machine utility rate, low RGV and low stocker utility rates are our three material handling strategies. We use the following attributes in the proposed method:
LS Number of lots waiting for source machine which a WIP is moved
from.
MS Number of machines whose type is the same as the source machine.
TS Operation time of a source machine.
LO Number of lots waiting for object machine which a WIP is moved to.
MO Number of machines whose type is the same as the object machine.
TO Operation time of an object machine.
DRS Distance between a RGV and a source machine.
TI Time interval from the creation of the command.
Tw Time waiting for a stocker to be free.
Table 3 is an example of a command table with three commands. For each command, a material handling strategy function f is proposed to calculate its priority of execution in this study. The command with a higher f value has the higher priority will be chosen to perform first. This material handling strategy function is defined as:
fw1,w2,w3,w4,w5 ¼w1AttFromw2AttTow3AttRGVþw4AttLOTw5AttSTK, where
AttFrom Status of source machine from which a WIP is moved.
Figure 6. The fabrication time of lot 1 in area A.
AttTo Status of object machine to which a WIP is moved.
AttRGV Distance between a RGV and a source machine.
AttLOT Time interval from which a command is generated.
AttSTK Time waiting for a stocker to be free.
0 w1, w2, w3, w4, w51, w1þw2þw3þw4þw5¼1
AttFrom is the status of the source machine which a WIP is moved from. If a source
machine is busier, more WIP should be removed from it as soon as possible and w1 is
higher. On the contrary, AttTois the status of the object machine to which a WIP is moved
to and therefore, if an object machine is busy, it should not allow more WIP to be moved in, and w2has a negative impact to f. AttRGVis the distance between a RGV and a source
machine. When the distance is shorter, the efficiency is better. Hence w3 has a negative
sign. AttLOTrepresents the waiting time of a command to be executed once it is generated.
To reduce the waiting time, a command with a longer AttLOTis given a higher priority.
The last factor AttSTKis time waiting for a stocker to be free. Because only one stocker is
provided for a WIP, the weight w5 has a negative sign.
To balance the influence power of the above affecting factors, these affecting factors are normalised to be between 0 and 1 as the following:
AttFrom¼NormaliseFrom
LSTS MS , 0 AttFrom1 AttTo¼NormaliseTo LOTO MO , 0 AttTo1
AttRGV¼NormaliseRGVðDRSÞ, 0 AttRGV1
AttLOT¼NormaliseLOTðTIÞ, 0 AttLOT1
AttSTK¼NormaliseSTKðTWÞ, 0 AttSTK1
Since the variable fabrication time for a lot in area A consisting of waiting for material handling time RWmhtij, waiting for machine time RWmatij, and material handling
time RMti
j, our goal is to minimise the total time
Pn i¼1 Pv j¼1ðR0tijÞ ¼ Pn i¼1 Pv
j¼1ðRWmhtijþRWmatijþRMtijÞ, where n is the total number of lots sent to the
fabrication system, and v is the number of a lot moved into area A. Therefore, the purpose of this study is to find out a material handling strategy fw1,w2,w3,w4,w5 with a set of weight ðw1, w2, w3, w4, w5Þ to minimise Pn i¼1 Pv j¼1ðR 0ti
jÞ and get the best productivity for
fabrication process R in area A.
3.3 Methodology
Assume n lots are sent to a factory, and a material handling strategy fw1,w2,w3,w4,w5 can be formulated as a linear combination of AttFrom, AttTo, AttRGV, AttLOT, AttSTK. GA is applied
Table 3. Example of a command table.
Lot From To LS MS TS LO MO TO DRS TI Tw
1 L1 Ma1 STK 5 4 1800 0 0 0 9 80 0
2 L2 STK Ma2 0 1 0 5 4 1800 0 70 40
3 L3 Mb1 STK 4 2 300 0 1 0 12 65 0
for seeking the suitable weights ðw1, w2, w3, w4, w5Þto have the largest productivity. Each
time, the command that has the largest value of fw1,w2,w3,w4,w5 is chosen to be performed. (1) Encoding
When a research problem is going to be solved by GA, encoding is the first step. Among a variety of encoding methods, the selection of encoding depends on the problem style. The most common method is binary encoding, which gives every chromosome Boolean values of 0 and 1. Permutation, direct value, and tree encoding are also successful in some cases. However, this study proposed a new kind of decimal fractions encoding, where the vector of weights (w1, w2, w3, w4, w5) are treated as chromosomes, for
0 w1, w2, w3, w4, w51 and w1þw2þw3þw4þw5¼1 as illustrated in Figure 7.
(2) Fitness
Each chromosome has an associated objective function called the fitness. A good chromosome is the one that has low fabrication time Pni¼1Pvj¼1R0ti
j. The strength of a
chromosome is represented by its fitness value. Fitness values indicate which chromosomes are to be carried to the next generation. A set of chromosomes and associated fitness values are called the population. This population at a given stage of GA is referred to as a generation. As for different material handling strategies which are performed in the simulator of this study, the fitness function in the simulator can be used to find the minimum fabrication time Pni¼1Pvj¼1R0ti
j and the highest productivity. Since the
chromosome with a larger fitness value should have a higher possibility to the next generation in GA, we use inverse functionP 1
n i¼1 Pv j¼1R 0ti j to seek maxP 1 n i¼1 Pv j¼1R 0ti j for the chromosomes. When a chromosome is specified, e.g. w1, i ¼ 1, 2, . . . , 5, are known, the
simulator will be run to simulate TFT-LCD array factory and obtain the fabrication time Pn
i¼1
Pv
j¼1R0tij, and then calculate the fitness value of this chromosome.
(3) Crossover
In a genetic algorithm, crossover combines two parent chromosomes to produce a new offspring chromosome. If the new chromosome takes the best characteristics from each of the parents, it may be better than both of the parents. Some crossover types, include one-point, two-one-point, uniform, arithmetic, and heuristic.
Since this study proposed a new kind of decimal fractions encoding, the crossover method should be modified. We use arithmetic (convex) crossover as an example. For two parent material handling strategies, a float value between 0 and 1 is generated randomly, where the new ith weights wiis the convex combination of the ith weights wiin two parent
strategies (chromosomes). Figure 8 explains the arithmetic (convex) crossover process in our GA.
(4) Mutation
Mutation operator alters one or more values in a chromosome from its original values. Mutation is an important part of the genetic search to help get better results. There are several types of mutation, including flip bit, boundary, non-uniform, uniform, and Gaussian. Different from the traditional GA mutation method of using 0 and 1 to control Figure 7. An example of a chromosome of GA in this study.
mutation, this study generates a new value between 0 and 1 for a randomly chosen weight. To assure w1þw2þw3þw4þw5¼1, all five weights in the strategy have to be
nor-malised by wi,normalized¼wi=ðw1þw2þw3þw4þw5Þas illustrated in Figure 9.
Our GA proceeds as follows: Genetic Algorithm()
Begin Initialise population; while (not terminal condition) do Begin
choose parents from population; /* Selection */
construct and normalise off_spring by combining parents;/* Crossover */ mutate and normalise off_spring; /* Mutation */
if suited (off_spring) then replace worst (population) with better off_spring; End;
End.
4. Computational results
To evaluate the performance of our methods, we have carried out experiments using the historical data of Chunghwa Picture Tubes Company, including the fabrication process, object working area features, other working areas features, machine operation time, and the way to send lots for fabrication. As mentioned above, this TFT-LCD factory is divided into six areas: S, A, B, C, D, and E. To simplify our discussion, only area A is used as an example for the proposed method. The interval between two subsequent entries of area A is defined according to the average time from the historical records. All fabrication processes through different areas are shown in Figure 10.
Where S is a process to initiate a new lot and the related information of area A is listed in Table 4.
4.1 Methodology
As mentioned before, it takes 20 min (1200 s) to initiate a lot for each machine in S area. In a real factory, the number of lots to be processed varies for each hour, each day,
0.1 0.5 0.2 0.1 0.1 0.2 0.3 0.05 0.05 0.4 0.12 0.46 0.17 0.09 0.16 X X + 0.8 1-0.8
Figure 8. An example of arithmetic (convex) crossover process in our GA.
Figure 9. An example of the process of mutation in our GA.
each week, and each month. Hence, we use the current FIFO material handling command choosing strategy for our simulator to seek the relation between number of lots generated and productivity. At the beginning, there is no lot in the system and the utility ratio is low. To avoid the bias of the data, we calculate the productivity from the second day. For the given different number of lots, the FIFO strategy using w1¼0, w2¼0, w3¼0, w4¼1,
and w5¼0 can be described as:
fw1,w2,w3,w4,w5¼0 AttFrom0 AttTo0 AttRGVþ1 AttLOT0 AttSTK Figure 11 shows time for material handling, time for waiting for material handling, time for waiting for machines, and variable fabrication time. As you can see both time waiting for material handling and waiting for machines increases when the number of lots increases. However, there is only a little increase in time waiting for material handling. Hence, time waiting for machines significantly influences the variable fabrication time. The variable fabrication time rises sharply at the number of lots approaches 62, 69, and 74. Before the previously mentioned numbers, the variable fabrication time stays almost the same. Hence, such certain numbers are sought because they have the largest number of lots in the same level of variable fabrication time.
Figure 12 plots the utility rate of four kinds of machines, RGV, and the stocker, where Ma and Mb have higher utility rates which can not be increased even if the number of lots is greater than 69. As mentioned above, 62, 69, and 74 are the suitable lot numbers for generation, because generating 69 lots has a higher machine utility rate and a lower RGV utility rate than generating 74 lots. Therefore, we generated 69 lots for further experiments in the system.
Table 4. The related information of area A.
Item Content
Type of machine Ma, Mb, Mc, Md
Number of each type of machine Ma: 4 (Ma01, Ma02, Ma03, Ma04)
Mb: 3 (Mb01, Mb02, Mb03) Mc: 1 (Mc01)
Md: 1 (Md01)
Operation time for machines Ma: 540 s
Mb: 400 s Mc: 300 s Md: 80 s
Distance between two adjoined machines 3 m
RGV speed 1 m/s
Time for a RGV takes a lot 8 s
Material handling time within a stocker 40 s
→ (11200 sec in C(2), B(5)) → A(5)
→ (10400 sec in D(1), B(3)) → A(3) → (13800 sec in E(1), B(4)) → A(4)
Generation → S → (8200 sec in B(1)) → A(1) → (13500 sec in C(1), B (2)) → A(2)
Figure 10. The processes of a TFT-LCD array fabrication.
4.2 Finding the weights of MHSF
In our experiment, 69 lots are generated in the manufacturing system, and the proposed method based on GA is applied to seek the best set of weights for the material handling strategy function. Population size is set as 100. The first population is generated randomly, crossover rate is 0.9, and mutation rate is 0.05. Many kinds of crossover methods are proposed, such as one-point, two-point, uniform, and arithmetic (convex) methods. The Arithmetic crossover method was used in this study. When the productivity stayed the
0 1000000 2000000 3000000 4000000 5000000 6000000 7000000 8000000 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 Time (second) Lots
Time for waiting for material handling Time for waiting for machine
Time for material handling Variable fabrication time
Figure 11. The fabrication time for different number of lots.
The analysis of utility rate
Ma Mb Mc Md RGV Stocker 0 20 40 60 80 100 120 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 Lots U ti lit y r a te ( % ) Ma Mb Mc Md RGV Stocker
Figure 12. The analysis of utility rate.
same after 50 generations, GA is converged and reduces the fabrication time. In Figure 13, the average fabrication time decreases very quickly and reaches around 500,000 s after the fifth generation in GA. In Figure 14, the lowest fabrication time value is gained after the 15th generation. Therefore, the proposed method can find the best solution quickly by the following best MHSF:
fw1,w2,w3,w4,w5¼0:064456AttFrom0:415093AttTo0:185991AttRGV þ0:039848AttLOT0:294612AttSTK
The lowest fabrication time for each generation
200000 220000 240000 260000 280000 300000 320000 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 Generation Low e r f a b ricat io n t im e ( s ec o n d )
Figure 14. The lowest fabrication time for each generation. Average fabrication time
0 200000 400000 600000 800000 1000000 1200000 1400000 1600000 1800000 Generation
Average fabrication time (second)
0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63
Figure 13. Average fabrication time for each generation.
It can be easily seen that w2has the largest absolute value, or the most important item
is AttTo. It means that when the next machine is busy, a material handling command has
a low possibility of being chosen, and the lot has to wait in the current machine. The lot also has a greater opportunity to be sent directly to the next machine in order to reduce the number of material handling commands required. In our experiment, there were 86.7% of commands directly sent for this set of weights in the system.
A comparison of the productivity of several methods using status data in Table 4, including HSMFS, LOMFS, FEEFS, FIFO, LTWSFS, and the proposed methods, is illustrated in Figure 15. The results indicate that the proposed method reached the best solution comparing with other methods.
4.3 Comparison with different number of lots generated
To seek the optimal weight set, the proposed method with 20 generations has been applied to different numbers of lots. In Figure 16, it is clear that when the number of lots increases, the total fabrication time increases. When the lot number is greater than 74, fabrication time and time difference increase greatly, where time difference is the distance between the largest and the smallest fabrication times. It indicates that the lot numbers from 71 to 74 have better results.
4.4 Further comparison in dynamic status
In some fabrication processes such as, wafer fabrication, the production process and machine operation status may affect the productivity. In order to evaluate the performance of the proposed method, two experiments have been done under different dynamic status. In the first experiment, four different processes were used to test the Figure 15. The comparison of the lowest time for product of several methods.
proposed method, and a machine break-down record of a real company was used in the other experiment.
(1) Using four different process statuses
Table 5 shows the statuses of four different processes of the TFT-LCD to check the proposed method, where Process 1 is the original process and Processes 2 to 4 are new processes. In the three new processes, machine operation time, stocker size, and time for a lot in a non-A area is reset. Productivities in different processes by HSMFS, LOMFS, FEEFS, FIFO, LTWSFS, and proposed methods are compared in Table 6. Still, the proposed GA method has the best productivity.
(2) Machines break-down data
In this subsection, a manufacturing data with machine break-down record is used to test the dynamic status for the proposed method. Using process 1, everything ran well on the first day. The status on the first day was recorded as status 1. On the second day, Figure 16. The minimal fabrication time for different lot numbers.
Table 5. The statuses of four processes.
Process 1 Process 2 Process 3 Process 4
Non-A(1) 8200 12,500 10,000 13,500 Non-A(2) 13,500 14,200 12,500 14,000 Non-A(3) 10,400 10,400 12,000 10,000 Non-A(4) 13,800 14,200 15,000 13,500 Non-A(5) 11,200 10,400 11,200 13,000 Ma 540 560 520 580 Mb 400 380 400 350 Mc 300 250 320 280 Md 80 60 80 100 Stocker 40 80 80 50
Optimal lot number by FIFO 69 70 67 75
Table 6. The comparison of four processes. HSMFS LOMFS FEFS FIFO LTWSFS (Heavy Source Machine First Service) (Light Object Machine First Service) (First Encounter First Service) (First In First Out) (Less Time Waiting for Stocker First Service The best strategy found by GA Process 1 Time for waiting for material handling (RW mh t i)j 389,979 187,644 226,088 145,870 237,747 569,82 Time for waiting for machine (RW ma t i)j 3,646,081 179,3020 1,631,759 709,639 166,3928 809,93 Time for material handling (RMt i)j 137,700 116,720 116,346 100,069 118,897 72,437 Variable fabrication time (R 0t i)j 4,173,760 2,097,384 1,974,193 955,578 2,020,572 210,412 Process 2 Time for waiting for material handling (RW mh t i)j 534,917 138,188 249,719 192,123 144,914 42,692 Time for waiting for machine (RW ma t i)j 7,657,363 496,348 1,533,672 506,433 344,900 13,649 Time for material handling (RMt i)j 152,106 99,498 120,537 105,879 102,818 78,998 Variable fabrication time (R 0t i)j 8,344,386 734,034 1,903,928 804,435 592,632 135,339 Process 3 Time for waiting for material handling (RW mh t i)j 346,467 169,747 180,093 156,749 106,768 63,070 Time for waiting for machine (RW ma t i)j 2,678,492 512,485 1,510,071 589,455 1,040,596 154,753 Time for material handling (RMt i)j 128,834 104,947 109,519 105,147 93,279 82,413 Variable fabrication time (R 0t i)j 3,153,793 787,179 1,799,683 851,351 1,240,643 300,236 Process 4 Time for waiting for material handling (RW mh t i)j 542,804 218,793 295,349 156,729 147,501 73,895 Time for waiting for machine (RW ma t i)j 11,488,346 2,591,821 4,636,849 907,298 1,268,945 263,086 Time for material handling (RMt i)j 161,870 126,307 135,335 109,054 111,471 92,764 Variable fabrication time (R 0t i)j 12,193,020 2,936,921 5,067,533 1,173,081 1,527,917 429,745
machine Ma030 broke down at 09:38:52 in the morning. The manufacturing status was recorded as status 2 in Table 7. At 14:03:24 pm, machine Ma030 was repaired and the manufacturing system was restored to status 1. Unfortunately, at 21:46:37, machine Mb010 broke down and the status became status 3 until 23:32:46.
With the three different statuses described above, five weight values were calculated by the proposed GA based MHSF method as listed in Table 7. According to the comparison of the productivities in different statuses shown in Table 8, the result of the proposed method is the best among the others.
4.5 Comparison of crossover method
Many kinds of crossover methods are proposed. Many factors including different crossover methods, problems, and encoding should affect the performance of GA. In this subsection, the performances of four crossover methods, including one-point, two-point, uniform, and arithmetic (convex) are compared for our proposed method. Each method runs 10 times and the learning time is recorded. The population size is 100, and crossover rate is 0.9. The results are shown in Table 9 and it indicates that the arithmetic (convex) Table 8. The comparison of different material handling methods for the dynamic status.
HSMFS LOMFS FEFS FIFO LTWSFS
(Heavy Source Machine First Service) (Light Object Machine First Service) (First Encounter First Service) (First In First Out) (Less Time Waiting for Stocker First Service The best strategy found by GA Time for waiting
for material handling
445,573 122,517 225,697 159,919 280,995 105,328
Time for waiting for machine
4,401,321 500,722 1,695,013 758,641 2,448,219 441,542
Time for material handling
147,432 100,571 119,854 103,372 125,047 95,566
Variable fabrica-tion time
4,994,326 723,810 2,040,564 1,021,932 2,854,261 642,436
Table 7. The weights calculated by the proposed method in different statuses.
Status 1 Status 2 Status 3
w1 0.06445612 0.33125799 0.16933685
w2 0.41509296 0.22320731 0.31999321
w3 0.18599089 0.16698497 0.20771212
w4 0.03984787 0.27662127 0.30160091
w5 0.29461216 0.00192846 0.00135691
crossover method has the lowest running time and the best performance in all 10 of the experiments. Therefore, all our experiments for the proposed method apply the arithmetic crossover method.
5. Conclusions
The competition in TFT-LCD industry is extremely intense. To increase fabrication productivity, this study proposes a MHSF which is based on GA to find out the best strategy for reducing material handling and waiting time in the array process of a TFT-LCD factory. A MHSF consists of five affecting factors in the fabrication. In the GA based method, the encoding, crossover and mutation operations have been designed specifically for the five affecting factors. After the optimal set of weights are found, the corresponding optimal strategy can be used to calculate the function value for each material handling command and the command which has the highest value will be performed first. From the results, it is clear that the busy status of the object machine in the fabrication process has a high degree of influence on productivity. A better material handling strategy function reduces the utility of the RGA and the stocker. Comparing to the FIFO strategy, the proposed method can save 86% of material handling and lot waiting time. For the case in the experiments, lot numbers 71 to 74 are sought to reach higher productivity. In brief, the proposed material handling strategy function indeed raises the TFT-LCD fabrication productivity.
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