Long-term tool elimination planning for a wafer fab
Shu-Hsing Chung
*, Ming-Hsiu Hsieh
Department of Industrial Engineering and Management, National Chiao Tung University, 1001, Ta Hsueh Road, Hsinchu, Taiwan, ROC Received 5 October 2006; received in revised form 30 August 2007; accepted 17 September 2007
Available online 21 September 2007
Abstract
Wafer manufacturers must make decisions regarding tool elimination due to changes caused by demand, product mixes, and overseas fab capacity expansion. Such a problem is raised by leading semiconductor manufacturers in Taiwan. This paper is aimed at developing a sound mechanism for tool portfolio elimination based on determining which equipment can be pruned. In the proposed mechanism, product mix, wafer output, capital expenditure, tool utilization, protective capacity, and cycle time are taken into the overall evaluation. This paper develops an integer programming model to avoid trial-and-error and to obtain the optimal solution. Compared to the current industry approach, the results show that the proposed mechanism can effectively identify the correct tools for elimination with a large capital savings and little cycle time impact.
2007 Elsevier Ltd. All rights reserved.
Keywords: Tool portfolio; Capacity planning; Semiconductor
1. Introduction
Modern wafer fabrication facilities being built today by such companies as Motorola, Intel, and Advanced Micro Devices require excess of 1 billion dollars investment, chiefly due to the high cost of machinery and the need for a clean room (Bard, Srinivasan, & Tirupati, 1999). More than 60% of the total cost is attributed to the equipment alone. Making efficient use of equipment is therefore of great strategic importance, especially since profitability is determined by amortizing the cost of the facility over all chips produced (Bard et al., 1999). Thus, even a small improvement in the procurement decisions could have a large impact on the manufacturer’s performance (Swaminathan, 2000). Practical experience in this industry indicates that a small capacity saving could result in millions of dollars in benefit per year (Wang & Lin, 2002).
Both 200 and 300 mm wafer manufacturers, especially multi-fab foundries, must make decisions regarding tool elimination due to the dramatic and frequent changes in the internal and external manufacturing environ-ments. These changes often originate from demand, product mixes, and oversea fab capacity expansion. Such a problem is raised by leading manufacturers of semiconductors in Taiwan, who strongly require help in
0360-8352/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2007.09.009
* Corresponding author. Tel.: +886 3 5731 638; fax: +886 3 5722392.
E-mail addresses:shchung@mail.nctu.edu.tw(S.-H. Chung),emilhsieh.iem92g@nctu.edu.tw(M.-H. Hsieh). Computers & Industrial Engineering 54 (2008) 589–601
solving the tool elimination issue, making decision regarding tool disposal or transferring to support overseas fab capacity expansion.
As different equipment types and corresponding quantities are eliminated from a fab, different influences will result in both fab production performance and the company-wide capital expenditure, or fab cost struc-ture. This shows that poor tool elimination planning will lose cost competitiveness in the market and impact production performance, even if a fab implements sound scheduling plans and dispatching rules. Conse-quently, a sound mechanism that can evaluate the impacts of tool elimination is needed to provide more suit-able information for management decision making.
Tool portfolio planning is a very complex problem. Quickly obtaining the optimal solution is very difficult. Yang (2000)proposed a procedure and decision-making criteria to make capacity expansion plans for a
Tai-wan Semiconductor Manufacturing Company (TSMC) fab. Witte (1996), Wu, Yang, and Liao (1998), and
Chou and You (2001)pointed out that many planners in industry often use static models for tool portfolio planning due to fast computation and ease of use. Alternatively, most authors used heuristics or omitted some of the important characteristics to solve the complex and difficult problem in their researches.
Simulation, heuristic, queuing network, and combinations of these programs are common techniques used to solve the tool portfolio planning problem in the literature.Chou and Wu (2002) and Wu et al. (2005)made the comparisons of advantages and disadvantages between simulation and queuing network. Queuing models require a very short time to run and provide the flow time, utilization, and WIP performance information with modest accuracy (Bretthauer, 1996; Chou, 1999; Chou & You, 2001; Chou & Wu, 2002; Connors, Feigin, & Yao, 1996; Wu, Hsiung, & Hsu, 2005; Yoneda et al., 1992). Simulation is usually used to analyze operation dynamics at very detailed levels but needs much of an effort on construction and maintenance for evaluating many alternative portfolios. Hence, it is not suitable for the early stages of tool portfolio planning (Chen & Chen, 1996; Grewal, Bruska, Wulfm, & Robinson, 1998; Mollaghsemi & Evans, 1994). Besides, heuristic and combinations of these programs are used to consider more important characteristics and provide more information under different manufacturing environments and complexities (Bard et al., 1999; Chung & Hsieh, 2004; Donohue, Hopp, & Spearman, 2002; Iwata, Taji, & Tamura, 2003; Neacy et al., 1993; Swaminathan, 2000, 2002; Wang & Lin, 2002).
Table 1summarizes the recent literature on new tool portfolio planning, and makes a comparison of the methodologies used and characteristics considered in 23 reviewed papers. On-time delivery and cost are two critical factors in deciding competitiveness in the semiconductor industry, 14 out of the 23 papers use cycle time as the primary consideration and 15 out of 23 papers use budget for new tool planning. However, only 8 out of the 23 papers use cycle time and budget characteristics simultaneously.
The above literature review reveals that many studies focused only on the new tool portfolio planning. The literature on tool elimination research for fab factories is insufficient in model development, even though this is critical to the industry.
This paper is aimed at developing a mechanism for making decisions regarding the tool elimination in a semiconductor wafer fab. Taking into consideration the product mix variations and wafer output targets, the proposed elimination mechanism evaluates which equipment can be pruned according to core competitive elements in production management, namely, output, delivery, and cost. For more practical considerations, engineering, and layout issue factors are also presented in the proposed mechanism.
The rest of this paper is structured as follows. The following section presents an approach for tool portfolio elimination. Section3presents a numerical example based on the actual data collected from a wafer fabrica-tion factory situated in the Science-Based Industrial Park in Taiwan. Conclusions are made in Secfabrica-tion4. 2. A mechanism for tool portfolio elimination
2.1. Basic principle and overall flow
This problem is raised by leading manufacturers of semiconductors in Taiwan, who strongly require help in solving the tool elimination issue due to the dramatic decreases in low-end technology demand at existing 800 fab. At the same time, a new factory for producing low-end products is planned to setup in other country, it seeks for any possible tool sources from this existing factory in order to reasonable deployment of assets
among multi-sites. For example, the real case happens when transferring the equipments and products from the existing 800 fabs in Taiwan to the new oversea 800 fab in Mainland China.
To meet the changes in the new product mix and corresponding output target at existing 800 fab, it is very helpful for semiconductor industry to determine which equipment needs to be kept in the existed fab and which equipment can be pruned for disposal or be transferred to an oversea fab being under expansion. This paper focuses on evaluating which equipment can be pruned. The detail scheduling of each output target plan is not within the scope, since it is the next planning level after making the decision on eliminable number of machines. However, the impact on cycle time is considered because of tool elimination.
To solve this complex and difficult problem, this paper proposes a mechanism for tool portfolio elimination
based on the current fab’s output plan that suffered low-end technology demand decreases.Fig. 1shows the
flow chart for the tool elimination mechanism. In the proposed mechanism, practical issues, product mix, wafer output, capital expenditure, tool utilization, protective capacity, and cycle time are taken into consideration.
When solving the tool elimination problem, more practical factors must be considered than the new tool investment problem. Initially, the proposed mechanism evaluates the execution feasibility from practical aspects, including engineering, layout factors, etc., to avoid invalid final elimination results.
Because different product mix and wafer output target plan will result in different equipment types and cor-responding equipment quantities being eliminated, Step 1 is to input all the possible output plans based on the market department’s forecast, including every possible product mixes and corresponding monthly output tar-gets. Each output plan is generated from the viewpoint of aggregate level of hierarchical production planning
Table 1
A summary of the recent literature on new tool portfolio planning
Methodology Recent literature Major characteristics considered Queuing Network Simulated annealing Yoneda et al. (1992) Budget, WIP cost
Marginal allocation procedure
Connors et al. (1996) Cycle time, budget Branch & bound
algorithm
Bretthauer (1996) Budget Qualitative reasoning Chou (1999) Cycle time
Chou and You (2001) Cycle time, budget, throughput Utility function Chou and Wu (2002) Cycle time, budget, risk, throughput Genetic algorithm Wu et al. (2005) Cycle time, budget, demand uncertainty Heuristic Lagrangean relaxation,
GB, SB
Swaminathan (2000) Demand uncertainty, stock-out cost, budget Lagrangean relaxation,
GB, SB
Swaminathan (2002) Demand uncertainty, multi-period, stock-out cost, budget
Genetic algorithm Wang and Lin (2002) Profit, budget BBCT Chung and Hsieh (2004) Cycle time, utilization
Simulation STEP method Mollaghsemi and Evans
(1994)
Cycle time, utilization Response surface
methodology
Chen and Chen (1996) Cycle time, budget Static capacity Grewal et al. (1998) Cycle time, budget Heuristic & Simulation Neacy et al. (1993) Cycle time Heuristic & Queuing
Network
Simulated annealing Donohue et al. (2002) Cycle time
Bard et al. (1999) Cycle time, budget
Iwata et al. (2003) Cycle time, budget, production cost
Linear Programming Yang (2000) Space, photo tool capability
Hsieh and Lin (2002) Cycle time, profit, photo tool capability
Hua and Banerjee (2000) Cost, budget Stochastic Integer
Programming
Eppen et al. (1989) Demand uncertainty, profit, cost, risk
(HPP). The planning horizon is 3 years for observing the possible demand variations during the ramp-down period.
Photolithography machine, the most expensive tool with the longest procurement lead time, needs to be placed at the special clean room to process the most critical operation for wafer fabrication with the charac-teristics of the highest re-entry frequencies. Hence, photolithography workstation is often defined as a bottle-neck for the entire fab in industry and the literature (Shen & Leachman, 2003; Yang, 2000). In the proposed mechanism, the photolithography workstation is also defined as a bottleneck for the entire fab.
The process of wafer fabrication comprises a series of chemical treatments with the characteristic of re-entry, and no accessories are assembled during the processing. The structure differences between any two
Flow Characteristics
Considered
•Engineering issue •Layout
•2nd-hand tool price
•Protective capacity •Cycle time •Tool utilization •Capital expenditure •Cycle time •Product mix •Wafer output
Estimate the impact on cycle time when eliminate each machine unit in workstation i
Determine the eliminable set for output plan s with maximum
capital savings
Finalize eliminable tool list under all output plans Make primary feasibility evaluation from practical aspects
Reserve protective capacity on non-bottleneck workstation
s=1
s=s+1
Set product mixes and output targets with demand uncertainty
s=S ? Yes No Demand forecast
0
3
4
5
6
Requested tool list1
Determine the maximal eliminable quantity of photolithography workstations
2
•Product mix •Wafer output
product types (or product families) are presented in their process plans in aspect of different re-entry times of each product type on different workstations, daily throughput of each workstation, yield of each product type, and monthly different output of each product type. For both bottleneck and non-bottleneck workstations, this paper considers these factors in deriving the required processing time of each workstation for fulfilling the product mix and corresponding monthly output target.
For reserving enough bottleneck capacity to fulfill the fab’s output targets and product mixes set in the pre-vious step, Step 2 calculates the required quantity of photolithography workstation and makes an estimation of the maximal eliminable quantity of this workstation. This step also helps Step 3 calculate the capacity requirements of non-bottleneck workstations based on output rate of bottleneck.
Based on theory of constraint (TOC), non-bottleneck workstations should reserve some capacity to protect the system output under system uncertainties. The mechanism proposes that the output rate of non-photo workstation must be greater than that of photolithography workstations and primarily filters the candidates for elimination in Step 3.
Shorter cycle time can improve cash flow, promote customer satisfaction, and reduce the risk of yield losses. Hence, the proposed mechanism takes cycle time into consideration in Step 4 and identifies the impact on pro-duction cycle time when one unit of specific equipment is eliminated.
As different equipment types and corresponding equipment quantities are eliminated from a fab, both the cycle time performance and the company-wide capital expenditure will be different. Hence, a sound tool elim-ination plan will win cost competitiveness in market and can maintain good cycle time performance. An inte-ger programming model is developed to avoid trial-and-error effort in obtaining the optimal solution. Step 5 can effectively identify the eliminable set with a large capital savings and little cycle time impact. And the final step is to finalize eliminable tool list under all output plans being considered. Since the eliminated tool quantity proposed by the mechanism will be practically used for supporting the overseas fab or tool disposal decision-making in industry, this paper thus adopts the conservative way to ensure that the remaining capacity in each workstation should be enough to achieve each market demand scenario. Accordingly, the eliminable tool units are determined as the minimal eliminable number among all output plans. The detailed step-by-step descrip-tions are presented as follows.
2.2. Procedure of the tool elimination mechanism
Before describing the mechanism, all required notations are defined as below: Notations
qphoto, qi the original tool quantity for photolithography workstation and non-photo workstation i, respectively. i = 1, . . ., I
os,d the monthly output target for product d in output plan s. d = 1, . . ., D; s = 1, . . ., S
fd,photo, fd,i the re-entry times of product d for photolithography workstation and non-photo workstation i, respectively
td,photo, td,i the daily throughput of product d for photolithography workstation and non-photo workstation i, respectively
yd the yield of product d
aphoto, ai the tool availabilities for photolithography workstation and non-photo workstation i, respectively RCAPs,photo the required monthly processing time of photolithography workstation in output plan s.
RCAPs;photo¼PDd¼1os;d fd;photo td;photo yd
RCAPs,i the required monthly processing time of non-photo workstation i in output plan s.
RCAPs;i¼PDd¼1os;d fd;i td;i yd
SCAPs,photo the monthly available capacity of one photolithography machine. SCAPs,photo= aphoto· day-s_per_month
SCAPs,ithe monthly available capacity of one non-photo machine. SCAPs,i= ai· days_per_month
Ms,photothe tool quantity for photolithography workstation which can be eliminated in output plan s
Ms,i the tool quantity for non-photo workstation i which can be eliminated in output plan s
bx
dx
ye the least integer that is equal to or larger than x divided by y.
Step 0: Evaluate execution feasibility from practical aspects
If the candidate tool violates the following practical considerations, it will not be eliminated. • Check whether the path width is large enough to move out the old tool.
• Check whether the old tool can serve a new fab’s advanced technology products. Step 1: Set product mixes and output targets with demand uncertainty
Different product mix and wafer output target plan will result in different equipment types and correspond-ing equipment quantities becorrespond-ing eliminated. Since the demand uncertainty existed for a fab, Step 1 takes all possible output plans provided by the marketing department as the inputs, considering the product mix and output target variations. Each output plan needs to be reviewed through Step 2 to Step 5.
Step 2: Determine the maximal eliminable quantity of photolithography workstations
For reserving enough bottleneck capacity to fulfill the fab’s monthly output target and product mix set in the previous step, Step 2 calculates the maximal eliminable quantity of photolithography machines. This step also helps Step 3 calculate the capacity requirements of non-bottleneck workstations based on output rate of bottleneck.
The formula of the maximal eliminable quantity is as follows: Ms;photo¼ max qphoto
RCAPs;photo SCAPs;photo ;0 ð1Þ whereRCAPs;photo
SCAPs;photo is the required quantity of photolithography machines for fulfilling the monthly output target
and corresponding product mix. The maximal eliminable quantity of photolithography workstations can be obtained by subtracting the required quantity from original quantity (qphoto). And this maximal eliminable quantity is just an initial solution because it needs to be reviewed further by Step 3 to Step 6.
Step 3: Reserve protective capacity on non-bottleneck workstation
Based on theory of constraint (TOC), non-bottleneck workstations should reserve some capacity to protect the system output under system uncertainties. Hence, the mechanism proposes that the output rate of non-photo workstation must be greater than that of non-photolithography workstations for reserving some protective capacity on non-bottleneck workstations. And the formula is
ðqi Ms;iÞ SCAPs;i
RCAPs;iP
D d¼1os;d
>ðqphoto Ms;photoÞ SCAPs;photo RCAPs;photoP
D d¼1os;d
for all i6¼ photo ð2Þ
where the numerators, (qphoto Ms,photo)· SCAPs,photoand (qi Ms,i)· SCAPs,i, represent available monthly capacity for photolithography workstation and non-photo workstation i after eliminating Ms,photo and Ms,i units, respectively. The denominators, RCAPs;photoP
D
d¼1os;d and RCAPs;iP D
d¼1os;d, represent the required weighted average process time per wafer piece for photolithography workstation and non-photo workstation i, respectively. ðqiMs;iÞSCAPs;i
RCAPs;iP D d¼1os;d
is the output rate of non-photo workstation. ðqphotoMs;photoÞSCAPs;photo
RCAPs;photoP D d¼1os;d
is the output rate of photolithography workstations. The output rate is represented as number of wafer pieces per month. For easy calculation on the eliminable candidates of each non-bottleneck workstations i, the Eq.(2)can be re-organized as the following equation.
Ms;i ¼ max qiðqphoto Ms;photoÞ SCAPs;photo RCAPs;i RCAPs;photo SCAPs;i
;0
for all i6¼ photo ð3Þ
whereðqphotoMs;photoÞSCAPs;photoRCAPs;i
RCAPs;photoSCAPs;i is the required quantity of non-bottleneck workstation i for reserving
pro-tective capacity. M
s;i is the maximal tool quantity for workstation i which can be eliminated in output plan s. Once, the quantity for elimination, Ms;iis derived for every non-bottleneck workstation, go to Step 4. Step 4: Estimate the impact on cycle time when eliminate each machine unit in workstation i
Shorter cycle time can improve cash flow, promote customer satisfaction, and reduce the risk of yield losses. Hence, the mechanism for tool portfolio elimination also needs to take cycle time into consider-ation. It also needs to identify the impact on production cycle time when one unit of specific equipment is eliminated.
Based on simulation data from SEMATCH for a 0.5 lm manufacturing line and the actual
photolithogra-phy toolset data from two IBM Microelectronics manufacturing lines,Martin (1997)proposed a mathematical
relationship between the cycle time and tool utilization, named X-factor theory. Kishimoto, Ozawa,
Watan-abe, and Martin (2001)used manufacturing simulator ‘‘ManSim’’ to evaluate the manufacturing performance and modified the basic X-factor equation as follows.
xs;i¼ wcs;i rs;i ¼ 1þð1 aiÞ li liþ 1 wmi rs;i þð1 oaiÞ oqi oqiþ 1 omi rs;i ! 1 us;i 2 1 us;i ð4Þ xs;fab ¼ PI i¼1wcs;i PI i¼1rs;i ð5Þ us;i¼ PD
d¼1ðos;d fd;i td;i ydÞ li ai days=month ð6Þ rs;i¼ PD d¼1ðos;d rd;iÞ P d¼1os;d ð7Þ
where xs,idenotes the X-factor for workstation i in output plan s. xs,fabdenotes the overall fab line X-factor in output plan s. wcs,idenotes the cycle time of workstation i in output plan s. rs,idenotes the raw process time for workstation i in output plan s. wmidenotes the mean length of the time periods that machines in workstation i are offline and unavailable, such as for repair, preventive maintenance, etc., liis the residual number of ma-chines in workstation i available for specific processing sector. oai(0 < value < 1) is the availability ratio that any one operator i at a certain period is able to process material. omidenotes the mean length of the time peri-ods that the operator is not available for product processing operations. omiincludes the situation where no operator is available because of breaks, oqiis the total number of operators available for the specific worksta-tion i. us,i denotes the utilization rate of workstation i in output plan s.
Eq. (4)implies the following three meanings: (1) The utilization rate of a corresponding workstation will change when any machine is eliminated, because the equipment quantities will influence the utilization rate of the corresponding workstation. (2) The cycle time of each workstation will be changed whenever the uti-lization rate of each workstation is changed, because the raw process time of each workstation is assumed a constant value. (3) The cycle time of each workstation will have a significant increase when any machine with small equipment quantities, shorter process time, or low availability is eliminated.
Based on Eq.(4), the cycle time for workstation i can be estimated using:
wcs;i¼ 1þ ð1 aiÞ li liþ 1 wmi rs;i þð1 oaiÞ oqi oqiþ 1 omi rs;i ! 1 us;i 2 1 us;i rs;i ð8Þ
When the jth equipment of workstation i is eliminated in output plan s, the cycle time increase, Dwcs,i,j, is
Dwcs;i;j¼ wc0s;i;j wcs;i;j ð9Þ
where wc0
s;i;j is the cycle time of workstation i after the jth equipment of workstation i is eliminated in output plan s. wcs;i;jis the cycle time of workstation i before the jth equipment of workstation i is eliminated in output plan s.
Since the maximal eliminable tool quantity for each workstation, Ms;i, was obtained in Step 3, the impact on cycle time for each jth eliminable machine unit of workstation i, Dwcs,i,j, is easily derived by using the above
formulation. When the calculation of impact on cycle time for each eliminable equipment unit of workstation i is completed in output plan s, the next step is to go for the final optimal solution.
Step 5: Determine the eliminable set for output plan s with maximum capital savings
As different equipment types and corresponding equipment quantities are eliminated from a fab, both the cycle time performance and the company-wide capital expenditure will be different. Hence, a sound tool elim-ination plan will win cost competitiveness in market and can maintain good cycle time performance. The Step 5 is to put these candidates that are bolted for elimination in the last step into the integer programming model to obtain the final optimal solution. From a company’s financial point of view, the problem can be formulated as an integer program as follows:
A. Decision variables
Es,i,j the jth equipment of workstation i being eliminated in output plan s B. Input parametric data
pi capital expenditure for each machine in workstation i after deducting disassembly expenses
rs,i raw process time of workstation i in output plan s
xs original X-factor in the donated fab in output plan s
x0s upper-limit of X-factor in the donated fab in output plan s
Dwcs,i,j cycle time increase if the jth equipment unit of workstation i is eliminated in output plan s
Ms,i the maximal tool quantity for workstation i which can be eliminated in output plan s
C. IP model Maximize X I i¼1 XMs;i j¼1 Es;i;j pi ð10Þ Subject to ct 0 PI i¼1rs;i 6x0 s ð11Þ ct0¼ xs XI i¼1 rs;iþ XI i¼1 XMs;i j¼1 Es;i;j Dwcs;i;j ð12Þ
Es;i;1P Es;i;2P . . . P Es;i;Ms;i for all i ð13Þ
Es;i;j¼ 1 or 0 for all i; j ð14Þ
In the above formulation, Eq.(10)is the objective function to measure the total capital expenditure savings on tool procurement which can be contributed to the requested fab. Based on the formulation of tool planning presented byConnors et al. (1996), Eq.(10)also implies that the donated fab’s total equipment capital expen-diture is minimized after elimination due to MaxPIi¼1PMs;i
j¼1Es;i;j pi¼ Min PI
i¼1ðqi PMs;i
j¼1Es;i;jÞ pi. Eq.(11)restricts the overall fab line’s X-factor after eliminating tools from the donated fab to less than the upper-limit of X-factor.
Eq.(12)defines the overall fab line cycle time after eliminating tools is equal to the original overall fab line cycle time before tool elimination plus the total cycle time increases because of eliminated tools.
Eq.(13)ensures that equipment elimination occurs in sequence.
Eq.(14)restricts the decision variables to 0–1 variables. In addition, Es,i,j= 1 if the jthequipment of work-station i is eliminated, Es,i,j= 0 otherwise.
Based on the possible eliminate number of machines calculated by Step 0 to Step 3 and the impact on cycle time calculated by Step 4, the proposed IP model can derive the optimal tool elimination plan on the premise of satisfying X-factor limitation.
Step 6: Finalize eliminable tool list under all output plans
The final step repeatedly executes the above procedures from Step 2 to Step 5 for all output plans defined in Step 1. At the end of each repeat, the eliminable tool quantity of workstation i for each output plan s, Ns,i, is
identified as the largest j value which makes the corresponding Es,i,jvalue be positive. And, Nmaxi , the final eli-minable tool units of workstation i under all output plans is come out as the minimum of the elieli-minable num-ber among all output plans, e.g., Nmax
i ¼ MinfN1;i; N2;i; ; Ns;i; ; NS;ig.
3. Application example
To demonstrate how the proposed mechanism can be used in practice and obtain an optimal set of elimin-able tools, the actual data was collected from a leading wafer fabrication factory located in the Science-Based Industrial Park in Taiwan. The real case happened that transferring the equipments and products from the existing 800 fabs in Taiwan to the new oversea 800 fab in Mainland China. This factory strongly required help in solving the tool elimination issue due to the dramatic decreases in low-end technology demand at existing 800 fab. At the same time, a new factory for producing low-end products is planned to setup in Mainland China, it seeks for any possible tool sources from this existing factory in order to reasonable deployment of assets among multi-sites. Thus, a comparison will be made between the proposed mechanism and the current approach used in this leading wafer fabrication factory, including eliminable quantity, capital saving, X-fac-tor, etc.. The comparison results show that the fab production performance and the cost are much improved by the proposed mechanism.
In the application example, there are 83 kinds of workstations, in which 37 are batch workstations. The related tool information includes procurement price, tool quantity, availability, throughput, re-entry times, process time, etc. And the following example will state step-by-step how the proposed mechanism can be used in practice.
Based on the specific output plan showed inTable 2, Eq.(1)is applied to calculate the maximal eliminable quantity of photolithography workstation. The initial solution shows that there are 4 units of photolithogra-phy tools as candidates for tool elimination.
Subsequently, Eq.(3)is applied to reserve the enough protective capacity for non-bottleneck workstations. There are 71 machine units which are extracted from 53 workstations being selected as elimination candidates. The increases in cycle time were calculated individually when each of 71 tools was eliminated based on Eqs.(8) and (9).
In practice, the information related to candidates chosen for elimination is put into the integer program-ming model with cycle time performance and capital expenditure considerations. LINDO R6.01 was applied to solve the integer programming model. Considering output targets achievement, the final optimal solution shows that only 59 tools extracted from 46 workstations can be eliminated.
This leading wafer fabrication factory treats 85% utilization rate as the threshold for tool elimination with-out considering cycle time impact. That is, the equipment will be not eliminated if the workstation utilization reaches 85%. Detail of the practical tool elimination procedure can be found inAppendix A.Table 3makes a comparison between the current industry’s approach and the proposed mechanism in this paper. The results show that the company-wide capital expenditure and X-factor are much improved 17.19 M USD (18.2%) and 0.16 (7.6%) compared to the current industry’s approach, respectively. The benefits are so significant because the proposed mechanism can effectively determine the right eliminable tools with large capital savings and lit-tle cycle time impact. Correspondingly, the current industry’s approach eliminates the tools with cheap price and/or great impact, such as workstation 24, 25, 28, 29, 30, 32, 47, 64.
For further showing the benefits from the proposed mechanism, the more comparisons showed inTable 4
are made between the current industry’s approach and the proposed mechanism. The 6 different scenarios of capacity scales, namely, 120%, 100%, 80%, 60%, 40%, and 20% of wafer output of the above application exam-ple, are included. The reason for such a setting is that 120% of wafer output is nearing upper-limit of tool capacity and 0% of wafer output is meaningless. The results inFig. 2andTable 5show that the company-wide
Table 2
Monthly output plan and product mix (28 days/month, yield is assumed as 100%, s = 1)
Product (1) Product 1/logic (2) Product 2/memory (3) Output = (1) + (2)
capital expenditures are evidently improved 13.88 M USD (24.5%), 17.19 M USD (18.2%), 14.81 M USD (11.5%), 8.64 M USD (5.6%), 7.48 M USD (4.0%), and 7.48 M USD (3.6%) compared to the current
indus-try’s approach, respectively. And the results inFig. 3 and Table 5show that the X-factors are observably
improved 0.43 (17.8%), 0.16 (7.6%), 0.29 (13.1%), 0.07 (4%), 0.08 (4.6%), and 0.03 (2.6%) compared to the current industry’s approach, respectively. Hence, for each kind of different capacity scales, the proposed mechanism is showed to have larger capital savings and better X-factor performance.
Table 3
A comparison for capital saving and X-factor (Upper-limit of X-factor = 2.00)
Eliminable tool (1) Industry’s approach (2) Proposed mechanism (3) Benefits = (2) (1)
Quantity 60 U 59 U –
Capital saving (M USD) 94.46 111.65 17.19 (Improve 18.2%)
X-factor 2.11 1.95 0.16 (Improve 7.6%)
Table 4
Monthly output plan and product mix under variable capacity scales (28 days/month, yield is assumed as 100%)
Scenario Capacity scale (%) (1) Product 1 (2) Product 2 (3) Output = (1) + (2)
Case 1 120 9780 9780 19,560 Case 2 100 8150 8150 16,300 Case 3 80 6520 6520 13,040 Case 4 60 4890 4890 9780 Case 5 40 3260 3260 6520 Case 6 20 1630 1630 3260 Unit: Wafers/month.
Quantity (Industry's Approach) Quantity (Proposed Mechanism) Capital Saving (Industry's Approach) Capital Saving (Proposed Mechanism)
30.00 50.00 70.00 90.00 110.00 130.00 150.00 170.00 190.00 210.00 230.00
Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
Capit al S a v ing ( M US D) 35 45 55 65 75 85 95 105 115 125 Quantity
4. Conclusions
Both 200 and 300 mm wafer manufacturers must make decisions regarding tool elimination, due mainly to changes from demand, product mixes, and overseas fab capacity expansion. As different equipment types and corresponding equipment quantities are eliminated from a fab, different influences will result in both the fab production performance and the company-wide capital expenditure.
This paper proposed a mechanism for tool portfolio elimination that determines which equipment can be pruned, to provide sound information for management decision making. In the proposed mechanism, product mix, wafer output, capital expenditure, tool utilization, protective capacity, and cycle time are taken into con-sideration. An integer programming model was developed to eliminate trial-and-error in obtaining the optimal solution.
Compared to the current industry approach, the results show that the proposed mechanism can effectively determine the right eliminable tools with large capital savings and little cycle time impact. For future research, we can apply this method to solve midterm or short-term capacity planning, such as the tool shut-down plan-ning for preventive maintenance. A decision support model to identify the trade-off between protective capac-ity reservation and capital savings may also be established.
Table 5
Performance comparison among different capacity scales (Upper-limit of X-factor = 2.00)
Eliminable toolnCase Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
Quantity Industry’s approach 42 60 81 93 111 121
Proposed mechanism 38 59 81 97 113 123
Capital saving (M USD) (a) Industry’s approach 56.70 94.46 129.14 154.27 187.47 209.57 (b) Proposed mechanism 70.58 111.65 143.95 162.91 194.95 217.05 (c) Benefits = (b) (a) 13.88 17.19 14.81 8.64 7.48 7.48
X-factor (d) Industry’s approach 2.420 2.110 2.210 1.770 1.750 1.324
(e) Proposed mechanism 1.990 1.950 1.920 1.699 1.670 1.290 (f) Improved rate = ((d) (e))/(d) 17.8% 7.6% 13.1% 4% 4.6% 2.6%
2 2 2 2 2 2 2.42 2.11 2.21 1.77 1.75 1.32 1.29 1.67 1.70 1.92 1.95 1.99 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6
Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
X factor
Upper-limit Industry's Approach Proposed Mechanism
Case Case 1 Case 2 Case 3 Case 4 Case 5 Case 6
Upper-limit 2 2 2 2 2 2
Industry's Approach 2.42 2.11 2.21 1.77 1.75 1.32
Proposed Mechanism 1.99 1.95 1.92 1.70 1.67 1.29
Acknowledgements
The authors graciously acknowledge the great supports from Frank Kao, human resources director; Charles Hung, production planning director; Chen-Fu Chien, IE deputy director; and Tom Wu, capacity planning manager in Taiwan Semiconductor Manufacturing Company.
Appendix A. Practical tool elimination procedure
Step 1: Calculate the utilization rate of workstation i in output plan s. ui¼
PD
d¼1os;d fd;i td;i yd qi ai days=month
ð15Þ Step 2: Calculate the maximal tool quantity for workstation i which can be eliminated in output plan s.
This leading wafer fabrication factory treats 85% utilization rate as the threshold for tool elimination with-out considering cycle time impact. That is, the equipment will be not eliminated if the workstation utilization reaches 85%. And the maximal tool quantity for workstation i which can be eliminated in output plan s is
Ms;i ¼ max qi qi ui 0:85 l m ;0 n o ; if ui<85% ð16Þ Ms;i ¼ 0; if uiP85% ð17Þ References
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Shu-Hsing Chung is Professor of the Department of Industrial Engineering and Management, National Chiao Tung University, Taiwan, ROC. She received her Ph.D. degree in Industrial Engineering from Texas A&M University, College Station, TX, USA. Her research interests include production planning, scheduling, cycle time estimation, and performance evaluation. She has published and presented research papers in the areas of pro-duction planning and scheduling for IC manufacturing.
Ming-Hsiu Hsieh is a manager in the Department of Industrial Engineering, Taiwan Semiconductor Manufac-turing Company, and a Ph.D. candidate at the Department of Industrial Engineering and Management, National Chiao Tung University, Taiwan, ROC. He received his MS degree in industrial engineering and management from National Chiao Tung University. His research interests include capacity planning and production/operation management.
