An integrated plant capacity and production model with economies of scales
3.4 Case study
A numerical example of T-company, which specializes in wafer foundry in the semiconductor industry and has its headquarters in Taiwan, is used herein to demonstrate the application of the proposed models. The final product of T-company are dies, which represents the starting form of an integrated circuit (IC) and can be produced in either 12-inch, 8-inch or 6-inch wafers. Because some of T-company’s operating costs and customer demand data are unavailable, the annual report data in Taiwan Semiconductor Manufacturing Company (TSMC) (2004) were employed to estimate them. Regarding customer demand, T-company has customers from six major areas, North America, Taiwan, Europe, Japan, Korea and Hong Kong, and the monthly customer demand for dies for the coming year totals approximately 2×108 dies. The demands from these customers in six areas are 6.4×107, 5.7×107, 3.6×107,3.2×107,
106
4 .
8 × , and 7.5×106 dies, respectively. The sizes produced in the manufacturing plants include 12-inch, 8-inch and 6-inch wafer fabrications (FABs), and they produce an average of 40000, 35000 and 30000 pieces per month, respectively. Note that each size of FAB can only produce its particular size of wafers due to the complexity of the technology employed in the manufacturing process of wafers. One piece of 12-inch wafer is 2.25 times the square area of an 8-inch wafer; and 4 times that of a 6-inch wafer.
Regardless of the yield, the number of dies produced by one piece of 12-inch, 8-inch and 6-inch wafer are 1233, 514, and 210, respectively, based on the 0.11 mµ process technology. To unify, the capacities of 12-inch, 8-inch and 6-inch FABs are revised based on the number of dies produced by one piece of wafer, that is 4.9×107,
107
8 .
1 × and 6.3×106 dies, respectively. Therefore, constructing a 12-inch FAB is more beneficial for satisfying customer demand in terms of dies as compared with the other two sizes of FABs.
T-company operates five manufacturing plants, which are located at different regions, namely, Taiwan (Hsinchu), Taiwan (Tainan), Shanghai, USA and Singapore.
The capital cost per month for different-size FABs can be estimated by the total costs for the FAB construction plus equipment set-up and the maximum usage period of the FAB. The data on the capital cost and the variable production costs for different-size FABs for manufacturing plants in different regions are listed in Table 3.1.
As shown in Table 3.1, the capital and the variable production costs for different-size FABs for some manufacturing plants, i.e. USA and Singapore are higher than in others, because of higher commodity price indexes in these regions. Moreover, the costs for T-company to operate a 12-inch FAB is higher than the other two sizes, due to the high capital and variable production costs as shown in Table 3.1. Considering the final products of T-company are dies, the average production cost per unit product of manufacturing plant nkˆ as shown in Eq. (3.7), can be further revised in terms of dies,
u represents the number of dies that one piece of wafer produces when the size FAB for manufacturing plant nkˆ, are
nk
F ˆ, and =
nk
F ˆ 6-inch, 8-inch and 12-inch, respectively. For example, if T-company decides to operate a 12-inch FAB in the USA, then u(12USA)=1,233. Taking the base production parameters of Taiwan (Hsinchu) as an example, the relationship between the average production cost per die and the production amount for different-size FABs can be further explored, and is shown in Figure 3.4.
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8
0 50 100 150 200 250 300 350 400 450
production amount (105 dies)
average production cost per die
6-inch 8-inch 12-inch
Figure 3.4 Average production cost per die vs. production amount
As shown in Figure 3.4, the average production cost per die for different-size FABs decreases as the production amount increases, but at different rates. The average production cost decreases at an increasing rate when the production amount is rather small; however, as the production becomes larger, the average production cost exhibits a constant number. In addition, all different-size FABs are characterized as having a high production cost due to a low capacity utilization when the production amount is small, such as less than 5×106 dies. However, the average production cost per die of a 12-inch FAB is the highest when the least capacity utilization is combined with the most expensive capital cost. Figure 3.4 also shows that there is an advantage of an 8-inch FAB over a 6-inch FAB when the production amount exceeds 3×106 dies.
Even though the curve representing the average production cost per die of a 12-inch FAB lies above those of the 6-inch and 8-inch FABs as shown in Figure 3.4, the 6-inch and 8-inch FABs cannot satisfy the market due to capacity constraints when the demand exceeds 6.3×106 and 1.8×107 dies, respectively. Furthermore, as the production amount of a 12-inch FAB approaches its full-capacity, a 12-inch FAB yields the lowest cost among all those with full-capacity production, implying there are economies of scale in the wafer foundry industry.
The main raw materials for producing wafers include silicon wafers, chemical source, photoresist and specialty gases (TSMC, 2004). To simplify the study, chemicals are selected as a raw material in this study. The amount of chemicals required to produce one piece of 6-inch, 8-inch and 12-inch wafers can be estimated as 0.585, 0.475 and 0.450 liters (L), respectively. Considering the difference in the amount of chemical resource required in producing one piece of different size wafers, then the total amount of chemical source required by manufacturing plant nkˆ can be
further revised as
k
k n
k n
k F f
wˆ−1,ˆ( ˆ) ˆ , where ˆ1,ˆ( ˆ)
nk
k
k F
w − represents the amount of chemical source required to produce one piece of wafer when the size FAB for manufacturing plant nkˆ is
nk
F ˆ. There are four chemical source vendors in the market, namely, Merck, Chem Sources (CS), Tai-Young High Tech (TY), and Chemical Sources International (CSI), and both Merck and TY have plant sites in Taiwan, while CS and CSI are located in the USA. Table 3.2 shows the initial values of the base procurement parameters.
Table 3.1 The alternative sizes of FAB and base production parameters for manufacturing plants
6 inch 8 inch 12 inch
Manufacturing
plant, nkˆ Capital cost (103 US$)
Variable production cost
(US$/wafer) Capital cost (103 US$)
Variable production cost
(US$/wafer) Capital cost (103 US$)
Variable production cost
(US$/wafer)
Taiwan
(Hsinchu) 1865 205 3000 323 10000 515
Taiwan
(Tainan) 1850 204 2978 321 9900 513
Shanghai 1900 208 3005 327 10032 520
USA 2100 212 3085 335 10090 523
Singapore 2030 215 3078 335 10065 525
Table 3.2 The initial values of base procurement parameters
Chemical source vendor, n kˆ−1
Fixed cost,
ˆ−1
nk
V (US$)
Unit chemical source purchase cost,
ˆ −1
nk
p (US
$/L)
Maximum amount supplied,
ˆ−1
nk
S (L)
Merck 53 5.50 40000
CS 98 5.55 45000
TY 82 5.51 37500
CSI 112 5.49 41000
Table 3.3(a) The transportation cost per kg between chemical source vendors and manufacturing plants
Chemical sources vendor, n kˆ−1
Manufacturing plant, nkˆ Merck CS TY CSI
Taiwan (Hsinchu) 2.8 6.1 2.8 4.9
Taiwan (Tainan) 2.9 6.2 3.0 4.4
Shanghai 4.1 6.6 4.5 5.5
USA 3.5 4.3 4.4 4.9
Singapore 5.5 5.1 5.0 5.1
Unit: US$/kg
Table 3.3(b) The transportation cost per kg between manufacturing plants and customers
in six areas.
Manufacturing plant, nkˆ Customer in
different areas,
n s Taiwan
(Hsinchu)
Taiwan (Tainan)
Shanghai USA Singapore
North America 5.5 5.8 6.4 3.2 6.0
Taiwan 2.6 2.7 2.9 6.2 3.4 Europe 6.1 6.2 6.3 4.5 6.0 Japan 3.3 3.3 3.9 4.8 4.3 Korea 3.2 3.3 4.0 4.7 4.4
Hong Kong 2.9 3.0 2.7 5.0 4.0
Unit: US$/kg
This study further assumes that the transportation cost per unit flow shipped is measured based on the weight and distance. The weight of one die after packaging can be approximately estimated as weighing 300 milligrams (mg), i.e. 3×10−4 kilograms (kg). According to the Taiwan Institute of Economic Research (TIER) (2004), the average transportation charges per kg are approximately US$ 2.8 to US$ 4. The transportation cost per kg between two locations can be further estimated by unit-distance transportation cost per kg and the distance between them, and the difference in unit-distance transportation cost between two locations is due to the transportation mode employed. Tables 3.3(a) and (b) show the transportation cost per kg between chemical source vendors and manufacturing plants, and between manufacturing plants and customers in six areas, respectively.
The model is programmed using Visual C++, a computer-modeling program developed by Microsoft, based on the developed heuristic algorithm. Tables 4-6 summarize the initial solution results.
In the case study, since Taiwan’s government provided incentives for developing high-tech industry, and since there is a large local customer demand due to economies of agglomeration in the semiconductor industry, T-company chose to construct 12-inch FABs in Taiwan, and they are located in Hsinchu and Tainan. Due to the large demand, the T-company also operates 12-inch FABs in Shanghai and the USA, respectively, as well as an 8-inch FAB in Singapore, as shown in Table 3.4. The capacity utilizations of the four 12-inch FABs are 100%, while that of the 8-inch FAB is 42%. Because of the low capacity of a 6-inch FAB, it is not employed when there is large demand. This can also be explained by the fact that the T-company expanded its capacity to operate more 12-inch FABs rather than 6-inch FABs. Table 3.4 also shows that four 12-inch FABs have the lowest average production cost per die, approximately US$ 0.62, while it
is 1.06 US$/die for an 8-inch FAB. In addition, the total average production cost per die for T-company is US$ 0.65. These results imply that because of the high customer demand, the manufacturer can operate its manufacturing plants with large-size capacity, combined with full-capacity production, thereby lowering the production cost. These results also imply that when determining the production amount for multiple manufacturing plants, manufacturing plants with large-size capacity have a high priority over others for filling the capacity, not only due to the high capability of satisfying the customer demand but also because they provide greater cost savings. Finally, Table 3.4 shows the amount of chemical supplies required by each manufacturing plant, with the total amount required being 100642 L.
Table 3.5 shows the initial results of the procurement decisions including the optimal active chemical source vendors, the procured amount of chemicals, and the amount of chemicals shipped from the chemical source vendors to the manufacturing plants. As shown in Table 3.5, the optimal active vendors include Merck, TY and CSI, and each serve different manufacturing plants. This is because the unit chemical source purchase costs offered by these vendors are relatively low. Although there is a high fixed cost with CSI, this high fixed cost per unit chemical source is reduced if the large procurement amount is large. The advantage from this low unit cost outweighs the disadvantage of the high fixed cost. Since the distance between two alternatives can be reflected by the transportation cost, active vendors tend to serve the manufacturing plants nearby. With reference to Table 3.3(a), the distance from vendors Merck and TY to the two manufacturing plants in Taiwan are due to the fact that they are all located in Taiwan; therefore, FABs in Taiwan are mainly served by Merck and TY rather than by CSI. The average inbound cost per die is US$
10 3
63 .
4 × − .
Table 3.4 The initial results of manufacturing plants Manufacturing plant Taiwan
(Hsinchu)
F ˆ 12-inch 12-inch 12-inch 12-inch 8-inch
Capacity,
nk
v ˆ (wafer) 40000 40000 40000 40000 35000
Production amount, measuring in wafer,
nk
f ˆ
40000 40000 40000 40000 14825
Production amount, measuring in die, ˆ ( ˆ)
Chemical sources required,
k
k n
k n
k F f
wˆ−1,ˆ( ˆ) ˆ (L) 23400 23400 23400 23400 7042 Capacity utilization ratio,
nk
Y ˆ 100% 100% 100% 100% 42%
Average production cost per die
(US$/ die) 0.62 0.62 0.63 0.63 1.06
Total production amount
Total average production cost per die Total amount of chemical source required
108
2× (Dies) 0.65 (US$/die) 100,642 (L)
Table 3.5 The initial results of the relationship between manufacturing plants and chemical source vendors
Active raw material vendor
Manufacturing plants served
Amounts of chemical sources shipped, ˆkˆ−1
k
n
fn (L)
Total amount of chemical sources supplied,
∑
Table 3.6 shows the initial results of the relationship between manufacturing plants and customers in six areas. Since in this study the customer is not constrained to be served by one single manufacturing plant, some customers are served by more than one manufacturing plant, such as customers in North America, Taiwan, Europe and Korea as shown in Table 3.6. For example, customers in North America are served by FABs in Taiwan (Hsinchu) and USA, while customers in Hong Kong is served by the FAB in Shanghai. In Taiwan the majority of customers are served by FABs in Taiwan due to their relative low transportation and production costs. In addition to the amount of customer demand, the main reason that customers are served by different FABs lies in the distance between the customer and the FAB. For example, customers in North America are served by the FAB in the USA, while customers in Taiwan are served by the FAB in Taiwan. These results imply that to reduce the outbound cost, the product should be shipped from a manufacturing plant to a customer with the shortest distance between them. These results also imply that for a wafer foundry company the benefits brought about by centralized production are larger than the increased transportation costs by decentralized production. The manufacturer may adopt a production strategy with centralized production in manufacturing plants with large-size capacity and then ship the product to customers in different regions. Summing up the average production, the inbound and outbound costs per die in Tables 3.4-3.6, the total average cost per die of T-company can be calculated as US$ 0.65579, with the portion of production cost being 99%, the highest of them all. This implies that the wafer foundry industry shows production with economies of scale, and that the production is the most valued-added in the entire supply chain. Therefore, the manufacturer must be aware of the impact on the total cost of capacity utilization of manufacturing plants with different-sizes capacity.
Table 3.6 The initial results of the relationship between manufacturing plants and customers in six areas
Customer in different areas,
ns Customer demand,
ns
f
(dies) Manufacturing plants, nkˆ
Amount of products shipped, k
s
n
fn ˆ (dies)
North America 6.4x107 Taiwan (Hsinchu) 1.5x107
USA 4.9x107
Taiwan 5.7x107 Taiwan (Tainan) 1.5x107
Shanghai 4.2x107
Europe 3.6x107 Taiwan (Hsinchu) 2.8x107
Singapore 7.5x106
Japan 3.2x107 Taiwan (Tainan) 3.2x107
Korea 8.4x106 Taiwan (Hsinchu) 6.3x106
Taiwan (Tainan) 2.1x106
Hong Kong 7.5x106 Shanghai 7.5x106
Average outbound cost per die 1.16×10−3 (US$/die)
0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1
3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 production amount in the USA (107 dies)
average production cost per die (US$/die)
USA Singapore T-company
Figure 3.5 Average production cost per die vs. production amount in the USA
So far, this study has conducted a numerical example for T-company specializing in wafer foundry in the semiconductor industry. Next, this study will further explore the influences of changes in key parameters on the average production cost and the optimal capacity and optimal production amount of the manufacturing plants.
In this study, the capacity utilization of different-size FABs significantly influences the total average production cost per die. As Table 4 shows, a minimum cost is yielded for T-company if four 12-inch FABs reach their full-capacity production. This study takes FABs in the USA and Singapore as an example to explore the impact of the production amount of different-size FABs on the total average production cost per die.
As shown in Table 4, the total production amount of FABs in the USA and Singapore are 5.66×107 dies, with the FABs in the USA and Singapore as 12-inch and 8-inch, respectively. Under the assumption that the size FAB of other manufacturing plants and their production amount remain the same, the number of dies produced by the USA and Singapore are negatively related. Figure 3.5 shows the total average production cost per die vs. the production amount in the USA.
As shown in Figure 3.5, as the production amount produced by the USA increases, the average production cost per die for both USA and T-company decreases, which also includes Singapore for exhibiting increased average production cost. This is because the number of dies produced by one piece of 12-inch wafer exceeds that of an 8-inch wafer. Also, the impact of the increased cost in Singapore on the total cost can be offset by the decreased cost in the USA. In other words, the total production cost can be reduced if there is more production assigned to a manufacturing plant with large-size capacity. This result also implies that with the existence of economies of scale, the mechanism for determining the production amount for manufacturing plants with different-size capacity is to assign the most demands to manufacturing plants with the
largest-size capacity, and to assign the remaining ones to those with small-size.
However, in addition to the size of capacity, the other important factor affecting the assignments of production is the amount of customer demand. As stated, when the customer demand is small, using manufacturing plants with large-size capacity may lead to high production cost. Consequently, a plant with a large-size capacity is preferred when the demand is large. Table 3.7 shows the optimal sizes of FABs and the capacity utilization of manufacturing plants with different amounts of customer demand.
As shown in Table 3.7, there is a high total average production cost when the amount of customer demand is low. Referring to Table 3.1, the advantages of Hsinchu and Tainan in Taiwan are low capital and variable production costs, which provided T-company with the incentives to construct two 12-inch FABs in those regions, as shown in Table 3.7. The optimal FAB size is 12-inch for Hsinchu and Tainan with full-capacity production regardless of the customer demand. This result implies that the determination of where to operate a manufacturing plant with large-size capacity lies in the labor costs involved as well as the corresponding land rental fee, expenses for equipment installation, etc. This finding also shows that high-tech manufacturers can operate a large-size capacity plant in regions with adequate and low-cost supplies and where low-paid skilled workers are available, or if the governments provide incentives, such as rent or tax free etc. to the high-tech industry. Table 3.7 also shows that not all FABs are being operated until the amount of customer demand exceeds 17.99×107 dies. For example, T-company needs only three manufacturing plants when the customer demand is 12.85×107 dies. This result implies that when the demand is extremely low, it is not necessary to operate all of the manufacturing plants, and in addition a manufacturing plant with a very high cost is not suggested. As the customer demand increases, in addition to two 12-inch FABs, T-company will start to operate a
smaller-size FAB at locations with high capital and variable production costs. For example, when customer demand is 11.82×107 dies, then there are three 12-inch FABs, i.e. Hsinchu, Tainan and Shanghai with 100% capacity utilization and one 6-inch FABs in the USA, with a utilization as low as 25%. This implies that a company may incur high costs to operate a large-size capacity at a region with relative high capital and production costs when there is not large demand. As the customer demand increases, the tendency to operate 12-inch FABs increases; even though there is not enough demand to enable full-capacity production for all 12-inch FABs. This implies that rather than using small-size capacity with high capacity utilization, using large-size capacity with a relative low utilization is more cost effective for the manufacturer, as long as the customer demand is sufficiently high to share the high capital cost.
Furthermore, the capacity utilization of Singapore has the highest capital and production costs and shows a smaller number, i.e. 38% with a customer demand of 21.59×107 dies. This implies that when using the same-size capacity for all manufacturing plants, a manufacturing plant with lower capital and lower production cost should be assigned to produce more products.
Table 3.7 The optimal size FABs and capacity utilization of manufacturing plants with different amounts of customer demand
Taiwan (Hsinchu) Taiwan (Tainan) Shanghai USA Singapore Customer
demand (107 dies)
The total average production cost per
die (US$/die) (1) (2) (1) (2) (1) (2) (1) (2) (1) (2)
11.57 0.6823 12 100% 12 100% 12 94% - - - - 11.82 0.6869 12 100% 12 100% 12 100% 6 25% - - 12.85 0.6813 12 100% 12 100% - - 12 60% - - 15.42 0.6549 12 100% 12 100% 12 100% 8 34% - - 17.99 0.6530 12 100% 12 100% 12 100% 12 65% - - 20.56 0.6386 12 100% 12 100% 12 100% 12 100% 8 46%
20.82 0.6387 12 100% 12 100% 8 60% 12 100% 12 100%
21.07 0.6387 12 100% 12 100% 8 74% 12 100% 12 100%
21.33 0.6386 12 100% 12 100% 8 89% 12 100% 12 100%
21.46 0.6387 12 100% 12 100% 8 96% 12 100% 12 100%
21.59 0.6522 12 100% 12 100% 12 100% 12 100% 12 38%
21.85 0.6036 12 100% 12 100% 12 100% 12 100% 12 43%
22.10 0.5560 12 100% 12 100% 12 100% 12 100% 12 48%
23.13 0.5066 12 100% 12 100% 12 100% 12 100% 12 69%
24.41 0.5024 12 100% 12 100% 12 100% 12 100% 12 95%
(1): size FAB
(2): capacity utilization
3.5 Summary
Past studies have extensively investigated plant location issues. Most of these
Past studies have extensively investigated plant location issues. Most of these