Reliability evaluation and adjustment for supply chain network design with demand fluctuations
4.3 Supply chain network adjustment model
4.3.2 Customer demand shrinkage
The potential production amount of the manufacturing plants is significantly reduced due to a decline in customer demand, thereby resulting in production diseconomies. The production cost will be even higher if most manufacturing plants locate in regions with high commodity price index. On the contrary to demand expansion, this study proposes a production adjustment strategy in response to demand shrinkage such that the production could be focused on a few economical manufacturing plants, instead of dispersed production by all manufacturing plants. This study considers costs and benefits associated with production adjustment and formulates a mathematical programming model for determining the optimal production reallocation among the manufacturing plants by minimizing total adjustment cost during months with shrunk demand, given by the sum of allocation cost, difference in production cost, and transportation cost.
Let y {Ini,j, ns, i}
s ∀ ∀
≡ represent the set of months belonging to the time interval within which shrunk demand occurs and n(y) is the number of months in y, where the adjustment is scheduled and executed. Let I≡{n&&k} be the set of the unreliable manufacturing plants and nˆ , k nˆk ∈K−I, represents a reliable manufacturing plant under demand shrinkage, respectively. Moreover, let fn&&k and fn&&'k represent the unadjusted and adjusted average monthly production amount of manufacturing plant n&& , k
and fnˆk and fnˆ'k be the unadjusted and adjusted production amount of manufacturing plant nˆ over n(y) months, respectively. The relationships between unadjusted and k adjusted production amounts are stated as follows:
∑
∀ whether there is reallocation relationship between manufacturing plants n&& and k nˆ , krespectively. Indicator
k kn
en&&,ˆ can be either positive or negative, depending on whether
the production amount is allocated from manufacturing plant n&& to k nˆ and k ,ˆ >0
k k n
en&&
implies that there is production amount,
k k n
en&&,ˆ , reallocated from n&& to k nˆ . k
Let wn&&k and
nk
wˆ represent, respectively, the unit-product allocation costs of manufacturing plants n&& and k nˆ , depending on commodity price indexes in different k
regions. The total variable allocation cost of manufacturing plants n&& and k nˆ over k
n(y) months, Wn&&k and Wnˆk, is given, respectively, as:
The total allocation cost over n(y) months, W, can be obtained by summing up the fixed allocation cost and variable allocation cost of all manufacturing plants, namely:
∑
Though the production cost of a manufacturing plant with additional production
amount can be correspondingly reduced, the production costs of the other plants are raised since there is less production to share the high capital cost. The manufacturer should carefully investigate the difference in production cost for all manufacturing plants when it comes to production reallocation in response to demand shrinkage. Let
X and 1 X represent, respectively, the total difference in production costs for all 2 unreliable manufacturing plants and for all reliable manufacturing plants over n(y) months, namely:
Then, the total difference in production cost over n(y) months, X, can be shown as:
2
If X>0, there is a reduction in production cost; otherwise, the reallocation incurs an increased cost.
Similar to that discussed in Section 3.1, the transportation cost reflects the different assignment of customers to the manufacturing plants. Let tn&&k and tnˆk represent, respectively, the average unit-product transportation costs from manufacturing plants
n&& and that from k nˆ to customers. The total transportation cost over n(y) months, E, k
can be formulated as
)
From the discussions to date, the supply chain network adjustment model in response to demand shrinkage can then be determined by solving the following programming model (P3):
P3: min W +E−X (4.22a)
Eq. (4.22a) is the objective function that minimizes total adjustment cost over n(y) months. Eqs. (4.22b) and (4.22c) state the relationships between adjusted and unadjusted production amounts for the manufacturing plants. Eq. (4.22d) constrains decision variable en&&k,nˆk to be an integer and Eq. (4.22e) defines decision variable qnnˆ&&kk to be binary.
4.4 Case study
Following the study object in Chapter 3, a numerical example of T-company is also provided to demonstrate the application of the proposed models in this chapter. Base values for the cost-function relevant parameters are given to solve the problem of T-company’s supply chain network; however, some operating costs are unavailable, the annual report data in TSMC (2004) are employed to estimate them. In this chapter, total customers are classified according to the geographic distributions, which result in six major customers, namely North America, Europe, Japan, China and Taiwan.
T-company could operate either 12-inch, 8-inch or 6-inch wafer fabrications1 (FABs) to serve customers, which produce average monthly capacities of 50000, 70000 and 82000 pieces, respectively. In terms of area, one piece of 12-inch wafer is 2.25 times the size of that of 8-inch wafer; furthermore, it is 4 times of 6-inch wafer. To unify, customer demand, capacity and production amount are measured in terms of pieces of 8-inch equivalent (eq.) wafers. Thus the capacities of 12-inch, 8-inch and 6-inch FABs can be revised as 112500, 70000, 45920 8-inch eq. wafers. Regarding manufacturing plants, there are five available locations for T-company to operate various sizes of FABs, namely, Taiwan (Hsinchu), Taiwan (Tainan), Shanghai, USA and Singapore. The monthly capital cost for different-size FAB can be estimated by total expenses for the FAB construction and equipment set up and the maximum usage period of the FAB.
Tables 4.1 and 4.2 show, respectively, the forecast values for each of the 5 major customer demands in year 2007 and base production parameters for different-size FAB in different locations.
1 Each size FAB can only produce its particular size of wafers, i.e. 12-inch, 8-inch and 6-inch wafers due to the complexity of technology in the manufacturing process of producing wafers.
Table 4.1 Demand forecasts for five major customers in 2007
Customer in different areas Annual forecasts* Monthly forecasts*
North America 6165050 513754
China 207774 17315
Japan 508312 42359
Taiwan 333723 27810
Europe 497992 41499
Total 7712851 642737
Source: TSMC Annual Report
* 8-inch eq. wafers
Table 4.2 The base production parameters for different-size FAB in different locations
6-inch 8-inch 12-inch 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 9700 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 4.3 Initial results of manufacturing plants and their relationship with customers in different locations
Locations FAB
Customer in different locations
Monthly flows (8-inch eq.
wafer)
Taiwan (Hsinchu) 12-inch North America 112500
12-inch North America 112500
Taiwan (Tainan) 12-inch China 17315
Japan 42359
Taiwan 27810
Europe 25016
Total 112500
Shanghai 12-inch North America 112500
USA 12-inch North America 112500
Singapore 12-inch North America 63755
Europe 16480
Total 80235
Locations
Taiwan (Hsinchu) Taiwan (Tainan) Shanghai USA Singapore
FAB 12-inch 12-inch 12-inch 12-inch 12-inch 12-inch Capacity utilization (Ynk) 100% 100% 100% 100% 100% 71.32%
Proportion of production to totals (
nk
θ ) 0.175 0.175 0.175 0.175 0.175 0.125 Average production cost per 8-inch eq. wafer (US$) 322.85
Average outbound cost per 8-inch eq. wafer (US$) 8.61
This study determines the capacity of manufacturing plants, i.e. the sizes of FABs in various locations and their production amounts as well as the monthly flows from each FAB to customers in different locations using supply chain design model (Eqs.
3.17(a)-3.17(h)) in Chapter 3. This study employs the simulated annealing (SA) heuristic proposed by Kirkpatrick et al. (1983) to obtain the solutions. The initial solution results are listed in Table 4.3.
As shown in Table 4.3, T-company will operate six 12-inch FABs in the five locations, where there are two 12-inch FABs constructing and operating in Taiwan (Hsinchu) due to economical incentives provided by Taiwan government. To meet the high demands, all FABs, other than the FAB in Singapore, are planned to reach the full-capacity production, i.e. 100% capacity utilization. Though the production amount could efficiently share the high capital cost of constructing a 12-inch FAB in Singapore, the higher production cost hinders the FAB from a 100% capacity utilization as compared to that in other locations. Similarly, the proportion of output from FAB in Singapore is merely 0.125, while that of other FABs is 0.175. The results show that the production allocation among manufacturing plants depends not only on the capacities but also labor, utility and insurance costs with respect to the locations of the manufacturing plants. The average production cost per 8-inch eq. wafer for 12-inch FAB is US$ 322.85. The result shows that the manufacturer can reduce the impact of employing a large-size capacity plant on the total costs, by determining a full-capacity production for that plant. The results also imply that the wafer foundry production exhibits scale economies and a large-size capacity manufacturing plant combined with the full-capacity production yields a lowest cost. Table 4.3 also shows the relationship between the manufacturing plants and customer in different locations and their monthly product flows. Since demands from customers in North America account for the largest demands for T-company among all, most of the FABs solely serve customers
from that area.
A hypothetical scenario involving abnormal states is further considered in this case study. We suppose that an explosion in demand from customers in China occur owing to government policy in promoting the usage of integrated circuit identity card, which is a by-product of wafer foundry, from April to July. The data concerning this abnormal state, including occurrence duration, abnormal demand distribution and duration probabilities, is listed in Table 4.4. The expected demand distribution from the abnormal location, China, is also calculated and shown in Table 4.4. The reliabilities of the FABs, considering abnormal states, are listed in Table 4.5.
Due to the proposed full-capacity production of many FABs, demand expansion occurring in China has led these FABs to low reliability, where there are diverse reliability values as shown in Table 4.5. The acceptable utilization levels often reflect the expectations of T-company towards various FABs in different locations. In this study, the maximally acceptable capacity utilization is set to be 1, where there exists a lowest unit-product production cost, while the minimally acceptable capacity utilization is assumed to realize tolerable minimum revenue at the manufacturing plant. There would be a small chance that capacity utilizations fall within a narrow range of acceptable level due to a high expectation towards a manufacturing plant, thereby low reliability values. The above reason explains why the two FABs in Taiwan (Hsinchu) exhibit the lowest reliability values, as listed in Table 4.5. In addition to the acceptable utilization limits, the reliability value also depends on the production allocation among FABs in different location. Since there exists the surplus capacity of the FAB in Singapore, it maintains a good performance under demand expansion.
Table 4.4 Hypothetical data regarding abnormal state on customers in China
probability Abnormal demand distributions: ~ )) (
distribution N (46818, 1615) N(44617, 1477) N(43544, 1369) N(31435,1394) China
Normal demand distributions: ~ )) (
Japan - N(42100, 3900) N(42155, 3856) N(42578, 3912) N(42321, 3866) Taiwan - N(26955, 2881) N(27934, 2540) N(28142, 2725) N(28568, 2506) Europe - N(41746, 4264) N(42078, 4000) N(42256, 4231) N(42129, 4303) North America - N(513700, 61330) N(513650, 63954) N(514018, 58988) N(513755, 60418)
Table 4.5 Reliability of the manufacturing plants, given abnormal demand from China
Reliability in abnormal months Location FAB
Acceptable max. and min.
utilizations April May June July Taiwan
(Hsinchu) 12-inch Ynk =1,
nk
Y =0.85 0.3000 0.3068 0.3009 0.3684
12-inch Ynk =1,
nk
Y =0.85 0.3000 0.3068 0.3009 0.3684 Taiwan
(Tainan) 12-inch Ynk =1,
nk
Y =0.82 0.3132 0.3207 0.3114 0.3859
Shanghai 12-inch Ynk =1,
nk
Y =0.70 0.3228 0.3333 0.3192 0.4010 USA 12-inch Ynk =1,
nk
Y =0.75 0.3217 0.3319 0.3185 0.3994 Singapore 12-inch Ynk =1,
nk
Y =0.60 0.8430 0.9788 0.9999 0.9744
Furthermore, the fluctuant demands from customers in Japan, Taiwan, Europe and North America can be classified as normal by a comparison between the data in Tables 4.1 and 4.4. This study focuses on the unreliable situation arising from expanded demand from China and proposes an adjustment strategy by solving P2 (Eqs.
4.15(a)-4.15(g)). Suppose there are two available outsourcing firms in the market, which locate in Japan and Korea with limited outsourcing amounts. The set of adjustment months, t, is t={4, 5, 6, 7}, totaling 4 months. Table 4.6 lists the initial values of parameters in P2. Table 4.7 shows the results and the optimal objective function values with and without network adjustments.
As shown in Table 4.7, the expected production amounts of most FABs exceed their capacities, which are unattainable situations. In this circumstance, T-company could operate the FABs as initially proposed and bears a huge revenue loss of US$
39936000 in cases no adjustment is performed, as listed in Table 4.7. T-company could also alter and increase the production amount at a reliable FAB, i.e. the FAB in Singapore; meanwhile, consider an outsourcing so that the high demands are satisfied.
As shown in Table 4.7, performing an adjustment yields a reduction in total production cost which offsets the derivative additional costs, such as allocation costs, extra material purchase costs and transportation costs, etc. Furthermore, the high penalty cost is avoided. However, there are still unfulfilled demands due to limited outsourcing amounts, remaining a penalty cost of US$ 4161600. By comparing between total costs with and without an adjustment, the production adjustment is shown to benefit T-company.
Table 4.6 The initial values of parameters in P2
Definition Initial values
Average unit-material purchase cost (p) 2.5
Unit-product penalty cost (φP) 240
Fixed allocation cost (Ok) 350000
Outsourcing firms in different locations
Singapore Japan Korea
Unit-product compensation cost (
nk
h ) 67 - -
Unit-product outsourcing cost (
mk
o ) - 402 405
Average unit-product transportation cost 2.4 2.28 1.5 Limitation of outsourcing production
amounts - 2000 3000
Table 4.7 Initial proposed, expected and adjusted monthly flows, related costs and the results of adjust/do-nothing judgments in response to demand expansion
Manufacturing plants Monthly flows (8-inch eq. wafer) Abnormal months (Apr.,
May, Jun., Jul.) Operated by
T-company in
different locations FAB
Customer in different
locations Initial proposed Expected Adjusted Taiwan (Hsinchu) 12-inch North America 112500 122035 112500
12-inch North America 112500 122035 112500 Taiwan (Tainan) 12-inch China 17315 17315
Japan 42359 42359
Taiwan 27810 27810
Europe 25016 25016
Total 112500 122035 112500
Shanghai 12-inch North America 112500 122035 112500 USA 12-inch North America 112500 122035 112500 Singapore 12-inch North America 63755 63755
Europe 16480 16480
China - 32265
Total 80235 87165 112500
Japan* China - 2000
Korea* China - 3000
Total penalty costs without adjustment (US$) Total adjustment costs (US$)
(+) Allocation costs
(+) Extra material purchase costs (-) Differences in production costs (+) Penalty costs
(+) Transportation costs Judgment
39936000 20284256 17073020 322652 1619000 4161600 345984 Adjust
*Outsourcing firms
In the case study, T-company gains a high profit margin on wafer foundry;
consequently, it will suffer a great loss if the market price of the product is high and the adjustment is not made. On the other hand, the outsourcing cost is paid to the outsourcing firms, which include not only production and material purchase costs borne by the outsourcing firm, but also a premium charged. This study further performs sensitivity analysis to investigate how changes in unit-product penalty cost and outsourcing cost affect the judgments of do-nothing and adjustments. Let o be the m average unit-product outsourcing cost and φP be the unit-product penalty cost, respectively. Thus,
P om
φ reflects the ratio of the outsourcing to penalty cost. A large value of
P om
φ indicates an increased outsourcing cost as compared with the penalty cost, which reflects the situations of product being less value or a high premium charged by outsourcing firms. Figure 4.2 shows the threshold of adjust/do-nothing judgments by comparing between various unit-product outsourcing and penalty costs. The left-hand and right-hand sides of the solid line in Figure 4.2 represent, respectively, the judgments being do-nothing and judgments.
As stated, do-nothing is suggested if the adjustment benefits cannot offset the adjustment cost, where the adjustment benefits are given by the sum of savings in production cost and the exemption from the penalty cost. Given the savings in production cost, a decreased penalty cost leads to a shrunk adjustment benefit; thus, the tendency towards adopting an adjustment is small, as shown in Figure 4.2. Since the penalty cost reflects the market value of the product, the result suggests the manufacturer to stick to the initial proposed decisions and neglect the abnormal demand if the product value is low. On the other hand, it is worth performing an adjustment and continuing to outsource for a high value-added product, even though the payment is expensive, as shown in Figure 4.2.
0 5 10 15 20 25 30 35 40 45 50 55 60
78 79 80 81 82 83 84 85 90 100 240 300 310 320 330 340 350 360 370 Unit-product penalty cost (US$)
*
P om φ
) ( Pφ
Adjustment Do nothing
*Average unit-product outsourcing cost/unit-product penalty cost
Figure 4.2 The threshold of adjust/do-nothing judgments by comparing between unit-product outsourcing and penalty costs
0 500 1000 1500 2000 2500
1 1.5 2 2.5 3 3.5 4
Duration of abnormal months
Fixed allocation costs (1000US$
Do nothing
Adjustment
Figure 4.3 The threshold of adjust/do-nothing judgments by comparing between duration of abnormal months and fixed allocation costs
In this study, the fixed allocation cost includes production schedule change costs at the manufacturing plants, contract cost related to outsourcing firms, which is triggered once an adjustments is made. The fixed allocation cost can be also explained as the difficulty in searching qualified outsourcing firms. The fixed allocation cost will be extremely high if there are few available and qualified outsourcing firms, at which the disadvantage may outweigh the advantage of the adjustment. Furthermore, the total adjustment benefits during the execution of an adjustment depend on not only the considerable amounts of abnormal demand but also the duration of the abnormal months. An increased duration of abnormal months accumulates lots of savings in production costs and exempts heavy penalty costs, thereby an adjustment is suggested.
The advantage is diminished if the fixed allocation cost is high combined with a short abnormal period. This study further examines how changes in abnormal periods and fixed allocation cost affect the judgments of do-nothing and adjustments. Figure 4.3 shows the threshold of adjust/do-nothing judgments by comparing between the durations of abnormal months and fixed allocation costs, where the left-hand and right-hand sides of the solid line represent, respectively, do-nothing and adjust judgments.
As long as the adjustment benefits outweigh the adjustment costs, the production allocation among the manufacturing plants should be adjusted. In some ways, the adjustment decisions depend on whether the adjusted production amount can effectively share the high fixed allocation cost. As shown in Figure 4.3, the threshold of an adjustment is increased with an increase in the duration of abnormal months, meaning a high fixed allocation cost will not prevent the manufacturer from performing an adjustment. The results also encourage the manufacturer to look for qualified outsourcing firms and book their capacities when the abnormal event continues
influencing. Furthermore, the results imply the manufacturer could neglect the unreliable situations caused by an abnormal state with a short period, because the accumulated benefits during this short period might not compensate the high allocation costs. The results of the study provide a reference for the manufacturer in the decision making procedures of network planning under demand expansion, as they cope with related benefits, costs and the duration of abnormal months.
Another hypothetical scenario involving abnormal situations, causing demand shrinkage in North America, is considered in the case study. Suppose a sudden declined demand from customers in North America due to the occurrence of finance crisis from January to March. The data concerning this abnormal state, including duration, abnormal demand distributions and duration probabilities, are listed in Table 8.
The expected demand distribution from the abnormal location, North America, is calculated and shown in Table 4.8. The reliabilities of the FABs in different locations, considering demand shrinkage, are listed in Table 4.9.
Table 4.8 Hypothetical data regarding abnormal state on customers in North America
Abnormal month
January February March Customers in
different regions
State occurrence duration and
probability Abnormal demand distributions: ~ )) (
v1=2.3, p1=0.2 N(406936, 45631) N(415972, 41330) N(459639, 40629) v2=2.6, p2=0.4 N(417712, 47778 ) N(409685, 44852) N(442366, 38844) v3=3.0, p3=0.4 N(418964, 45711) N(409119, 41567) N(422587, 44753) Expected demand
distribution
N(416058, 27979) N(410716, 25820) N(437909, 25058) North America
Normal demand distributions: ~ )) ( Taiwan - N(27693, 2896) N(28131, 2688) N(27585, 3022) Europe - N(41500, 5626) N(42015, 6025) N(42134, 6060)
Table 4.9 Reliability of the manufacturing plants, given abnormal demand from North America
Reliability in abnormal months Location FAB Acceptable max. and min.
utilizations January February March Taiwan
Demands from North America account for nearly 80% output of T-company, as shown in Table 4.1. To satisfy the considerable demands, most FABs produce the products to serve customers solely from this location, as shown in Table 4.3. The occurrence of an abnormal event in North America will markedly influence the performance of the FABs in different locations. As shown in Table 4.9, the abnormal demands from North America result in low reliabilities for most FABs, yet the FABs in
Demands from North America account for nearly 80% output of T-company, as shown in Table 4.1. To satisfy the considerable demands, most FABs produce the products to serve customers solely from this location, as shown in Table 4.3. The occurrence of an abnormal event in North America will markedly influence the performance of the FABs in different locations. As shown in Table 4.9, the abnormal demands from North America result in low reliabilities for most FABs, yet the FABs in