Locating manufacturing and distribution centers:
An integrated supply chain-based spatial interaction approach
Jiuh-Biing Sheu
*Institute of Traffic and Transportation, National Chiao Tung University, 4F, 114 Chung Hsiao W. Rd., Sec. 1, Taipei 10012, Taiwan, ROC
Received 7 October 2002; received in revised form 14 March 2003; accepted 18 March 2003
Abstract
This study investigates the facility location problem of transnational personal computer (PC) manu-facturing for the domestic market of China. An integrated supply chain-based spatial interaction model is formulated to determine facility locations of the transnational PC manufacturing centers and regional product distribution centers in China, with the goal of maximizing the potential rate of return on facility investment. The numerical results show that the Shanghai municipality is ranked highest for siting both the manufacturing and distribution centers for a transnational PC manufacturing enterprise.
2003 Elsevier Ltd. All rights reserved.
Keywords: Supply chain; Spatial interaction; Transnational personal computer manufacturing; Transnational operations
1. Introduction
Mainland China has the potential to dominate the personal computer (PC) market in the Asia-Pacific area. With the rapid growth of PC demand in China, the domestic PC market in China has surpassed GermanyÕs, becoming the third largest in the world. According to related statistics (Chen, 2001), the annual national PC demand of China exceeded seven million units in 2001, a growth of 12.7% over 2000. Furthermore, such growth may be further stimulated in the future given that China became a formal member of the World Trade Organization (WTO) in 2001. With economic globalization, overseas PC manufacturers, relying mainly on transnational
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operational strategies to satisfy the growing demands from their world-wide customers, may grasp this opportunity to enhance their international business competitiveness worldwide.
Nevertheless, the facility location problem in China is critical to transnational PC manufac-turing enterprises for the following reasons. First, uncertainties in logistical factors, e.g., inter-province shipment risks and costs, the diversity of local governmental regulations in logistics, and complexity of the market are still significant factors in China. In addition, external factors such as different exchange rates, trade barriers, transfer prices, labor resources, and cultural differences and consumer behavior should also be considered in the transnational operational scenario. As described by Bowersox and Closs (1996a), the globalization of logistics activities is driven mainly by five forces: (1) deregulation, (2) supply chain perspective, (3) economic growth, (4) regional-ization, and (5) technology, and thus increasing the complexity of transnational business opera-tions. Accordingly, transnational PC manufacturing enterprises must rely on sophisticated inbound and outbound logistics management strategies in response to corresponding business operating challenges in China. In this situation, the facility network design problem plays a key role in determining the performance of logistics systems. Supporting arguments can also be found elsewhere (Bowersox and Closs, 1996b).
Research on facility location models has mainly dealt with assigning facilities to serve their nearest demand areas, in order to minimize aggregate operational costs (Hakimi, 1964; Cor-nuejols et al., 1977; Neebe and Rao, 1983; Klincewicz and Luss, 1986; Mirchandani and Francis, 1990; Daskin, 1995; Pirkul and Jayaraman, 1996; Bramel and Simchi-Levi, 1997). To achieve this goal, appropriate decisions in terms of the number and location of facilities as well as the demand area potentially served by each facility, should be made using the facility allocation logic rules. Herein, the properties of the spatially interactive travel behavior have been increasingly incor-porated in formulating facility location problems to make these models more suitable for practical applications (Wilson, 1969; Coelho and Wilson, 1976; Leonardi, 1978; Beaumont, 1980; Erlenkotter and Leonardi, 1985; Jacobsen, 1986; Holmberg, 1996).
One typical example is use of the spatial gravity model, which characterizes the strength of spatial interaction between each pair of nodes in an activity-corresponding network. In LeonardiÕs study (1983), random utility theories are used to formulate the resulting models as nonlinear integer programming models with the entropy-maximizing objective. It addition, a variety of techniques, including dynamic programming models (Campbell, 1990; Drezner and Wesolowsky, 1991; Bean et al., 1992; Webster and Gupta, 1995) and heuristic algorithms (Friesz et al., 1988; Miller et al., 1992), have been utilized to increase the efficiency in searching for a final solution. One distinctive feature of these advanced methods is that demand-related attributes, e.g., demand patterns and demand growth rates, are treated in either the dynamic or the stochastic extent rather than in the static domain as in traditional approaches (Drezner and Wesolowsky, 1980; Daganzo, 1987, 1988; Erlenkotter, 1989; Ghosh and Craig, 1991; Hakimi and Kou, 1991).
In view of limited in-depth investigations in the aforementioned subject in the literature, here we propose an integrated supply-chain based spatial interaction model to formulate the overseas facility network design problem, considering the Chinese PC domestic market. In addition to utilizing the fundamentals of spatial interaction approaches, the concept of supply chain management (SCM) is employed, where corresponding facilities including manufacturing and distribution centers are considered. In formulating the proposed model, we also consider the nation-wide multi-member inbound and outbound logistics-related factors, e.g., material source
accessibility, transportation and inventory costs, potential benefits, inter-province distribution restrictions, and long-term regional market conditions to alleviate the decision bias for locating the corresponding facilities.
2. Model
The proposed model incorporates the concept of logistical distribution channels of the PC supply chain into a comprehensive spatial interaction framework. Herein, a simple three-layer PC supply chain is specified, as shown in Fig. 1, which groups traditional PC supply chain members into three major layers: (1) supply, (2) manufacturing and (3) demand, representing functions of supplying PC assembling materials, manufacturing, and product demand, respectively. According to previous tasks on regional market analyses, given regions, referring to chain members of the specified PC supply chain, can be selected as candidates for facility location, and then are
assigned to corresponding layers. Using the proposed spatial interaction model, the nation-wide multi-layer physical flows of the PC supply chain, referring to state variables of the proposed framework, are estimated. Then these estimated state variables are used as the basis to finalize the decision of locating corresponding manufacturing and distribution centers in the layers of manu-facturing and demand, respectively.
There are two types of state variables:
(1) xi;j represents the amount of potential physical distribution flow between a given pair of the
PC chain members i and j in the layers of supply and manufacturing.
(2) xj;kindicates the amount of potential physical distribution flow between a given pair of the PC
chain members j and k in the layers of manufacturing and demand.
It is noteworthy that the specified state variables serve to characterize the strength of the spatial interaction in the PC supply chain framework. In contrast with the decision variables, which are controllable in mathematical programming models, these state variables are not controllable by transnational PC manufacturing enterprises in the overseas facility network planning scenario. This may also explain why the use of mathematical programming methods is not considered in this study. In addition, some pioneering researchers (Tong and Walter, 1980; Schemmer, 1982; Allen, 1991) may have raised issues in terms of the effects of qualitative factors, e.g., restrictions and incentives of overseas governmental regulations, labor availability, and accessibility of transportation facilities, on the corresponding decision-making process. In reality, these uncer-tainties can be regarded as the corresponding effects on the degree of spatial interaction between given dyad geographical regions, and thus be readily incorporated into the proposed model. Herein, they are treated as factors influencing spatial interaction frictions in the proposed model, and quantified by parameters associated with corresponding spatial interaction cost functions.
The model assumes:
(1) The spatial interaction strength between any given pair of chain members in two different lay-ers changes proportionally with the physical amounts associated with the chain memblay-ers. (2) The regional long-term supply and demand amounts, referring to annual physical quantities
originating from each given region of PC assembling-material supply and demanded by each
given regional demand market, respectively, are known. 1
(3) The spatial interaction friction function is a negative exponential function with respect to the
logistics and manufacturing costs. 2
1
This assumption also implies that the proposed model is affected mainly by the long-term market changes rather than the short-term market changes in the facility network decision-making process. Correspondingly, the short-term changes of market conditions are supposed not to have a profound impact on the corresponding decision-making problem in this study. In reality, such a postulation is consistent with the results of our preliminary analyses conducted elsewhere (Lee, 2002).
2
This postulation exhibits the property that the spatial interaction strength decreases following a negative exponential form, whereas the corresponding friction effect increases. Similar treatments can also be found elsewhere (Wilson, 1969).
The generalized form of the proposed model is presented as (see Appendix A for variable and parameter definitions): XðIJ þJ KÞ1 ¼ Fbxi; x aj j ; x ak k ; CcðIJ þJ KÞ1 ð1Þ
The two vectors XðIJ þJ KÞ1 and Fbxi; x
aj
j; x ak
k ; CcðIJ þJ KÞ1 both have the same dimensions
ððI J þ J KÞ 1Þ, and can be further expressed as XðIJ þJ KÞ1 ¼ Xi;j Xj;k ðIJ þJ KÞ1 ð2Þ where Xi;j ¼ ½xi;j; i¼ 1; 2; . . . ; I; j ¼ 1; 2; . . . ; J T ð3Þ Xj;k ¼ ½xj;k; j¼ 1; 2; . . . ; J ; k ¼ 1; 2; . . . ; K T ð4Þ F½xi; x aj j ; x ak k ; CðIJ þJ KÞ1¼ Fi;j Fj;k ðIJ þJ KÞ1 ð5Þ where Fi;j¼ bfxi;j; i¼ 1; 2; . . . ; I; j ¼ 1; 2; . . . ; J c T ð6Þ Fj;k¼ bfxj;k; j¼ 1; 2; . . . ; J ; k ¼ 1; 2; . . . ; Kc T ð7Þ
Both the disaggregate spatial interaction functions, fxi;j and fxj;k are given respectively by
fxi;j ¼ xi x aj j Ci;j P 8j0xaj0 Ci;j0 ð8Þ fxj;k ¼ xaj j x ak k Cj;k P 8j0xaj0 Cj0;k ð9Þ
According to Assumption 3, both Ci;j and Cj;k are formulated with specific exponential forms
with respect to the corresponding unit costs of manufacturing and logistics. These unit costs
include four main items: (1) costs of assembling-material procurement ðca
Þ, (2) transportation
costs ðct
Þ, (3) storage/inventory costs ðcs Þ, and (4) manufacturing costs ðcm Þ. Therefore, Ci;j and
Cj;k are expressed as follows.
Ci;j¼ expbbi c a i bi;j c t i;j bj c m j c ð10Þ Cj;k¼ expbbj c s j bj;k c t j;k bk c s kc ð11Þ
In addition, it is worth mentioning that some external factors such as different labor resources, unknown facility investment risks, political uncertainties, and inconsistency in local governmentsÕ laws and regulations for corresponding manufacturing and logistics activities may exist in China. However, these factors are quite difficult to incorporate in other mathematical models, such as mixed integer programming models, which are extensively used for the strategic design of do-mestic supply chains. Employing the proposed spatial interaction model, these external factors are aggregated with the forms of the aforementioned parameters using a proposed calibration
procedure. As described later, these parameters can then be used to quantify the corresponding resisting effects in the procedure of determining appropriate facility locations for transnational PC manufacturing in China.
The next stage is to derive the monetary measures used in the final decision-making logic for appropriately locating corresponding facilities in layers M and D of the supply chain-based spatial interaction framework. From the viewpoint of business operations, the quantities of costs and benefits could be more meaningful in the final decision-making process than any other measure-ments, including the estimated spatial interaction strength. Therefore, employing the concept of utility functions, similar to Wilson (1969), we derive the monetary measures as follows, by transforming these proposed spatial interaction functions. Let the physical amounts of logistical xaj
j and x
ak
k shown in Eqs. (8) and (9) be two exponential functions with respect to the given PC
manufacturerÕs benefits, uj and uk, originating from the physical amounts of assembling materials
distributed from chain layers S to M, and from M to D, respectively.3 Accordingly, the
afore-mentioned postulations can be mathematically expressed as xaj
j ¼ expðbj ujÞ ð12Þ
xak
k ¼ expðbk ukÞ ð13Þ
Combine Eqs. (12) and (13) with the corresponding spatial friction functions shown in Eqs. (10)
and (11). Then, we have the disaggregated net benefit indexes denoted by ~lli;j and ~llj;k, which
accompany the physical amounts distributed between the given chain members of i and j, and
those of j and k, respectively. Herein, ~lli;j and ~llj;k are given by
~ l li;j¼ uj ðcai þ c t i;jþ c m j Þ ¼ aj bj lnðxjÞ ðcai þ c t i;jþ c m jÞ ð14Þ ~ l lj;k ¼ uk ðcsjþ c t j;kþ c s kÞ ¼ ak bk lnðxkÞ ðcsjþ c t j;kþ c s kÞ ð15Þ
Accordingly, we specified two monetary measures dj and dk given respectively by
dj ¼ X 8i ~ l li;j xi;jþ X 8k ~ l lj;k xj;k !, 2X 8k xj;k ð16Þ dk ¼ X 8j ~ l lj;k xj;k , X 8j xj;k ð17Þ
Using these monetary measures, we propose the following decision-making logic to determine the locations of the corresponding facilities in layers M and D.
Step 0: Initialize system states of an integrated supply chain-based spatial interaction framework. Herein, the potential regions, which may be suitable for allocating corresponding
faci-3
The amounts of both PC assembling materials and products are accompanied with the benefits that may be potentially gained in layer D, and thus can be characterized with the functions of the corresponding benefits ujand lk.
lities, are targeted according to the missions and goals in strategic planning of business operations.
Step 1: Forecast the state vector, i.e., XðIJ þJ KÞ1, using the proposed integrated supply
chain-based spatial interaction model.
Step 2: Calculate the monetary measure associated with each facility candidate (e.g., dj and dk)
employing Eqs. (16) and (17) together with the predicted state variables.
Step 3: Rank these facility location candidates of a given layer in descending order according to the corresponding monetary measures calculated previously. Then determine the appro-priate facilities for layers M and D with the following rules:
(1) For layer M :
IF P dj
8j2Mdj
cj>kM; for all j ð18Þ
THEN the facility associated with the given chain member j of layer M is allocated to the corresponding region
(2) For layer D:
IF P dk
8k2Ddk
ck >kD; for all k ð19Þ
THEN the facility associated with the given chain member k of layer D is allocated to the
corresponding region.4
where cj and ck are given by
cj¼ P 8kxj;k P 8ixi;j ð20Þ ck¼ P 8jxj;k P 8j P 8kxj;k ð21Þ 3. Parameter calibration
This section presents the scenario of calibrating the parameters (i.e., a and b ) shown in the
spatial interaction functions using the collected statistical data. The proposed parameter cali-bration procedure was constructed according to the fundamentals of maximum likelihood esti-mation approaches, which were extensively utilized in the previous literature (Evans, 1975; Hyman, 1983; Stetzer, 1983). Under the goal, as shown in Eq. (22), the estimation errors in terms
of the physical quantities associated with the chain members j and k (i.e., xaj
j and x
ak
k ) and the
spatial friction functions (Ci;j and Cj;k) are calculated in iteration, and compared with pre-set
4
In real-world applications, the corresponding decision makers of a given transnational PC manufacturer, e.g., the managers of marketing and manufacturing sections, are allowed to determine these two thresholds (i.e., kDand kM)
thresholds. With the help of the Newton–Raphson technique to search for the final solutions, the maximum likelihood estimates of these parameters can be determined once the rule-termination conditions are satisfied.
Min z¼ ½Xðxaj j ; x ak k Þ X realT ½Xðxaj j ; x ak kÞ X real þ ½CðC i;j; Cj;kÞ Creal T ½CðCi;j; Cj;kÞ Creal ð22Þ The calculation steps involved in the calibration procedure are summarized in Appendix B for reference.
To conduct the aforementioned calibration procedure using related statistical data, we gener-ated an input database, which mainly included the potential annual physical amount associgener-ated with each facility location candidate, and the expected logistical distribution time between any two given location candidates in different layers of the proposed 3-layer PC supply chain
framework. These input data correspond to the aforementioned real vectors Xrealand Crealshown
in Eq. (22), which will be utilized in Step 1 of the proposed parameter calibration procedure (Appendix B).
The following summarizes the major procedures executed in the numerical study of model calibration. Using the statistics of the Chinese domestic PC market-sharing percentages collected in a series of reports by the Taiwan (2000a,b,c), a total of thirty major provinces and munici-palities of China were clustered into seven regional groups. Herein, these targeted regions are regarded as the major sources for both the supply of PC assembling materials in layer S, and for the demand of PC products in layer D, as summarized in Table 1. Then five representative mu-nicipalities and seven others were selected as the facility location candidates for consideration of siting the corresponding manufacturing centers and regional logistical distribution centers in layers M and D, respectively. It is worth mentioning that according to the previous literature, these location candidates are reported to have relatively higher potential for conducting the corresponding activities of transnational PC manufacturing in China. Compared with other local regions, the location candidates may exhibit higher levels of the social and economic attributes, and more profitable environments for business operations in China.
Table 1
Candidates for facility locations in the proposed PC supply chain framework Region Sources of assembling
materials layer S
Candidates of facility location for Regional market sharing (%)
Layer M Layer D Supply Demand
1. CE Shanghai (municipality) Shanghai (municipality) Shanghai (municipality) 16 24 2. CN Beijing (municipality) Beijing (municipality) Beijing (municipality) 29 28
3. CC Hubei (province) Wu–Han (municipality) 9 7
4. CS Guangton (province) Guangzhou and Fuzhou (municipality)
Guangzhou (municipality) 22 23 5. NE Liaolin (province) Shenyang (municipality) Shenyang (municipality) 9 6
6. NW Shanxi (province) Xian (municipality) 7 3
7. SW Sichuan (province) Chengdu (municipality) 8 9
CE: Chinese eastern region; CN: Chinese northern region; CC: Chinese central region; CS: Chinese southern region; NE: Northern-east region; NW: Northern-west region; SW: Southern-west region.
Given the pre-specified 3-layer PC supply chain framework coupled with potential facility lo-cations in China, the following several procedures were conducted in this parameter calibration scenario. First, the potential physical amounts associated with these targeted regions were gen-erated using the related historical data. For this, we collected the related historical data reported in Chinese annual statistics report (Institute for Information Industry, Taiwan, 2000a,b,c), and aggregated these data in Table 2. Secondly, the physical distribution times in any given distri-bution channels of the proposed framework, mimicking the corresponding real spatial interaction functions, were estimated. Herein, the geographic distances among these facility location candi-dates together with the forecast in terms of the local accessibility within the service area associated with each facility location candidate are considered. Data regarding inter-facility geographic distances can be collected readily from related literature (Wu, 2000). The estimate of local ac-cessibility is determined mainly according to the levels of corresponding local social and economic attributes associated with the targeted provinces and municipalities. Details of the calibration procedure coupled with related numerical results are stated elsewhere (Lee, 2002), and so are omitted in this paper.
4. Applications
This section describes a numerical study which demonstrates the feasibility of the proposed model in determining the appropriate locations for siting both regional PC product
manufac-turing and distribution centers in China.5
Following the aforementioned decision-making logic proposed to determine the locations of the corresponding facilities in layers M and D, the execution steps together with the corresponding numerical results are summarized as follows. Given the input database determined previously, the state variables of the 3-layer supply chain-based spatial interaction system were forecasted using
Table 2
Statistical physical quantities of PC manufactured products and demands in China The statistical amount of PC manufactured products in 2000
Shanghai (municipality) Beijing (municipality) Guangton (province) Fujen (province) Liaolin (province) Total 420,400 3,367,700 2,287,000 887,900 837,000 7,800,000 The statistical physical amounts of PC product demands in China
CE region CN region CC region CS region NE region NW region SW region Total 1,872,000 2,184,000 546,000 1,794,000 468,000 234,000 702,000 7,800,000
5
Herein, the generation of corresponding input database coupled with preliminary analyses of PC demand and supply market conditions in China are conducted previously in our related literature to alleviate the corresponding effects of demand and supply data bias on modelÕs performance (Lee, 2002). Results of our preliminary analyses imply that short-term changes of PC market conditions in China may not have a significant effect on the long-term decision making for logistical network planning, and such a hypothesis may hold true in the next couple of years.
the proposed method, as addressed in Step 1 of the proposed decision-making logic. The fore-casted values of state variables are summarized in Table 3. Then, according to Step 2, the
monetary measure associated with each facility candidate, e.g., djand dkassociated with layers M
and D, was calculated, and herein the corresponding numerical results are summarized in Table 4. Utilizing the proposed decision-making rules presented in Step 3, the facility locations associated
with layers M and D were then determined, as presented in Table 5. For this, the thresholds kM
and kD were predetermined according to our interview surveys with 15 managers sampled from
five transnational PC manufacturers in Taiwan in Spring, 2002 (Lin, 2002). Further discussions associated with these numerical results are described below.
In addition to physical quantities of inter-layer logistical distribution, Table 3 also provides the information referring to the present supply-demand relationships in given distribution channels of
Table 3
Forecasted logistical distribution amounts in the 3-layer PC supply chain in China
From To Manufacturing centers From To Supply of assembling materials Shanghai (municipality) Beijing (municipality) Guangzhou (municipality) Fuzhou (municipality) Shenyang (municipality) Product demand Shanghai (province) 68,525 548,935 372,781 144,728 136,431 100,896 808,248 548,880 213,096 200,880 CE region Beijing (province) 123,598 990,104 672,378 261,043 246,078 117,712 942,956 640,360 248,612 234,360 CN region Hubei (province) 36,995 296,358 201,256 78,135 73,656 29,428 235,739 160,090 62,153 58,590 CC region Guangton (province) 34,893 279,519 189,821 73,696 69,471 96,692 774,571 526,010 204,217 192,510 CS region Liaolin (province) 91,227 730,791 496,279 192,674 181,629 25,224 202,062 137,220 53,274 52,220 NE region Shanxi (province) 37,416 299,725 203,543 79,023 74,493 12,612 101,031 68,610 26,637 25,110 NW region Sichuan (province) 27,746 222,268 150,942 58,601 55,242 37,836 303,093 205,830 79,911 75,330 SW region Table 4
Calculated monetary measures
Estimated monetary measures associated with the location candidates in layer MðdjÞ
Shanghai Beijing Guangzhou Fuzhou Shenyang
44268 87 197 214
Estimated monetary measures associated with the location candidates in layer DðdkÞ Shanghai (CE region) Beijing (CN region) Wu–Han (CC region) Guangzhou (CS region) Shenyang (NE region) Xian (NW region) Chengdu (SW region) 613 92 123 286 306 176 314
the domestic PC market of China. Compared to the other candidates for facility locations in layer M, Beijing appears to surpass the others in both the demand and the supply markets for PC products. Nevertheless, the phenomenon of supply exceeding demand, where the value in a shadowed cell is less than the corresponding value in the un-shadowed cell, is observed in most inter-layer cases associated with Beijing. The most significant example can be found in the lo-gistical distribution channels for the Liaolin–Beijing–NE region, where the corresponding ratio of the supplied amount to the demand amount increases up to 3.62. Note that Liaolin is the rep-resentative supplier of assembling materials in the NE region. Accordingly, such a phenomenon implies that relatively greater investment risks resulting from supply overflows may exist in the Beijing location. Similar inferences also apply to the other location candidates.
In addition to Tables 3 and 4 provides another interesting implication for determining facility locations. Herein, the numerical results presented in Table 4 refer to the unit benefits of PC products associated with given facility locations, and thus may also reflect the potential rate of return on investment at each location candidate. Compared to the results of Table 3, it appears that Shanghai could replace Beijing as the first priority for siting corresponding facilities since it has the highest monetary measure, even though Beijing has the greatest logistical quantities on both the demand and supply sides. Following Shanghai, both Shenyang and Chengdu also show potential for yielding higher rates of return on investment than Beijing, despite the fact that their logistical amounts are much less than the corresponding value of Beijing in either the supply or demand market.
As can be seen in the shadowed regions of Table 5, two corresponding facility locations are suggested in both layers M and D, with the decision-making rules. Herein, the municipality of Shanghai, located in the CE region, is suggested as the first priority for siting both the PC manufacturing center and the distribution center. As the second priority, the municipalities of Fuzhou and Guangzhou, in the CS region, are also suggested for siting the manufacturing center and the distribution center, respectively, given the investment resources available. Such a final result appears reasonable, despite the fact that the present annual supply of PC products in Shanghai may not be competitive with either Beijing or Guangzhou. According to the numerical results, Shanghai appears to dominate the other facility locations in two primary aspects. The first is its relatively higher rate of return on investment, as reflected by the corresponding monetary
measures (i.e., dj and dk). And the second is the corresponding demand-over-supply operational
Table 5
Determination of final facility locations
Layer M Layer D Location Measure Pdj 8j2Mdj cj Priority Location Measure Pdk 8k2Ddk ck Priority
Shanghai (CE) 663 1 Shanghai (CE) 147 1
Beijing 66 5 Beijing (CN) 26 4
Guangzhou 91 4 Wu–Han (CC) 9 6
Fuzhou (CS) 206 2 Guangzhou(CS) 66 2
Shenyang 143 3 Shenyang (NE) 18 5
Xian (NW) 5 7
status, which may contribute to the urgent necessity of expanding local corresponding facilities to satisfy the deficiency of PC supply volumes from Shanghai. It should also be noted that other superior operational conditions, such as the high degree of social and economic attributes, and the accessibility to international harbors and airports, can make Shanghai readily extend its distri-bution channels for PC global logistics. Similar factors may also apply to Fuzhou and Guangzhou. Despite the applicability of the proposed method that has been demonstrated above, there are still some practical difficulties and limitations of data acquisition in this study, as follows. First, directly collecting nation-wide real data or surveys in China to ideally fit to our needs for the input data is impossible in the current phase. Such an issue could remain in any other studies, which aim at analyzing an emerging economy in a developing country using nation-wide data. Second, the related statistics reported officially by the corresponding governmental agencies of China are quite limited for further use in the analysis. Third, in-depth investigations in qualitative influencing factors, e.g., restrictions and incentives of local governmental regulations and the corresponding effects on inter-province logistical distribution activities, appear inadequate in the current study owing to limitations of time, manpower, and data sources. Our tentative solution is to incorporate these potential factors into the parameter calibration procedures, reflecting their corresponding effects on the magnitude of corresponding spatial interaction frictions.
5. Conclusion
This paper has presented an integrated supply-chain based spatial interaction model to deal with the facility location problems of transnational PC manufacturing in China. By specifying a 3-layer PC supply chain framework, and corresponding state variables, a spatial interaction model is formulated, and then followed by decision-making rules proposed to determine the locations of the corresponding facilities for PC manufacturing and distribution.
Compared to previous literature on facility location problems, the proposed method has two distinctive features. First, by coordinating the inter-layer logistical flows of a specified 3-layer PC supply chain, the proposed method can readily solve the chain-based multi-facility location problems for the transnational PC manufacturing and physical distribution in China. Second, factors including network-wide logistical costs and benefits, as well as economies of facility are considered in formulating the supply-chain based spatial interaction model, thus making the problem formulation more realistic.
Results from applying this model to a real study case study indicate that Shanghai has the highest potential advantages for transnational PC manufacturing enterprises to locate both manufacturing and distribution centers. In addition, the municipalities of Fuzhou and Guang-zhou have the second highest priority for locating the manufacturing and product distribution centers, respectively.
The manager of a transnational PC manufacturing enterprise can conveniently use the pro-posed model as a decision-making support tool to help strategically determine priorities for lo-cating corresponding facilities, according to the operational goals and overseas investment resources. In our future research, extension of the proposed model to formulate the globalized supply-chain based facility network design problems will be a topic of interest. Moreover, in-depth identification of qualitative influencing factors, e.g., overseas investment risks,
trans-national channel climate, market environmental variability, culture diversity, and label avail-ability, also warrants more research for the extension.
Acknowledgements
This research was supported by grant NSC 89-2416-H-327-028 from the National Science Council of Taiwan. The author would like to thank my research assistants Sin-Shen Lee and Chen-Wei Lin for their assistance in data collection and model calibration. The author is also grateful to the referees for their helpful comments. Also, special thanks to Professor Wayne K. Talley for his valuable suggestions to improve this paper. Any errors or omissions remain the sole responsibility of the author.
Appendix A. Definitions of model variables and parameters
Definitions of variables and parameters in the proposed supply-chain based spatial interaction model are as follows:
• aj ¼ a positive parameter representing the effect of the economies of facility scale in terms of
manufacturing associated with the given chain member j in the layer of manufacturing.
• ak ¼ a positive parameter representing the effect of the economies of facility scale in terms of
inventory associated with the given chain member k in the layer of demand. 6
• bj ¼ a parameter involved in the corresponding benefit function uj to make the assumed
expo-nential form hold.
• bk ¼ a parameter involved in the corresponding benefit function lk to make the assumed
expo-nential forms hold.
• bi ¼ a parameter indicating the resisting effect on the corresponding manufacturing and
logis-tics activities associated with a given chain member i in layer S.
• bj ¼ a parameter indicating the resisting effect on the corresponding manufacturing and
logis-tics activities associated with a given chain member j in layer M .
• bk ¼ a parameter indicating the resisting effect on the corresponding manufacturing and
logis-tics activities associated with a given chain member k in layer D.
• bi;j ¼ a parameter reflecting the resisting effect on logistical distribution activities between the
given chain members i and j.
• bj;k ¼ a parameter reflecting the resisting effect on logistical distribution activities between the
given chain members j and k.
• CðCi;j; Cj;kÞ ¼ a ðI J þ J KÞ 1 vector of the spatial friction function which is composed of
the estimated spatial friction functions (Ci;j and Cj;k).
6
Herein, ajand akreflect the corresponding effects of the economies of facility scale on state variables in layers M and
D. In general, greater values of these two parameters imply greater effects resulting from the corresponding facilities on the state variables, i.e., the amounts of physical flows.
• Ci;j ¼ the spatial interaction friction function associated with xi;j.
• Cj;k ¼ the spatial interaction friction function associated with xj;k.
• Creal ¼ the real vector associated with CðC
i;j; Cj;kÞ involving unknown real parameters.
• Fbxi; x
aj
j ; x ak
k ; CcðIJ þJ KÞ1 ¼ a state-estimation function vector which depends on the physical
quantities of logistics distribution associated with the chain members i, j, and k in layers S,
M, and D, respectively (i.e., xi, x
aj
j , and x
ak
k ), and the corresponding spatial interaction friction
functions (C for short).
• fxi;j ¼ the spatial interaction function proposed for the estimation of xi;j.
• fxj;k ¼ the spatial interaction function proposed for the estimation of xj;k.
• I ¼ the number of chain members in the layer of supply (S for short).
• J ¼ the number of chain members in the layer of manufacturing (M for short). • K ¼ the number of chain members in the layer of demand (D for short).
• cj ¼ a market-oriented index
7associated with the given facility location candidate j of layer M .
• ck ¼ a market-oriented index8 associated with the given facility location candidate k of layer
D.
• XðIJ þJ KÞ1 ¼ aðI J þ J KÞ 1 state vector which contains all the state variables specified in
the proposed spatial interaction framework.
• Xðxaj
j; x ak
k Þ ¼ aðJ þ KÞ 1 state estimation vector which contains the estimates of the physical
amounts xaj
j in layer M and x
ak
k in layer D.
• Xreal ¼ the real vector associated with Xðxaj
j ; x ak
k Þ, involving unknown real parameters.
• uj ¼ the given PC manufacturerÕs benefits originating from the physical amount of assembling
materials distributed from chain layers S to M .
• lk ¼ the given PC manufacturerÕs benefits originating from the physical amount of the PC
product distributed from chain layers M to D.
• ~lli;j ¼ the disaggregated net benefit index which accompanies the physical amount distributed
between the given chain members i and j.
• ~llj;k ¼ the disaggregated net benefit index which accompanies the physical amount distributed
between the given chain members j and k. • z ¼ the objective function value.
• ðhÞ ¼ the calibration error vector calculated at any given iteration h.
• dj ¼ the monetary measure associated with a given facility candidate j of layer M.
• dk ¼ the monetary measure associated with a given facility candidate k of layer D.
• kD ¼ a pre-determined threshold decision of locating a given distribution center; kDis bounded
by the values 0 and 1.
• kM ¼ a pre-determined threshold for decision of locating a given manufacturing center; kM is
bounded by the values 0 and 1.
7
A value of cjgreater than 1 may indicate that there is a deficiency of the supplied PC products from the given chain
member j of layer M to satisfy the demands of layer D. Therefore, the higher the value of cj is, the more the
corresponding monetary measure shown in Eq. (18) is amplified, which may prompt a final decision of siting a manufacturing center at the corresponding location.
8
ck, referring to the proportion of the local demands to the total demands in the product demand market, may reflect
the degree of relative significance of a given location candidate k, and thus is involved in the above decision-making rules for determining the corresponding distribution centers in layer D.
Appendix B. Model calibration
The major computational procedures conducted for model calibration are summarized below
Step 0: Initialization. Let the unknown real parameter vector ðUÞ and the in-calibration
para-meter vector calibrated at iteration hðUðhÞÞ be given respectively by
U¼ ½aj;ak;bi;bi;j;bj;bj;k;bk; i¼ 1; 2; . . . ; I; j ¼ 1; 2; . . . ; J ; k ¼ 1; 2; . . . ; KTðIþ2J þ2KþIJ þJ KÞ1 ð23Þ UðhÞ ¼ ½ah j;a h k;b h i;b h i;j;b h j;b h j;k;b h k; i¼ 1; 2; . . . ; I; j ¼ 1; 2; . . . ; J ; k ¼ 1; 2; . . . ; KTðIþ2J þ2KþIJ þJ KÞ1 ð24Þ Furthermore, ðhÞ ¼ U UðhÞ ð25Þ
In addition, let h¼ 0, and then give the initial values of the elements in Uð0Þ; and specify the
preset threshold vector used for terminating the calibration procedure.
Step 1: By using the first-degree Taylor series with respect to the real vectors Xreal and Creal , we
have Xreal XðhÞ Creal CðhÞ ¼ oXðhÞ=oUðhÞ oCðhÞ=oUðhÞ ðhÞ ð26Þ
Step 2: Use the Newton–Raphson method to search for ðhÞ, and then conduct the following ter-mination rule:
If all the elements of ðhÞ are less than the corresponding elements of ðh 1Þ, then let
U ðh þ 1Þ ¼ UðhÞ þ ðhÞ ð27Þ
and let U ðhÞ be the targeted parameter vector calibrated for the use in the proposed model.
Otherwise, let
Uðh þ 1Þ ¼ UðhÞ þ ðhÞ ð28Þ
In addition, let h¼ h þ 1, and then go back to Step 1 to continue the calibration procedure at the
next iteration.
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