Dynamic location and entry mode selection of multinational manufacturing facilities under uncertainty: A chance-constrained goal programming approach

Pergamon

Int. Trans.Opl Res. Vol. 3. No. 1, pp.65-76, 1996 Copyright ~ 1996 IFORS. Published by Elsevier Science Ltd. Printed in Great Britain. All rights reserved $0969-6016(96)00001-9 0969-6016/96 $15.00 + 0.00

Dynamic Location and Entry Mode Selection of Multinational Manufacturing Facilities under Uncertainty: A Chance-constrained Goal Programming Approach HOKEY MIN 1 and EMANUEL MELACHRINOUDIS 2 1Auburn University, USA and 2Northeastern University, USA As the global marketplace continues to expand, the firm's location strategy should shift from domestic to international. An international location problem is different from the traditional domestic location problem in that the former is influenced by a greater variety of uncontrollable, unpredictable, and dynamic factors than is the latter. These factors may include political conditions, expropriation risks, trade regulations, currency exchange rates, cultural differences, and global distribution channel structures. Consequently, the international location problem is more diverse, volatile and complex. Nevertheless, a vast majority of the location literature overlooked many important international aspects. To help the multinational firm formulate viable location strategies in the changing world marketplace, this paper proposes multiple-period, multiple-plant, multiple-objective, and stochastic location model. Copyright © 1996 IFORS. Published by Elsevier Science Ltd.

Key words: international location, goal programming.

1. INTRODUCTION Over the last few years, we have witnessed a series of revolutionary changes overseas that are exemplified by three historical events: (1) the formation of regional trading blocks such as European Union (EU) under the auspices of the Single European Act, North American Free Trade Agreements (NAFTA), and Asia-Pacific Economic Cooperation (APEC); (2) the gradual adoption of the General Agreement on Tariffs and Trade (GATT); and (3) the demise of communism in East bloc nations. These changes made a great impact on the world economy by opening up the global market wider than ever before. As the global market expands, many firms that once concentrated on beating the domestic competition are heavily pressured to replace nationalism with globalism. Globalization of a firm's business activity means the entry into a foreign market that entails production and distribution of goods in unfamiliar foreign markets. Generally speaking, survival in the foreign market is tightly linked to the firm's ability to satisfy the unique needs and preferences of foreign customers. Due to faster response times to their needs and preferences, foreign customers tend to give the edge to the firms located in or near their countries. Consequently, location of manufacturing or assembly facilities in the foreign countries is one of the most effective ways of entering a foreign market. There are some other reasons why a firm should locate its facilities overseas. One of them is to increase the firm's global market share by taking advantage of low production cost available in overseas operations and evading tariff barriers. Another is to protect the firm's domestic market share by fighting its foreign competitors on their turf and weakening their will to penetrate into the US market (Hamel and Prahalad, 1985). For these reasons, international site selection is of vital importance to the success of the firm's globalization. The international site selection decision, however, is not without serious obstacles. In comparison to purely domestic site selection, international location is much more complex and risky due to the uncertain and volatile nature of global business environments. Besides, many elements influencing international location decisions are in conflict with each other. For instance, the low cost of labor in a certain foreign site can be offset by a lack of skilled workers or chronic political instability. Conversely, the easy access to good workmanship and high technology at a foreign site Correspondence: Hokey Min, Department of Marketing and Transportation, Room 238, Collegeof Business, Auburn University, Auburn, AL 36849, USA

66

H. Min and E. Melachrinoudis--CCGP Model

can be undermined by strict government regulations or high material cost. To make matters more complex, labor or material cost may rapidly increase as the foreign economy develops or as currency exchange rates fluctuate over a period of time. Even government incentives or regulations may change as the foreign government changes its policy. These illustrate only a few examples of obstacles that companies must face when locating facilities abroad. From the above, it is obvious that an effective international location plan must not only deal with a host of'time-sensitive' variables that are not under the control and authority oflocation planners, but also consider multiple and conflicting factors. As a useful tool for such a plan, we propose and develop a chance-constrained goal programming (CCGP) model.

2. PRIOR STUDIES In contrast with the abundant literature dealing with various domestic location problems, previous analytical studies on international location are sparse [see, e.g., Verter and Dincer (1995) for the comprehensive review of these studies]. This is understandable given that the significance of international location to a firm's success in the global market was not fully recognized by many practitioners and academicians until recent years in which foreign trade barriers gradually crumbled. To cope with fierce foreign competition that was spurred by free trade movements, an increasing number of multinational firms need an analytical model for international site selection. In fact, Dymsza (1987) reported that many multinational firms had begun to develop a more analytical framework for international strategic planning as a basis for making decisions under risk and uncertainty. As a result, some serious attempts have been made to develop rigorous mathematical models for evaluating various location alternatives in international domains. These models were often built upon earlier conceptual foundations (e.g., Will, 1965; Groo, 1971; Schollhammer, 1974; Welles, 1982) that identified a multitude of international location variables and determined their relative importance to international investment strategies. One of the pioneering modelling efforts includes Hanik's work (1985) which assessed the impact of risks on the profitability of various sits in foreign countries. To elaborate, Hanik attempted to maximize the expected return on investment (ROI) associated with new plant setups in foreign countries given the estimated level of risks. In so doing, he used a modified version of Markowitz's mean-variance portfolio model (1959). Similarly, as an extension of their own previous work (Hodder and Jucker, 1982) that first recognized the interaction between international location and financing decisions, Hodder and Jucker (1985a,b) refined a mean-variance model to consider the uncertain nature of international location parameters such as price and foreign exchange rates. Although these mean-variance based models may be useful in evaluating risk equivalents of uncertainty involved in international location (ILOC), they mainly considered risk factors rather than simultaneously taking into account all of the critical factors such as political and cultural elements. Another potential shortcoming of these models includes consideration of a single-period, single plant, and uncapacitated location problem. To overcome some of these shortcomings, Hodder and Dincer (1986) incorporated additional factors such as market demand and cost into their model. The focus of the model was to combine foreign financing decisions with location decisions so that the firm could maximize after-tax profits. The rationale for the mixture of financing and location was that many firms might need to borrow the investment money from the host country bank when they decided to open new facilities abroad. Under this premise, the model extended the mean-variance approach by including financing cost and numerous ingredients such as interest, tax, and exchange rates which greatly affected financing cost. Despite its merits, the model was still confined to a single-period problem. Rather than adopting a mean-variance approach that might lead to enormous computational difficulty, Haug (1985) developed a linear mixed-integer program that could capture many realistic aspects by considering cost, demand, revenue, and labor quality. More importantly, the model had the capability to incorporate time-sensitive environmental factors into the multi-period framework. However, the model solved a small problem with only two potential sites. Another simple model that aimed to ease computational complexity was proposed by Hunt and Koulamas (1989). Despite its simplicity, their weighted scoring model was not designed to handle multiple periods, capacity restrictions, risk and uncertainty. Cohen and Lee (1989) considered a variety of international

International Transactions in Operational Research Vol. 3, No. I

67

Table 1. Comparison of the international location models Author

Hanik

Haug

Hodder & Dincer

Min & Melachrinoudis

Year Model formulation

1985 Mean-variance (unconstrained 0-1 quadratic) Maximization of expected return

1985 Mixed-integer Maximization of after-tax profits

1986 Mean-variance (constrained 0--1 quadratic) Maximization of after-tax profits

No

No

No

Present Mixed-integer, non-linear chanceconstrained GP 1. Max. of aftertax profits 2. Max. of intangible benefits 3. Min. of risks Yes

No No No Single Single Yes No

Yes Yes No Multiple Multiple No No

Yes Yes No Single Single Yes No

Yes

No Unknown

No 2 Sites, 2 periods

Yes Unknown (prohibitive for over 7 site problems)

Yes 5 Sites, 3 periods

Goal(s)

Entry modes Constraints 1. Demand 2. Capacity 3. Budget Period Plant Risk factor Uncertainty (stochastic) Financing Solved problem size

Yes Yes Multiple Multiple Yes Yes

locational factors including duties, tariffs, and transfer pricing and evaluated tradeoffs among these locational factors. Their model, however, did not capture risk factors and was limited to a single-period problem. Schniederjans and Hoffman (1992) also identified a number of both internal and external factors crucial for the successful location of multinational firms. These factors included political risks, government laws and regulation, tax rate, interest rate, inflation, literacy rate, work ethics, and so forth. Although the identification of these factors helps select the appropriate host country for locating overseas manufacturing facilities, the deterministic goal programming model developed by Schniederjans and Hoffman (1992) was primarily designed to select a firm for acquisition or merger in multinational environments. Haug (1992) formulated a multi-period, manufacturing cost model which aimed to determine a high technology firm's locational choices and transfer of production facilities from domestic to foreign manufacturing sites. The important feature of this model is its consideration of learning effects on material and labor costs over time. However, the model still was designed to solve a relatively small problem despite the fact that the proposed enumeration algorithm somewhat alleviated severe computational difficulties encountered in Haug's earlier study (1985). As the literature review shows, most of the existing ILOC modelling efforts pose some computational difficulties and did not fully consider the randomness (stochasticity) of ILOC parameters and constraints. In addition, most of these models did not consider the multiple objective nature inherent in facility location problems, thereby failing to analyse the important tradeoffs among conflicting locational factors (Current et al, 1990). The current study goes beyond the previous literature by not only considering all the dynamic factors relevant to international location under uncertainty, but also analysing the various tradeoffs among these factors in multiple criteria decision environments. Further, the current model is formulated to reflect the stochastic aspect of location parameters and constraints (see Table 1).

3. PROBLEM SCENARIO The selection of manufacturing or assembly plant sites in foreign countries is not a process to be taken lightly due to its great potential impact on overseas operations. Imagine the consequences if the selection is either inappropriate or suboptimal. Such consequences may include the firm's dissemination of its knowhow, foreign asset expropriation, mounting production costs, legal liabilities, labor conflicts, foreign currency inconvertibility, production and distribution bottlenecks.

68

H. Min and E. Melachrinoudis--CCGP Model

As such, the location decision in an international setting is complex because it involves a large number of closely interrelated decision on the financing, sourcing, distribution, market segmentation, and product specialization. Since all of these decisions cannot be made at once, the decisions should be made in sequences. Prior to selecting a specific site, the first decision to be made is a choice of international market entry model that greatly affects the firm's resource commitments and risk associated with international location. In general, the firm can consider three distinct modes of entry into a foreign market: licensing (or franchising), entering into a joint venture, and setting up a wholly owned subsidiary (Hill, et al, 1990). 'Licensing is a method of foreign operation whereby a firm (licensor) agrees to permit a foreign licensee to use the manufacturing, processing, trademark, knowhow, technical assistance, merchandising knowledge, or some other skills provided by the licensor (Kahler and Kramer, 1977, p.86).' Accordingly, licensing does not require a large capital investment, and can escape tough restrictions and interventions of a foreign government. In the case of licensing, the location decision should focus on distribution aspects rather than production; that is, the location of licensees can be viewed as the location of overseas distribution centers. However, since the licensee has free access to the licensor's knowhow, the licensor always bears the risk of disseminating knowhow to foreign licensees that can be future competitors. As an alternative, the firm may consider overseas joint ventures. A joint venture can lower the risk of dissemination and allows the firm to utilize the foreign partner's local marketing information and established distribution networks. However, in this case, the firm cannot fully control the foreign operation and must share profits with the foreign partner. Another alternative is to own foreign subsidiaries. This mode can be useful, especially when the firm-specific knowhow constitutes the basis of the competitive edge of the firm (e.g., a high-tech firm) or when the firm wants to exercise complete control of the foreign operation and then enjoy global economies of scale. Unfortunately, in this mode, the firm is highly vulnerable to economic or political instability. For example, when the firm decides to exit from the waning foreign market, the excessive resource commitments tied to a foreign subsidiary can result in substantial sunk costs (Hill et al., 1990). Also, if a politically unstable foreign government decides to nationalize the subsidiary, the firm can lose a large amount of assets tied to subsidiary facilities (Stock and Lambert, 1982). From the above, it is apparent that the choice of entry mode significantly affects various location factors (parameters) that, in turn, influence location scenarios. Accordingly, to properly assess the impact of entry mode choice on the location decision, we must identify a multitude of factors relevant to international location. These factors are: (1) Cost: It was commonly assumed that establishments of international manufacturing facilities were made to take advantage of plentiful and low-cost labor (Jucker, 1977). Likewise, the firm must find a low-cost haven that can provide low-cost labor, material, distribution, land and utility. (2) Economic stability: The cost advantage can be negated if the host country constantly suffers from high inflation, high interest rates, unstable currency exchange rates, and chronic labor union problems. (3) Productivity: Regardless of cost benefits, lagging productivity in foreign plants can gradually cripple the foreign operation. In this regard, the availability of skilled labor forces, automation, and leading-edge high technology is essential for the plant setup. (4) Market opportunity: The firm cannot succeed in the foreign market if competition in the given market is too tough or the firm's product does not conform to the unique need and preference of foreign customers. As such, the potential demand around the site should be measured by identifying the market boundaries. (5) Government incentives and interventions: The prevalence of government involvement is much greater internationally than domestically (Coyle et al, 1988). A government wants to attract economic investments from other countries, while at the same time regulating such investments in an effort to protect its own industries from competition. For example, countries such as Ireland, Puerto Rico and the U.S. Virgin Islands, used to provide great tax incentives (Marshall, 1983). Most European countries never allow a firm to lay off its workers and close a plant without imposing enormous penalties (Karp, 1984). (6) Risk level: Due to a number of exogeneous factors influencing international operations,

International Transactions in Operational Research Vol. 3, No. I

j • • • • •

P r o(:luc t I v It y

wage rate

• labor productivity • literacy rate

material cost distribution land utility

"ct°rs"-......

En0og.n. s.clots

COSt

cost

69

i[c~emlc S|eDillty

t'larlt e t Oeee't t e l l y ,per capita income

,population

• ~tomotatlon • technology

,competition

• quality assurance

~cultural similarity

,product li(ecycle

• • • e •

tn(lation interest rate excl~ange r a t e unlon strength economic

64vecfvllenlAttitude • • , ,

tax Incentives

laws regulations

preferential treatment

Intrastructure

• Insurance

Risk • exproprlatlon • knOW hOW dissemination • repatrlatlon

allowances • price control

i-

InternatlonalEntry Mode

Foreign Site Selection

• licensing

• location

• Joint venture

• size

• w h o l l y owned

• number

subsidiary •

timing

Fig. 1. Key factors of dynamic international location.

international location is much riskier than its domestic counterpart. International risks include risks of political instability, expropriation, knowhow dissemination, currency inconvertibility, and local price control (Root, 1987). Since these risks can incur high hidden costs for foreign plant operations, these risks need to be factored into the international location decision. So far, we have shed some light on the entry modes and locational factors that contribute as important parameters to the international location scenario (see Fig. 1). Given the parameters, the international location problem should address the following issues: (1) Where and when to locate multiple facilities of different capacity given financing constraints. (2) How to evaluate the sensitivity of location scenarios to the changing entry mode and parameters. (3) How to analyse the tradeoffs with profit maximization for risk avoidance, long-term stability or other intangible benefits.

4. INTERNATIONAL SITE SELECTION CRITERIA Before coming to the final location decision, a location planner should evaluate each potential site according to several conflicting criteria: (1) maximization of the after-tax profits of open plants; (2) minimization of all the risks associated with resource commitments made to open plants; (3) maximization of intangible benefits such as skilled labor and innovative technology available at the plant site. The first criterion is a typical monetary measure in international location. This criterion can be met in two ways. One is to minimize total costs including labor, material, financing, and distribution costs needed for the establishment and operation of open plants. Another is to maximize the expected revenues generated from the foreign markets that open plants are to serve. Since the value of money can change over time, we also discount future costs and revenues to their net present value. Therefore, this criterion can measure the long-term monetary effect of open plants. The second and third criteria include non-monetary measures that cannot be expressed in dollar terms. Consequently, these criteria are not comparable to the first criterion. Although previous international location studies attempted to convert these criteria into their monetary equivalents and

70

H. Min and E. M e l a c h r i n o u d i s - - C C G P Model

then evaluate them as part of monetary loss or benefit, the current study investigates these criteria separately so that the tradeoffs among profitability, risk and intangible benefits can be analysed based upon their relative importance.

5. MODEL DESIGN To help location planners set systematic guidelines for evaluating the profitability, risk and intangible benefit of international location, we developed a chance-constrained goal programming (CCGP) model. CCGP is a multiple objective technique for determining solutions that 'satisfice' multiple conflicting goals where there are elements of risk and uncertainty associated with parameters and/or constraints (Wynne, 1978). We employed a CCGP approach for two major reasons. First, a GP aspect reflects the diverse and conflicting nature of goals (e.g., maximizing the profitability versus minimizing risk) inherent in international location. Second, a chance-constrained aspect reflects the dynamic and uncertain nature of constraints (e.g., government restrictions or budget limitations) associated with long-term foreign investments. Within the CCGP modeling framework, the generic model formulation is presented with the following indices, decision variables and parameters.

5.1. Indices

J = number of potential sites, T = number of periods in time horizon.

5.2. Decision variables X jr =

the number of units to be manufactured by facility j in period t,

Y j , = 1, if facility j is opened in period t, 0, otherwise,

4=

the number of foreign workers to be employed by facility j in period t,

d~= negative deviational variable that represents a difference between the target and achieved after-tax profit (in dollars),

d;= negative deviational variable that represents a difference between the target and gained d;=

intangible benefit (in scores), positive deviational variable that represents a difference between the risk involved in the establishment of a facility and the target risk level (in scores).

5.3. Parameters (AP)j, (FC)j, (MC)i ,

= discounted unit price in a host country where facility j is located in period t, = discounted cost of establishing facility j in period t, = discounted unit material cost in a host country where facility j is located in period t,

= discounted unit inbound and outbound transportation cost in a host country where facility j is located in period t, discounted unit labor cost in a host country where facility j is located in period t, ( L c b, = (FIN)~, = total amount of financing cost of establishing facility j in period t, (,N)j, = aggregate intangible benefit accrued from facility j established in period t, (O)j, = estimated, weighted aggregate demand (in units) of foreign customers for the products manufactured by facility j in period t in a host country. (TC)j,

(Note: In practice, the demand level for a product can vary according to its life cycle stage. Also, a product may be in different stages of the life cycle in different countries. Therefore, the following weights were assigned to the estimated aggregate demand of the host country in accordance with the

International Transactions in Operational Research Vol. 3, No. I

71

life cycle stage of products manufactured in that country.) 0.2 : introduction phase 0.4 : growth phase 0.8 : maturity phase 1.0 : saturation phase 0.6 : decline phase (RI)j, (PR b (CAP)i (COF)i (YON) i (MN) (MXP)

= = = = = = =

(MXB) = (MNR) =

i¥;

= = =

aggregate risk measures in a host country where facility j is located in period t, estimated total production quantity per worker at facility j established in period t, production capacity limit of facility j, the corporate fund set aside for the establishment of facility j, the maximum amount of loan available from a host country where facility j is located, the desired number of facilities to be opened during the entire planning horizon, the maximum after-tax profit (target level) that can be generated by the establishment of facilities during the entire time horizon, the maximum intangible benefit that can be gained by the establishment of facilities during the entire time horizon, the minimum risk level or 0 associated with the establishment of facilities during the entire time horizon, adjusted cardinal weight determined by relative importance of after-tax profits, adjusted cardinal weight determined by relative importance of intangible benefits, adjusted cardinal weight determined by relative importance of risk factors.

5.4. Formulation Minimize +

+

Z = W~d~ + W2d ~ + W3 d 3

(1)

Subject to: Prob. ~

[(APj, - MCj, - TCj,)Xj, - (FCj, + FINj,)Yi, - LCj, Zj,] + d~ >1 M X P

>1 ~p,

(2)

kj=It=l

where an element ap is a statistical significance level that is a probability measure of the extent to which the violation of constraint (2) is allowed. That is, it is not strictly required that constraint (2) always holds, but constraint (2) will be satisfied if it holds with a prescribed probability of :,p. For example, if ap = 0.95, probabilistic constraint (2) states that there exists at least a 95 % chance that the after-tax profits are below the target level by no more than a profit deviation equal to d~-. If the parameters of constraint (2) are uncertain and normally distributed, the deterministic equivalent form of constraint (2) will become (Charnes and Cooper, 1963): J

T

Z [E(APj, - MC~, - TCj,)Xj, - E(FCj, + FINj,)Yj, - E(LCj,)Zj,] j=It=l

- Z,,

[Var(AP~,)+ Var(MCj,)+ Var(TCj,)]X],+ [Var(FCi,)+ Var(FINj,)]Y], + Var(LC~,)Z + d[ >1NIXP, i

I t •l

(2.1) where E(aj,) = expected value of random parameter aj,, Var(ajp) =variance of random parameter at,, Z,, = Z-score of standard normal variable with an area %. By the same token, we can construct the other two chance-constrained goal constraints in the following manner. Prob.

INj, Yj, + d~ >1 M X B It

>I ~B,

(3)

H. Min and E. Melachrinoudis~CCGP Model

72 rewritten as

E(INi,) Yj, - Z~

Var(INj,) Y~ + d~ >t MXB,

j=lt=l

(3.1)

It=

and Prob.

tii

RIj, Yj, - d~ <~M N R

[.j= I t = 1

1

>I C~rt,

(4)

rewritten as

E(RIi,)Yi, + Z,,

Var(Rli,)Y~, - d; <~MNR,

j=lt=l

(4.1)

lt=l

where aB and aR are the statistical significance levels for the intangible benefit chance constraint (3) and the risk chance constraint (4), respectively, and Z~8 and Z,R are their corresponding Z-scores. For example, ifa R = 0.90, probabilistic constraint (4) states that there exists at least a 90% chance that the risk involved in the establishment of facilities does not exceed the target level by no more than a risk deviation equal to d~. T

~. Yj, >< 1,

for all j

(5)

t=l J

T

~ Yj, = MN,

(6)

j=lt=l

X~, <~Dr,, X~, <~(CAP)j f

for all j,t

Yj~,

X~, <~PRj, Z~,,

for all j,t

t

(8)

for all j,t

[FCj, Yj, + LCj, Zj, + (MCj, + TCj,)Xj,] <~COF i + LONj

Prob.

(7)

(9)

>~~v,

for all j, (10)

!

rewritten as T

~ [E(FCj,)rj, + e(LCj,)Zj, + e(MCj, + rCj, lXj,] t=l

+ Z,F

[Var(FCj,)Y~, + Var(LCj,)Z~, + [Var(MCj,) + Var(TCj,)]X~.,] + Var(COFj + LONj) t

<<.E(COF i + LONj),

for all j

0o.1) where a v is the statistical significance level for the budget chance constraint (10) and its Z-score, Z,F.

Yjt = (0,1),Xjt >/0,Zj,/> 0,

for all j,t

(11)

d( ,d f ,d ; >10 The objective function (1) minimizes the weighted sum of deviations from the goals of profit maximization, intangible benefit maximization, and risk minimization. Constraints (2)-(4) are chance-constrained goal constraints. Constraint (2) maximizes total discounted after-tax profits from open facilities with some degree of uncertainty. Specifically, the after-tax profits are adjusted to take into account the time value of expected revenues, rate fluctuations, cost changes and various financial commitments. In addition, to account for some degree of uncertainty, constraint (2) states that, given the prescribed significance level ofap, the location planner is willing to have the profit maximization goal unsatisfied at most (I - ap) proportion of time. As such, the location planner implicitly considers the possibility that location parameters will be affected by a variety of uncertain future events such as

International Transactions in Operational Research Vol. 3, No. I

73

Table 2. Values for base-line model parameters Potential sites Parameters

j/j

1

2

3

4

5

AP~r (in $)

APjt AP,~2 APjs

MCjt (in $)

MCjt MCj2 MCD TCjt TCj2 TCD FCi~ FCj2 FCD FINjt FIN j2 FIN j3 LCj~

979 1,413 1,694 100 103 106 I0 I0.1 10.2 8,000 6,630 5,392 2,250 2,453 2,673 15,523 17,232 19,128 25 22 19 7 5.5 5 102,179 82,547 78,725 300 308 315 125 20 40

1,008 1,365 1,843 150 155 160 12 12.1 12.2 10,000 8,410 6,218 2,000 2,160 2,333 18,600 22,079 26,208 15.5 16 16.5 I0 10.5 11 82,700 73,260 63,300 300 305 311 150 15 40

1,003 994 986 50 52.5 55 20 20.2 20.4 6,000 4,872 3,781 3,400 3,978 4,654 2,954 2,868 2,785 27 25 23 57 55 53 66,489 100,600 135,220 300 318 337 75 15 35

994 1,058 1,126 100 102 104 5 5.1 5.2 6,000 5,147 4,301 2,100 2,247 2,404 21,421 21,000 20,589 19 22 25 13 12 11 134,090 157,530 177,670 300 305 309 150 20 45

837 1,232 1,811 40 39.6 39.2 7 7.2 7.4 4,700 3,428 2,325 3,000 3,600 4,320 1,551 1,053 714 32.5 35 37.5 65 67 69 119,522 135,281 128,842 2130 201 202 200 20 30

TCj, (in 5) FCj, (in $1,000) FINja (in $ 1,000) LCj, (in 5)

LCj2

INj~ (in scale ranging from 1 to 100)

Rljt (in scale ranging from 1 to 100)

Djt (in units)

LCj3 INjl INj, IN j3 Rljt RIj2 RIj3 Djt Dj2 Dj3

PRjt (in units of products) CAPj (in 1,000 units) COFj (in 51,000,000) LONj (in 51,000,000)

PRjt PRj2 PRj3

M N = 2, ~ , = % -- ~ , = ~F = • = 0 . 9 5 ,

w?

=

vG = w ; =

1/3

Note: Parameters are defined in Section 5.3.

unexpected economic slumps, labor strikes, wars and poor weather. Under uncertainty, constraint (3) maximizes the foreign investment incentives such as government-sponsored worker training programs, accessibility to industrial complexes, local suppliers and science parks. Constraint (4) minimizes a variety of environmental risks that exist in the global operation. To reflect the stochastic nature of risk factors, constraint (4) also has a chance-constrained form. Constraints (5)-(11) are feasibility requirements. Constraint set (5) insures that no more than one facility can be built in the same site. Constraint (6) limits the number of facilities to open during the given time period. Constraint set (7) insures that total quantity of goods produced by any open facility cannot exceed the total estimated demand. Constraint set (8) represents capacity limits of facilities. Constraint set (9) is included to estimate the workforce size required by any open facility. Chance-constraint set (10) requires that the total fixed and variable operating costs of any open facility should not exceed the firm's total budget with a prescribed probability ctF. Constraint set (11) assures the integrality of variable Yj, and the non-negativity of variables Zj,,X~,, and all the deviational variables.

6. M O D E L TEST A N D RESULTS To help the location planner identify the international location configurations, the proposed model was tested under the base-line scenario which involves selecting the foreign site of multiple wholly-owned subsidiaries that manufacture and sell personal computers (PCs) in a foreign country. For illustrative purposes, this base-line scenario considered five potential sites in the three-period time horizon: Manchester, England (j = 1); Lyon, France (] = 2); Pohang, Korea (j = 3); Toronto,

74

H. Min and E. Melachrinoudis--CCGP Model

Table 3. Rangesof objective functions Expected profit (in millions) Expectedintangiblebenefit Best levee Worst level Target level

765.40 - 22.25 607.87

64.5 34.5 58.5

Expectedrisk 15 126 37.2

Canada (j = 4); Mexico City, Mexico (j = 5). Under this scenario, hypothetical but realistic data shown in Table 2 were generated. These data include all normally distributed random parameters that were defined by their means (averages). Standard deviations were assumed to be 10%o of the respective means. To determine meaningful target levels, each one of three objective function values were maximized and minimized individually and then the feasible range for each objective function value was determined in Table 3. For example, the highest expected profit of $765.40 million resulted from the maximization of expected profit associated with chance-constrained goal constraint (2.1) subject to all but the chance-constrained goal constraint. By the same token, the minimization of expected profit resulted in the lowest expected profit which was actually a loss of $22.5 million consisting of only the fixed cost component. For illustrative purposes, the target level was set at 80% of the feasible range, i.e., M X P = - 22.5 + (0.80)[765.40 - ( - 22.5)] = $607.87 million. Similarly, using 80% of the feasible range criterion, the target levels for intangible benefits and risk were set at M X B = 58.5 and M N R = 37.2; respectively. In addition, the three objectives were brought to the same order of magnitude by scaling, because such scaling would make the magnitude of normalized weights wi-, w~-, and w~" meaningful, reflecting the importance of the respective objectives. Using the above data, the base-line stochastic model resulted in a non-linear, mixed-integer goal program with 75 constraints, of which 9 are non-linear, and 48 variables, of which 15 are zero-one integer variables. This model was run on a 486/33 PC using the LINGO mathematical programming and modelling package [LINGO (1991)]. The execution time of this model and subsequent runs ranges from 30 s to 5 min. The model solution revealed that the M N F should open one facility in Manchester, England in the first period and another one in Toronto, Canada in the second period. The elaborate, the Manchester facility is expected to produce 99,513 units, 82,548 units, and 78,725 units in periods 1, 2, and 3, respectively. That is to say, the production levels in periods 2 and 3 are equal to the estimated demand in England, whereas the production level in period 1 is a little short of the estimated demand in that period. This shortage is due to the limited budget allocated to the Manchester site, i.e., constraint (10) is binding for j = 1. Since unit profit margin (unit price minus unit variable cost) is higher for periods 2 and 3 than for period 1, production of the maximum possible quantities in these two periods makes economic sense. Also, the production schedule in the Manchester site requires the hiring of 332 workers, 268 workers, and 250 workers in periods 1, 2, and 3, respectively. In the meantime, the Toronto facility is scheduled to manufacture 138,336 units in period 2 and 150,000 units in period 3. Here, the production level in period 3 is restricted by the Toronto site's production capacity, while the production level in period 2 is limited by the budget constraint at this site. To comply with such a production schedule, the Toronto facility needs 454 workers in period 2 and 485 workers in period 3. Overall, this base-line scenario will generate $550 million of expected profits for the M N F with the moderate level of 47 scores of intangible benefits (i.e., 42% achievement level) and the relatively small level of 19 scores of risk (i.e., 96% achievement level). Also, the deviation (di-) from the profit goal turns out to be $206.41 million, while the deviation (d~) from the intangible benefit goal is 16.98 and the deviation (d~') from the risk total is 0. For instance, from a practical standpoint, the aforementioned profit deviation means that there exists more than an cte (95%) chance that the profit will be short of the target level by no more than $206.41 million. The same analogy can be used for the interpretation of the other two deviations. So far, we have assumed ownership of foreign subsidiaries. As stated earlier, however, different international entry modes for the M N F often require different levels of resource commitments, market opportunities, and risks for the location alternatives and consequently may change the location configuration. Considering this, we carried out 'what-if' analyses to explore the response of model solutions to changes of the entry modes and the subsequent changes of certain model parameters. To elaborate, we altered some parameters associated with the expected intangible benefits and risk to reflect the potential benefit/risk sharing with foreign business partners (i.e., joint

International Transactions in Operational Research l,'ol. 3, No. I

75

Table 4. Changing parameter values for differententry modes Potential sites Random parameters*

Joint venture IN~ Joint venture RI jf Licensing IN i, Licensing Rij,

t/j

1

2

3

4

5

IN~ INi2 INj3

27 24 21

25 26 27

34 32 30

22 25 28

40 45 50

Rljt Rljz RIi3

12 I1 10

15 16 17

67 65 63

15 14 13

75 77 79

INjl INi2 INj3

36 33 30

35 36 37

49 47 45

32 35 38

60 65 60

RIjt

17 16 15

20 21 22

77 75 73

20 19 18

85 87 89

RIj2 RIj3 *Scale ranging from 1 to 100.

ventures and licensing firms- see Table 4 for the changed parameters). Under the joint venture mode, we presumed that the two partners split the profits equally. Under the license mode, we assumed that the foreign licensees pay the MNF a certain percentage of profit as licensing fees (e.g., 10% for the first period, 9% for the second period, and 8% for the third period). According to the model test, a change in the entry mode from subsidiary to joint ventureship did not affect the production schedule, although it brought different profit, intangible benefit, and risk. Specifically, when the MNF considered establishing two 50/50 joint ventures with foreign partners rather than building its own subsidiaries, its total estimated profits declined by one-half ($275 million), while increasing the level of both intangible benefits (from the score of 47 to 52) and risk (from the score of 19 to 26). The profit decline was due to the equal profit sharing with foreign joint ventures. On the other hand, an increase in intangible benefits may result from the increased incentives often provided by host governments to the joint venture, whereas increased risk may stem from the MNF's potential conflicts with the foreign partners in determining pricing and employment policies, marketing strategies, and resource utilization. When changing the entry mode from subsidiary to licensing, the M N F needs to establish two separate licensing firms at two different sites (i.e., Manchester, England in periods 2 and 3; Toronto, Canada in period 3). Such a change reduced the expected profit considerably (from $550 to $28.84 million), because the only source of revenue for the MNF under the licensing mode was licensing fees paid by its licensees. On the other hand, it increased the expected intangible benefits from the score of 47 to 71, because host governments tend to offer preferential treatment to their domestically-owned licensing firms compared to the foreign-owned subsidiaries. Under the licensing mode, however, the risk level was the highest (a score of 34) due to the extremely high risk of disseminating the licensor's knowhow and technology.

7. C O N C L U D I N G REMARKS Over the past decade, international site selection has emerged as an important procedure for establishing global operations and marketing global products internationally. To help evaluate international location strategies under dynamically changing scenarios, we developed a new analytical model that was based on a chance-constrained goal program. The model developed in this paper has the following practical advantages over existing models: (I) The model is capable of handling multiple conflicting goals (e.g., highest profit, best incentive, lowest risk) inherent in international location; consequently, it helps the location planner to make various tradeoffs between competing criteria such as profit versus risk, especially when the firm shifts its priorities (e.g., from profit to risk) in site evaluation.

76

H. Min and E. Melachrinoudis--CCGP Model

(2) The model enables the location planner to evaluate 'what-if' scenarios associated with distinct international market entry. Therefore, the model can be easily adapted to potential changes in the firm's resource commitment, production schedule, and organizational structure. (3) The model incorporates some degree of uncertainty and randomness stemming from the volatility of location factors such as interest rates, currency exchange rates, prices, demand levels, market competition, and government policy. The proposed model, however, is still far from being perfect. The model should be extended to explore more comprehensive international location problems with multiple commodities, multiple foreign market coverage, and hierarchical network planning.

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