Optimal Operating Policies for a Multinational Company under Varying Market Economics

doi:10.4236/me.2013.411073

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Modern Economy, 2013, 4, 673-680

Published Online November 2013 (htt p://www.scirp.org/journal/me)

http://dx.doi.org/10.4236/me.2013.411073

Open Access ME

Optimal Operating Policies for a Multinational Company

under Varying Market Economics

Shu-Chen Chang

Department of Business Administration Nati onal Formosa University, Taiwan

Email: shu-chen@nfu.edu.tw

Received March 14, 2013; revised April 29, 2013; accepted May 7, 2013

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

This paper proposes a mathematical programmin g model for Multi-National Corporations (MNCs) by considering both

the flexibility of ex ch ange rate an d market price un certainties. Th e results sho w that the facto ry in a host coun try should

supply the produ cts demanded by the home coun try for the next period when exchange rate decreases. The quantity of

products being produced and shipped should be adjusted according to the variation of market-price. Conversely, a MNC

in the host country should produce products ahead of time when exchange rate increases and must adjust quantity of

production and inventories according to the variation of market-price.

Keywords: Exchange Rate Uncertainties; Multi-National Corporation s ; Market Price Uncertainties

1. Introduction

Previous reports have showed a significant increase in

the number of Multi-National Corporations (MNCs) and

a tremendous growth in foreign direct investment in re-

cent two decades. A MNC is defined as the corporation

that owns or controls production or service facilities o ut-

side the host country and operates in two or more coun-

tries. However, a fundamentally different form of inter-

national commercial activity has developed since World

War II. The form has greatly increased worldwide eco-

nomic and political interdependence. The MNCs now

make direct investments in fully integrated production

process including production planning and distribution

under varying environments. Due to the current trend of

market and economic globalization, multinational corpo-

rations must face more ambiguities such as different cul-

tures, values, ru les, varying degrees of business, po litical

and economical uncertainties. Investments of a MNC

under uncertainty have been studied in several literatures

which show that sunk costs and the revenue of a MNC

can be affected by the exchange-rate uncertainty [1-4]

and the government policy uncertainty [5,6].

With market and economic globalization, MNCs now

gradually tend to design and manage their supply chains

more efficiently on a worldwide basis. The network ac-

tivities of a corporation’s supply chain such as sourcing,

manufacturing, and distribution are based on handling all

flows of materials, information, and funds effectively and

efficiently within and across the chain. When a firm

faces a more complicated market environment, the mul-

tinational Supply Chain Management (SCM) becomes

more and more important. The managerial issues cover

problems with strategic and operational dimension such

as design and location of facilities, specification of sup-

ply contracts, choice of product variety, management of

inventories, and selection of transportation forms.

Many researchers have focused on how the flexibility

of exchange rate may affect a MNC’s operation; however,

they seldom consider the variability of market prices at

the same time. In this paper, we extend Huchzermeier

and Cohen’s [2] and Mohamed’s [4] model to develop a

new multi-period production-distribution model with

varying exchange rate and market price. Then, we use

quantitative approach to investigate for a MNC’s supply

chain design process for finding its optimal operating

decision by emphasizing the effects of uncertainties in

exchange rate and product price. The uncertainties of

exchange rate and product price are defined as stochastic

dynamic processes. Using stochastic dynamic program-

ming, we simulate the changes, the volatility, and the

variation speed of exchange rate and market price.

The goal of this research is to understand that the pro-

duction and distribution decisions for a MNC are over a

finite planning horizon. In other words, we would like to

determine a firm’s decision when facing to the variations

S.-C. CHANG

674

in market price and exchange rate. Therefore, the objec-

tive function is to maximize the profit of a MNC by re-

ducing production, distribution, and inventory costs un-

der the variations in exchange rate and market price. By

exercising this model, we can provide useful guidance

for a MNC to make operating decisions which involve un-

certainties in exchang e rate and market price.

This paper is organized as follows. Section 1 provides

a brief literature review for SCM related to MNCs. In

Section 2, we develop an integrated production planning

and distribution model for a MNC suitable for varying

exchange rate and market price. In Section 3, we estab-

lish a stochastic dynamic programming model by incor-

porating seven parameters including exchange rate and

market price. We verify the correctness of this model and

its optimal operation through a numerical example in

Section 4. Finally, conclusions are given in Section 5.

2. Literature Review

The previous studies on SCM for multinational opera-

tions within a network have largely involved the up-

stream and downstream flows of products, services, in-

formation, and finance. The term SCM was originally

introduced by consultants in the early 1980s and has

subsequently received much attention in manufacturing

operations. SCM was described by the logistic literature

as a new integrated logistic management approach across

different business processes such as purchasing, manu-

facturing, distribution, and sales. Later on, many manu-

facturing companies are willing to locate their facilities

in any part of the world in order to obtain cheap labor,

more reliable materials, parts, and subassemblies [7].

This integrated approach is extended outside the firm’s

boundaries to customers and suppliers. Such a trend has

incurred the problem of managing global operations for a

firm in different cultures, values, rules, and politics. Also,

since the Bretton Woods System was broken up, the sta-

bility of the competitive environment in the early 1970s

has been replaced by increasing uncertainty. Thus, a

MNC must face more ambiguities in the internal and

external environment such as shorter product life cycle,

quick change of customer’s preference, and many com-

peting rivals.

Many literatures have dealt with designing and man-

aging a network of facilities lo cated in different countries

in response to growing environmental uncertainty [8-12].

Hodder and Jucker [8] incorporated market price and

exchange-rate uncertainty and adopted cost minimization

via using a mean-variance objection function to analyze

the effect of uncertainty in one-period. De Meza and Van

Der Ploeg [9] also tried to capture th e value of flexibility

under uncertainty stochastic model of shifting production

in one-period. Koqut and Kulatilaka [10] analyzed ex-

plicitly the net present value of shifting production be-

tween two plants which located in two different countries

with exchange-rate movement using multi-period sto-

chastic model. Although these approaches have made con-

siderable progress in analyzing cost-minimization or pro-

fit-maximiz ation for multin ational operatio ns within a net-

work under market price or exchange-rate uncertainty,

they did not cons ider the flexibility of exchange-rate and

market price uncertainties over multiple periods.

On the other hand, the importance of global issues in

supply chain management and analysis has gradually

received more attention in recent literatures [6,13,14].

Cohen and Lee [13] developed a comprehensive mathe-

matical programming model for option valuation of

global manufacturing and distributing strategy and con-

structed a maximizing objective function for after-tax

profits. Although their approach included stochastic

variables in the su b-mode ls, the facility location, capacity

of plant and technology are assumed to be fixed. Thus,

they did not consider the random fluctuations of cur-

rency’s exchange rate on the network operation. Kulati-

laka and Koqut [14] explored how a MNC provides in-

centives to managers to modify production plans appro-

priately. They developed a stochastic dynamic program-

ming model to evaluate the cost based on varying ex-

change rate in multi-periods. They also determined the

quantity of shifting production between two manufactur-

ing locations in two different countries. However, the

decisions about material flow, product distribution, de-

mand and processing time uncertainties were not consid-

ered in their model.

Several literatures have proposed models for uncer-

tainty management in global supply chain. Such models

emphasize centralized decision-making and optimization

[2,15]. Huchzermeier and Cohen [2] extended Cohen and

Lee’s work [13] by taking exchange-rate uncertainty into

account to develop a stochastic dynamic programming

formulation for the evaluation of global manufacturing

strategy options with switching costs. Their model con-

sists of three sub-models: the stochastic exchange rate

sub-model, the valuation sub-model, and the supply chain

network sub-model. Moreover, they also considered plant

capacity and customer demand in their model. Among

these sub-models, the supp ly chain network sub-model is

to maximize the expected discounted after-tax profit of a

multinational firm. However, the formulation did not

include stochastic market prices and processing time.

Dasu and Li [12] analyzed the structure of the optimal

policies for a firm with operating plants located in two

countries based on a randomly changing exchange rate

and switching costs. Their approach can determine when

and how much to alter the quantities produced in differ-

ent countries. However, they failed to consider the in-

ventories carried from one period to the next in their

model.

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S.-C. CHANG 675

3. The Proposed Model

The MNC decisions discussed in this paper include pro-

duction strategies, international lo cations, and operation s.

Production strategies will determine the levels of prod-

ucts to be made and sold. The operation decisions in-

clude the distribution of products to various markets, and

different inventory levels of products. In this paper, we

would like to develop a stochastic dynamic programming

model which includes a stochastic exchange rate sub-

model, a pricing sub-model with varying sub-demand,

and a supply chain network sub-model to analyze global

manufacturing strategies.

Many research works proposed the measures for sup-

ply chain performance using objective functions directly

based on minimizing cost, maximizing sales, maximizing

profit, or maximizing returns from investments. Among

these objective functions, cost-minimization and profit-

maximization are widely used. In our model, the objec-

tive function is to maximize a MNC’s profit by consid-

ering plant capacity and demand satisfaction.

Profit is total revenue subtracted by total cost. Total

cost includes manufacturing cost, inventory cost, and dis-

tribution cost. Total revenue and total cost should incor-

porate exchange rates. We define the related variables

shown in Table 1.

3.1. The Exchange Rate Function and Total

Revenue Sub-Model

According to Harvey and Quinn’s model [16] and Mo-

hamed’s model [4], we assume that predicted exchange

rate in the t-th period for a target market in the

m-th period is a probability distribution function. Then,

the exchange rate can be expressed as



ˆmt







ˆmt mmt

epee.

According to Kaihara’s [17] argument, we assume that

dynamic price of a product is associated with the demand

for that product. So, the price of a product





depends on its market demand







TR . Hence, in any

given period, the total revenue from all markets

can be described by the foll o wi n g expression:



,, ,

tmtjmtjmt

mmt jmtjmt

TRe PD

pee PDD

















 ,

(1)

Based on the total revenue as described above, the

price is non-constant and can be expressed as being de-

pendent on the demand. That is,





,,jm tjm t

PPD

abD, , .



0PPD







0DPP

 



3.2. The Total Cost Sub-Model

The total cost can be expressed as

Table 1. Notations.

Notation Remark

Set of target markets





1,2, ,, ,mM

Set of facilities





1,2, ,, ,kK

Set of products





1, 2,,,,jJ

T Set of time periods





1,2, ,, ,tT

,jm t

P Unit price of sales for product j in period t for

target market m

,jm t

Demand quantity for product j in period t for

target market m

,mt

e The initial exchange rate in period t for target

market m





e Probability value of exchange rate for target

market m

,kt

e The initial exchange rate in period t for target

facility k





e Probability value of exchange rate for target

facility k

,kj t

CN Manufacturing cost per unit of pro d uct j at facility

k in period t

,kj t

Q Quantity of produc t j at facility k in period t

,jk t

P Inventory ho l ding cost per unit of product j at

facility k in period t

,jk t

I nventory quantity of product j at facility k in

period t

,jm t

P shipping cost of product j in period t for target

market m

,jmk t

DQ Quan t i t y of product j produced from facility k to

market m in period t

a Constant coefficient (i.e. intercept of

product-price equation)

b Constant coe f ficient (i.e. partial adjustment

coefficient of product-price)



DICOST MCOST INCOST

tktkt





,

(2)

where , is the distribution cost, ,

is the manufacturing cost, and , is the inven-

tory cost. Each of these costs is described as follows:

DICOSTkt MCOSTkt

INCO S Tkt

The distribution cost

In any given period, the distribution cost





DICOSTkt is expressed in dollars as follows:



,,,

DICOST MJ

ktkt jmtjmkt

eDP DQ





 ,

(3)

The manufacturing cost

The manufacturing cost is incurred by production cost

including labor cost, machine maintenance cost, and other

costs directly related to the capacity and raw material

purchasing cost. In any given period, manufacturing cost





MCOSTt is given by the formula:

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S.-C. CHANG

676



,,,

MCOST J

ktktkjtkjt

eCNQ





,



jmt



(4)

The inventory cost

If a MNC has excess in supply (i.e. the quantity of

good supply exceeds the quantity of good demand), they

will incur inventory expense. The inventory cost

IN ) can be expressed in dollars by incorpo-

rating the exchange rate in any given period as follows:

C O S Tkt



,,,

INCOST J

ktktjkt jkt

eIPI





 (5)

Total profit can be maximized by total revenue sub-

tracted by total cost. Therefore, the complete integrated

production and distribution model can be described as

follows:

Max

subject to

TR TC



 



,, ,

tmtjmt

TRe PD













,,,

MCOST INCOST DICOST

t ktktk









,,,

MCOST J

ktktkjtkjt

eCNQ









,,,

INCOST J

ktktjkt jkt

eIPI









,,,

DICOST MJ

ktkt jmtjmkt

eDP DQ







mt jmkt

DDQ





,,1 ,

kjt jktjmktjkt

QIDQI



 

,



ˆmt mmt

epee



ˆkt kkt

epee



mt jmtjmt

PpD abD

,,,,, ,,

,, ,,1

,,,,, ,

,, ,,,0

kt mtjmtjmtkjtkjtjkt

jk tjmtjmk tjk t

ee PDCN QIP

IDPDQIab



4. An Example

We demonstrate the usefulness of our proposed model

through a numerical example. The following scenario is

considered in this example. Assume that manufacturing

facilities exist (or to be built) in both home and host

countries and there is no capacity requirement. Any ma-

nufacturing facility only produces one kind of products

and supplies both home and host countries without any

arbitrage. There are two planning periods and two types

of demand function for products in our example. In addi-

tion, the unit manufacturing cost, unit distribution cost,

and unit inventory cost are kept constant in each same

period. However, product unit price is uncertain in each

individual market since this price must depend on market

demand.

Before simulating the effects of exchange rate and

market price function, we list all giv en parameters in Ta-

ble 2. The model is simulated using LINGO simulation

language.

5. Results and Discussion

The simulation results can be classified into three cate-

gories. The first category is the effect of production be-

havior when exchange rate has no significant change

while the market price is changing. The second category

is the effect of production behavior when exchange rate

decreases while the market price is changing. The third

category is the effect of production behavior when ex-

change rate increases while the market price is changing.

The simulation results for the above three categories are

given in Tables 3-5, respectively.

5.1. Exchange Rate Insignificant Change but

Market Price Changes

As we can see from Type A in Table 3, the optimal

products for home country and host country are 1470 and

1476 units, respectively, in both periods. The optimal

Table 2. Input parameters.

Home country Host country

Unit manufacturing cost$59.73 $23.28

Unit distributing cost $22 $20

Unit inventory holding

cost of product $4.57 $3.88

3000



 15000.5

PD

Price function for

product 3000



 2000

PD

Value of exchange rate in

initial period $2

The type of flexibility

exchange rate in next

period

no significantly

change Increasing Decreasing

The composite type of

flexibility exchange rate

in next period ($1 $2 $3) ($2 $3 $4) ($0.5 $1 $2)

Probability value of

exchange rate occurring

in second period (0.2 0.6 0.2) (0.2 0.6 0.2) (0.1 0.8 0.1)

Note: the value of exchange rate is exchange rate of currency of home coun-

ry. t

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677

Table 3. Results for no significantly changing exchange rates.

Type A Type B

Market

Period 1 Period 2 Period 1 Period 2

Home country 1470 1476 1470 1470

The produced quantity Host country 1470 1476 988 988

(From home country to host country)0 0 0 0

The shipped quantity (From host country to home country)0 0 0 0

Home country 0 0 0 0

The inventoried quanti ty Host country 0 0 0 0

Home country 1470 1476 1470 1470

The quantity of demand for

product Host country 1470 1476 988 988

Home country $1530 $1530 $1530 $1530

The price of product (expressed

by currency of ho me country) Host country $1544 $ 15 44 $2024 $2024

Total profits (expressed by currency of home country) $8,683,997 $8,230,016

Notes: Type A: demand function for product is in home country, and t

3000

P

DD1500 0.5



 in host country. Type B: demand function for

product is in home country, and t

in host country. 3000

P

DD2000

P

demands for products in home country and host country

in both periods are also 1470 and 1476 units, respectively.

Type B of Table 3 shows that the optimal products for

home country and host country are 1470 and 988 units,

respectively, in both periods. The optimal demands for

products in home country and host country are also 1470

and 988 units, respectively, in both p eriods. Based on the

results of Type A and Type B as described above, we

find that no matter how the market price changes, the

optimal demand is always equal to the production quan-

tity in both demand functions when exchange rate has

insignificant changes. However, the production quantity

will decrease when th e price-function becomes more fle-

xible.

The products of each country are produced internally

to supply the demands in both periods when exchange

rate has insignificant changes. Th e production quantity is

different as market-price varies. In other words, the best

operating decision of a MNC is to make products inter-

nally in each country and supply that country’s demand

without shipping and inventory if there is no significant

change in exchange rate. Moreover, a MNC should pay

attention to the change in production quantity if mar-

ket-price varies.

5.2. Exchange Rate Decreases and Market Price

Changes

When the currency of a host country is strong (decreas-

ing exchange rate) in the second period, we find that the

unit manufacturing cost in host country will decline. At

that time, a MNC must face two operating decisions. One

is to produce products in host country for both periods

and the other is to produce products for home country in

the factories at host country in the second period. Based

on the above decisions, we find that the first decision de-

rives $62.72 unit cost from the manufacturing cost in home

country and the second on e derives $45.44 un it cost fro m

the manufacturing and distributing costs. For a MNC, the

second decision is more economically efficient than the

first. The simulation results are shown in Table 4.

As we can see from Type A (Type B) in Table 4, the

optimal products for home country and host country are 0

and 2954 units (0 and 2465 units), respectively, in second

period. In addition, the optimal demands for products in

home country and host country are 1478 and 1476 units

(1477 and 988 units), respectively, in the second period.

The behavior of shipping products from host country to

home country occurs in the second period, and the quan-

tity of shipping is 1478 and 1477 units in Type A and

Type B, respectively. Hence, the market demand of home

country is supplied by the products produced in host

country if exchange rate decreases in the second period.

In other words, we choose an optimal operating decision

that will decrease the quantity of products being pro-

duced and shipped according to the variation in mar-

ket-price in host country for the second period, and sup-

ply the market’s demand in home country with the prod-

ucts manufactured in host country for the second period.

Hence, the quantity of producing and shipping is signifi-

cantly affected by the price-function forms. Thus, the

variation of market-price will affect the operating deci-

sions of a MNC.

5.3. Exchange Rate Increases and Market Price

Changes

When the currency of host country is weak (increasing

S.-C. CHANG

678

exchange rate) in the second period, we find that the unit

manufacturing cost in host country will increase. At that

time, a MNC must face two operating decisions. One is

that the products d emand ed by ho st co un tr y in the seco nd

period will be produced ahead of time. The other is that

the products demanded by host country in the second

period will be produced in home country. Based on the

above decisions, we find from Type A and Type B in

Table 5 that the first decision derives $54.32 unit cost

from the manufacturing and inventory cost in host coun-

try, while the second one d erives $64.3 unit cost from the

manufacturing and distributing costs. Thus, for a MNC,

the first decision is more economically efficient than the

second.

As we can see from Type A (Type B) in Table 5, the

optimal amount of products produced in host country are

2958 and 0 units (1479 and 0 units) in the first and sec-

ond period, respectively. In addition, the optimal de-

mands for products in host country are 1470 and 1482

units (988 and 991 units) in the first and second period,

respectively. Hence, the products to supply host country

in the second period will be produced ahead of time

when exchange rate increases. The behavior of invento-

rying products occurs in the first period and this quantity

is 1482 and 991 units in Type A and Type B, respec-

tively. In other words, a MNC in host country should

choose the optimal operating decision: decreasing the

quantity of products being produced and inventoried ac-

cording to the market-price change in host county in the

first period, and producing products ahead of time for the

Table 4. Results for decreasing exchange rates.

Type A Type B

Market

Period 1 Period 2 Period 1 Period 2

Home country 1470 0 1470 0

The produced quantity Host country 1476 2954 988 2465

(From home country to host country)0 0 0 0

The shipped quantity (From host country to home country)0 1478 0 1477

Home country 0 0 0 0

The inventoried quanti ty Host country 0 0 0 0

Home country 1470 1478 1470 1477

The quantity of demand for product Host country 1476 1476 988 988

Home country $1530 $1522 $1530 $1523

The price of product (expressed by

currency of home country) Host country $1544 $762 $2024 $1012

Total profits = (expressed by currency of home country) $7,669,216 $7,323,056

Notes: Type A: demand function for product is in home country, and t

3000

P

D1500 0.5





in host country. Type B: demand function for

product is in home country, and t

in host country.

3000

P 2000

P

Table 5. Results for increasing exchange rates.

Type A Type B

Market

Period 1 Period 2 Period 1 Period 2

Home country 1470 1476 1470 1470

The produced quantity Host country 2958 0 1479 0

(From home country to host country)0 0 0 0

The shipped quantity (From host country to home country)0 0 0 0

Home country 0 0 0 0

The inventoried quanti ty Host country 1482 0 991 0

Home country 1470 1476 1470 1470

The quantity of demand for product Host country 1470 1482 988 991

Home country $1530 $1530 $1530 $1530

The price of product (expressed by

currency of home country) Host country $1544 $2277 $2024 $3027

Total profits (expressed by currency of home country) $9,797,307 $9,222,230

Notes: Type A: demand function for product is in home country, and t

3000

P

D1500 0.5





product isin home country , and in host country .

in host country. Type B: demand function for

3000

PD 2000

PD

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S.-C. CHANG 679

eriod. Henduction

6. Conclusions

tend and modify the previous gl

sions under the environment with exchange-rate and mar-

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[1] J. M. Camparms in the United

States under Ey,” Review Eco-

second pce, quantities of pro and in-

ventories are significantly affected by price-functions.

This implies that the variation of market-price will affect

the operating policies o f a MNC.

In this paper, we exobal nomic Statistic, Vol. 74, No. 5, 1993, pp. 614-622.

supply chain network models to develop an integrated

production and distribution model for a MNC operating

under the environment with varying exchange rate and

market price. Our model incorporates two new charac-

teristics. First, exchange rate and processing time uncer-

tainties are considered in the model. Second, we allow

the market price of products to be dependent on the de-

mand levels and stock of existing products. The results

derived from the model show that planning a MNC’s cost

is the main factor for deciding which operating decision

should be chosen. This is similar to Mohamed’s [4] re-

sults, where the profit will decrease when the exchange

rate is decreased under the assumption of constant mar-

ket price for products. We demonstrate that a MNC can

utilize machines in the inventory or distribution to avoid

possible fluctuation in exchange rate. Through the com-

putational experiment, a MNC may choose to maintain

current operating decisions when exchange rate has no

significant change. However, if exchange rate decreases

and a flexible p rice-function form is used, the host coun-

try should overproduce and distribute the excess part of

products to the home country in order to minimize the

total cost. In addition, the host country should pay atten-

tion to the ch ange in quantity of produ cts being pro duced

and shipped according to the variation of market- p ri ce.

If exchange rate increases and price-function forms

ange, the firms of a MNC in the host country should

produce products ahead of time in order to minimize the

total cost and adjust the quantity of products being pro-

duced and inventoried according to the change in price-

function forms. That is, the firms of a MNC in the host

country should choose the optimal operating decision to

produce products ahead of time for the second period and

the host country should be able to adjust the quantity of

products being produced and inventoried, according to

the market-price’s variety. The potential benefit of this

operating strategy increases the firm’s profit and reduces

its downside risk. An interesting and somewhat surpris-

ing outcome of this an alysis is that the operating strateg y

is affected by the fluctuation in exchange-rate and mar-

ket-price’s variety because the quantity of products to be

produced, sh ipped, and inventoried will change based on

the variation in market-price when exchange rate is con-

sidered. In conclusion, we claim that the contribution of

this paper is to provide a manufacturing planning strat-

egy for a MNC to make more accurate operating deci-

ket-price uncertainties.

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