A MULTI-PERIOD MIXED INTEGER PROGRAMMING

MODEL FOR THE PROBLEM OF RELOCATING A GLOBAL

MANUFACTURING FACILITY

Abraham Zhang* and George Q. Huang

Department of Industrial and Manufacturing Systems Engineering, University of Hong Kong

Citation: Abraham Zhang, George Q. Huang. (2010). “A multi-period mixed integer programming

model for the problem of relocating a global manufacturing facility”. Journal of the Chinese Institute of

Industrial Engineers, 27(6), 407-417.

ABSTRACT

In recent years, changing business conditions have triggered labor-intensive global

manufacturers to consider relocating out of the Pearl River Delta (PRD) of China, known as

“The World’s Factory”. This paper presents a multi-period mixed integer programming

(MIP) model for the problem of relocating a global manufacturing facility. The objective

function of the model is to maximize total after-tax profit. The model addresses dynamic

aspects of timing, including potential developments in business factors and the need of a

gradual capacity transfer in order not to disrupt supply chain activities. The model application

generates an optimal capacity transfer schedule and forecasts after-tax profits. In general, a

stable exchange rate for the Chinese currency RMB would make lower-cost areas of China

more competitive. Also, dramatic RMB appreciation would enhance the comparative

advantage of Asian lower-cost countries. A rapid hike in oil prices would make locations near

major markets more favorable in order to avoid high transportation costs.

Keywords: facility relocation; global manufacturing; supply chain management; mixed

integer programming; Pearl River Delta

* Corresponding author: abraham.zhang@hkusua.hku.hk

1. INTRODUCTION

During the 1990s, the Pearl River Delta (PRD)

of China emerged as “The World’s Factory” for a

variety of labor-intensive products. A large number of

global manufacturers, funded mainly by investment

from Hong Kong and Taiwan, established their

operations in the region to take advantage of its low

labor costs and favourable industry policies. In recent

years, however, business conditions have changed

dramatically. Since 2005, the Chinese currency (the

Chinese Yuan also known as RMB) has appreciated

over 20% against the United States dollar (USD).

Labor costs in the region have climbed rapidly with

minimum wage standards increasing by about 70%

from 2004 to 2008 [4]. During the same period, the

price of international crude oil hit historical heights.

Transportation costs rose in line with oil prices.

Industrial policies for labor-intensive manufacturing

have also changed direction. In 2006 and 2007,

China’s central government reduced export

value-added tax (VAT) rebates for a very large

category of labor-intensive products. Local

governments in the PRD region started an industrial

restructuring program. Further set-up of

labor-intensive production operations has been

discouraged and existing ones encouraged to relocate.

With these changes, the business profit margin for

labor-intensive global manufacturing has dropped

sharply. Consequently, many global manufacturers

have started to relocate all or part of their production

activities or have made plans to do so [2, 3].

The facility relocation problem shares some

common attributes with the well-known facility

location problem [9, 17]. They are both concerned

with the determination of the optimal number,

capacity, and location of a set of facilities to serve

demands from a set of spatially distributed customers

[9, 10]. Both problems are strategic in supply chain

planning. Decisions made usually lead to a substantial

amount of irreversible investment on new site

construction and setup as well as hiring and training.

Nevertheless, the facility relocation problem is still

distinctively different from the facility location

problem in several ways. For facility relocation,

equipment and employees may be transferrable and

incur moving expenses and employee compensation.

Productivity may decrease at both existing facilities

and relocated facilities during the transition. In

addition, the relocation process must carefully manage

the phase-out of existing facilities and smooth the

transition into new facilities to minimize potential

disruption of supply chain activities [7].

The facility location problem has received

considerable attention from both academicians and

practitioners [9, 11, 13]. Due to their similarity, facility

relocation can draw insights from facility location

studies. Facility location problems are often modelled

through mixed integer programming (MIP) techniques

[18]. However, most MIP models assume static

business conditions and use a single-period planning

horizon [9]. These models are inadequate for the

realistic settings where there are significant changes

over time in the business environment. Such changes

are often the major cause of relocation [7], as now

experienced by global manufacturers in the PRD

region. It is thus essential to use multiple planning

periods to address the dynamic aspects of timing for

the relocation decision.

In contrast to the attention given to the facility

location problem, only a few models have been

developed for facility relocation. Melachrinoudis and

Min [7] built a multi-period MIP model for the

relocation and phase-out of a hybrid

plant/warehousing facility. Melo et al. [8] proposed a

MIP model for the strategic design of supply chain

networks. These two models considered relocation

costs and a gradual capacity transfer, factors unique to

facility relocation. However, both models dealt with a

domestic context and did not include international

factors which are crucial for global manufacturing.

The objective of this research is to develop a

multi-period MIP model for the facility relocation

problem faced by global manufacturers in the PRD

region. The model considers international factors

including currency exchange rates, tariffs, and transfer

pricing [15]. Dynamic aspects of time-sensitive

business factors are incorporated through multi-period

parameters and the design of experimental scenarios.

Model application is illustrated through a

representative case. An optimal capacity transfer

schedule is generated and after-tax profits are forecast.

The case study also offers managerial insights about

where and when to relocate global manufacturing

operations.

The rest of this paper is organized as follows.

Section 2 describes the research problem. Section 3

develops a multi-period MIP model. Section 4

illustrates the model application and gives results.

Section 5 concludes the research and identifies future

work.

2. PROBLEM DESCRIPTION

The problem faced by global manufacturers in

the PRD region can be illustrated through a

hypothetical footwear business representative of

business in the region. Footwear is a typical

labor-intensive product. The global manufacturer

operates under the business mode of processing trade,

which is characterized by processing locally while

utilizing imported raw materials and exporting finished

products. Processing trade involves about 70,000

enterprises in the PRD region and accounted for 47.2%

of China’s total foreign trade in 2006 [1]. Figure 1

depicts its supply chain configuration. The

headquarters in Hong Kong controls business level

communications. Finished products are first sold from

factories to the headquarters under internal transfer

prices, and then traded with overseas customers. Long

term customers include large retailers like Wal-Mart

Stores, Inc. and they set free on board (FOB) prices.

The global manufacturer bears trucking costs to the

nearest seaports. Production relocation will not affect

market demand as long as it does not affect supply

chain costs born by customers.

Offshore trade allows physical cargoes to be

shipped from factories to customers directly. The

trading affiliate acts as a consigner but is not involved

in the day to day order fulfilment. Such a business

arrangement minimizes tax duties as Hong Kong levies

taxes on a territorial basis. In fact, offshore trade

represented 93% of total exports of goods in Hong

Kong in 2005 [1]. This study considers the preferred

situation that business negotiation also occurs outside

of Hong Kong, and thus corporate income tax levied

on the trading operation is reduced to zero.

Figure 1: A representative supply chain

Global manufacturers face several challenges as

they consider relocation. The first challenge is

choosing where to relocate. Possibilities can be

grouped into three categories: lower cost areas in

China, lower cost countries in Asia, and low cost

countries near major markets. Though labor costs in

the coastal areas of China have climbed rapidly in

recent years, most non-coastal areas have maintained

relatively stable labor costs. Relocation to lower cost

countries in Asia avoids risks from continual RMB

appreciation and the decrease of export VAT rebates in

China. Relocation to low cost countries near major

markets minimizes risks associated with high oil

prices. A qualitative appraisal has shortlisted a

representative location from each category. They are

Qingyuan, Guangdong, China (O-PRD), Chennai,

Tamil Nadu, India (India) and Baja California, Mexico

(Mexico). Investment incentives are available at all

three locations. However, such a qualitative analysis is

not sufficient for the facility relocation decision. It is

necessary to employ a sound analytical tool to quantify

costs and profits.

The second challenge arises from the strategic

nature of the decision. New facilities are expected to be

in operation for an extended time period in order to

recover relocation costs. With changes in the business

environment, a currently profitable factory could

become unprofitable in the future. Decision makers

need to understand the optimal relocation destinations

under various business environment scenarios. Such an

understanding will help decision makers weigh the

risks against benefits before committing a substantial

investment.

The third challenge is the planning of a gradual

capacity transfer in order not to disrupt demand

fulfilment. A realistic approach is to divide relocation

into several phases and implement them step by step. If

more than one new facility is to be established, the

sequence of facility setup needs to be optimized.

3. MODEL DEVELOPMENT

3.1 Model assumption

This research builds a multi-period MIP model to

help resolve the above facility relocation problem and

overcome its challenges. It is assumed that trade

operation remains at the headquarters in Hong Kong

due to its favourable tax policies. Multiple

manufacturing facilities in the PRD region are viewed

as a single facility by consolidating all their

transferrable capacity. Their facility index f is 1. It is

possible that the global manufacturer may keep some

capacity in the PRD region to support its product

design and development in the region. Such a residual

capacity is excluded from the scope of this study. The

planning horizon is 10 years, which is typical for a

strategic facility location/relocation decision. The

planning horizon is divided into 10 periods and each

period represents one year. Model formulation

assumes that freight costs vary linearly with oil price.

Prevailing tariff rates do not change in the planning

horizon. Following Melachrinoudis & Min [7], the

model has several other underlying assumptions:

Model formulation is based on the

single-product case. Model application

considers multiple commodities in the same

product family by using weighted average prices

and costs.

Demand in a period is met by production in the

same period. Just-in-time production mode has

gained popularity. As the duration of a period is

as long as one year, inventory carried over from

one period to another could be neglected.

No capacity transfer occurs in period 0 to

account for the time required for planning and

new site setup. New site setup and capacity

transfer are finished at the start of a period.

Closure of an existing facility happens at the end

of a period.

Capacity at a new location is non-decreasing in

the planning horizon. It often takes several years

to recover relocation costs and overcome the

learning curve at new sites. Thus, newly

installed capacity is not expected to be removed

during the planning horizon.

Current capacity is sufficient to meet future

demand in the planning horizon and capacity

expansion is not considered. However, the

model can be extended for capacity expansion

and reduction scenarios [8].

3.2 Notations

Indices

m The index for markets, Mm ,...,1

f The index for facilities, Ff ,...,1

t The index for time periods, Tt ,...,0

Parameters

mtD Yearly demand at market m in period t

mtSCC Unit supply chain cost for goods to arrive at

market m in period t

fDFC Base domestic freight cost per unit from

facility f to nearest seaports

fmIFC Base international freight cost per unit from

facility f to market m

ftRMC Delivery duty paid raw material cost per unit

at facility f in period t

ftOVC Other variable cost per unit at facility f in

period t

ftFSC Fixed one time cost for the setup or closure of

facility f in period t

ftFOC Fixed operating cost at facility f in period t

tFHQ Fixed operating cost of the headquarters in

period t

tCHQ Capacity retaining cost of the headquarters in

period t

ftCRC Unit capacity retaining cost at facility f in

period t

ftRLC Unit capacity relocation cost from existing

facility to facility f in period t

ftDLC Unit direct labor cost at facility f in period t

tOP Oil price average in period t

OPB Oil price at base level

fte Exchange rate to USD from the currency used

at facility f in period t

ftTAX Corporate income tax rate at facility f in

period t

ftVAT Realized VAT rate at facility f in period t

fmIDT Inventory days for finished products in transit

from facility f to market m

fmTAR Tariff rate imposed by market m for products

from facility f

Correlation factor between freight costs and

oil price

Inventory holding cost coefficient

t A fraction of total transferrable capacity up to

period t

fLB Lower bound of the transfer price at facility f

Q Initial transferrable capacity

L A sufficiently large constant

Variables

fmtq Production quantity at facility f for market m

in period t

ftCAP Capacity of facility f in period t

ft Operating status of facility f in period t (1 if in

operation; 0 otherwise)

fmtSP Selling price per unit at FOB term from

facility f to market m in period t

ftOI Operating profit at facility f in period t

ftOI Operating loss at facility f in period t

3.3 Model formulation

Based on the above defined notations, several

cost components can be derived. Variable

manufacturing cost consists of raw material cost, direct

labor cost and other variable cost:

ftftftftft eOVCDLCRMCMFGC )( tf ,

(1)

Domestic freight cost is a function of base

domestic freight cost and oil price:

fttfft eOPBOPDFCDFCC ))1/(1( tf ,

(2)

The headquarters in Hong Kong has the lowest

tax rate and a lower transfer price always leads to a

higher after-tax profit. Thus, upper bounds are not

considered in the model. The transfer price at its lower

bound can be derived as:

))(( ftftftftfftffmt OVCDLCeRMCLBMFGCLBTP

tmf ,,

(3)

Value-added tax is charged based on the

difference between the transfer price and raw material

cost. It can be obtained as:

ftftfmtfmt VATRMCTPVATC )(

ftftftftftftf VATRMCOVCDLCeRMCLB )))(((

tmf ,,

(4)

The objective function

The objective function is to maximize total

after-tax profit from period 1 to 10. By summarizing

net profits at the headquarters and manufacturing

facilities, the objective function can be expressed as:

Maximize:

T

t

F

f

M

m

F

fftttfmtfmtfmt CAPCHQFHQqTPSP

1 1 1 1

))((

+

T

t

F

fftftft OIOITAX

1 1

))1((

(5)

Constraints

Operating income at manufacturing facilities is

the difference between sales revenue and operating

costs. Operating costs include variable manufacturing

cost, domestic freight cost, value-added tax, capacity

retaining cost, fixed operating cost, relocation cost and

fixed setup cost. Using non-negative variables

ftOI and

ftOI to distinguish operating profits and

operating loss [15, 16], operating income can be

expressed as:

ftft OIOI

M

mfmtfmtftftfmt qVATCDFCCMFGCTP

1

)(

ftftftft FOCCAPCRC

)1()1( tfftfttfftft FSCCAPCAPRLC

1, tf

(6)

Substituting fmtTP , ftMFGC , ftDFCC and

fmtVATC with equations (1)~(4), constraint (6) can be

rewritten as:

ftft OIOI =

))((

))(((1

ftftftft

M

mftftftftf

eOVCDLCRMC

OVCDLCeRMCLB

fmtftftftftftftf

fttf

qVATRMCOVCDLCeRMCLB

eOPBOPDFC

))))(((

))1/(1(

ftftftft FOCCAPCRC

)1()1( tfftfttfftft FSCCAPCAPRLC

1, tf

(7)

Supply chain costs born by customers include

purchasing cost, inventory holding cost for goods in

transit, international freight cost and import tariffs paid

to the customs [5]. Production relocation is not

intended to affect supply chain costs and this condition

can be expressed as:

mtfmfmt

tfmfmfmtfmt

SCCTARSP

OPBOPIFCIDTSPSP

)1/(1(

tmf ,,

(8)

Besides constraints (7) and (8), the MIP model

includes other constraints listed as follows:

QCAPft 0,1 tf

(9)

0ftCAP 0,2 tf

(10)

QCAPCAP t

T

ttfft

1)1( 1,1 ft

(11)

QCAPF

fft

1

1t

(12)

0)1( tfft CAPCAP 1,2 tf

(13)

f

mtfmt Dq tm ,

(14)

M

mftfmt CAPq

1

tf ,

(15)

ftft LCAP tf ,

(16)

}1,0{ft tf ,

(17)

fmtq and ftCAP are integers tmf ,,

(18)

All variables 0

(19)

Equations (9) and (10) initialize production

capacity in period 0. Constraint (11) limits the fraction

of capacity transferred by each period. The upper

bound t is expressed as a fraction of initial capacity

and is an increasing function of time. It reflects the

practical need of a gradual capacity transfer in order

not to disrupt demand fulfilment [7]. Equation (12)

ensures that total capacity remains unchanged.

Constraint (13) sets production capacity as

non-decreasing at relocation destinations in the

planning horizon. Equation (14) is a demand

constraint. Constraint (15) is a capacity constraint.

Constraint (16) ensures no capacity remains in a closed

facility. Constraints (17) to (19) define the

characteristics of variables.

It is well known that MIP is non-deterministic

polynomial-time hard (NP-hard) due to the existence

of integer variables. The branch-and-cut method,

which integrates the branch-and-bound and the cutting

plane algorithms, has been widely used to solve MIP

models efficiently [6]. The MIP model presented

above is solved by the branch-and-cut method through

commercial mixed integer solver ILOG CPLEX

11.2.0. For the representative case given in the

following section, the model formulation requires 220

integer variables, 619 continuous variables, and 838

constraints. The CPU running time for all experimental

scenarios ranges from 2 to 10 seconds on a computer

with Intel® Dual-core 1.5G processor and 2G RAM.

This shows the computational performance of the

model is comparable with that of Melachrinoudis and

Min [7]. It is also reported in the literature that integer

programming models of a much larger problem size

can be solved through ILOG CPLEX solver within an

acceptable CPU running time [14, 19].

4. MODEL APPLICATION AND

RESULTS

4.1 Experimental data

The MIP model is applied with the

representative global footwear manufacturer in the

PRD region as described in section 2. Markets

considered are the United States (US), the European

Union (EU) and Japan. Their demands are 3,840,000,

2,880,000 and 1,920,000 units respectively in period

0, with annual increases of 96,000, 72,000 and 48,000

respectively in the following 10 periods. Initial

capacity Q is 10,800,000 units per year. Capacity

transfer limit t is 0% in period 0, 20% in period 1,

60% in period 2, and reaches 100% from period 3

onwards.

Tables 1 to 3 present input data according to

parameter definitions as given in section 3. All

transportation modes use 40FT containers, each

containing 4,800 units of finished products. The

correlation factor between oil price tOP and freight

costs, ftDFCC and fmtIFCC , is 40.4% in relation to

base oil price OPB of $75 per barrel [12]. Inventory

holding cost coefficient is 25% per year. All cash

values are in 2008 constant dollars.

Table 1: Import tariff rates, international freight costs and inventory days in transit

To

From fmTAR fmIFC fmIDT

US EU Japan US EU Japan US EU Japan

PRD 20% 16.9% 8% $0.593 $0.445 $0.240 28 28 10

O-PRD 20% 16.9% 8% $0.593 $0.445 $0.240 28 28 10

India 20% 11.9% 8% $0.752 $0.451 $0.646 35 18 18

Mexico 0% 0% 4% $0.167 $0.351 $0.844 7 14 28

Table 2: Domestic freight costs and tax related data

fDFC ftVAT fLB ftTAX

PRD ¥0.288 4% 1.3 15% for 5..0t ; 25% for 10..6t

O-PRD ¥0.552 4% 1.3 0% for 5..0t ; 12.5% for 8..6t ; 25% for 10..9t

India $0.049 0% 1.4 0% for 5..0t ; 22.75% for 10..6t

Mexico $0.042 0% 1.4 0% for 5..0t ; 20% for 10..6t

Table 3: Time-sensitive cost data for the first period

Costs closely related with labor cost Other costs

ftFSC ftRLC ftDLC Increase

per year ftFOC ftCRC ftOVC Increase

per year

PRD ¥500,000 0.00 ¥10.22 8.1% ¥500,000 ¥8.82 ¥1.20 2.3%

O-PRD ¥300,000 ¥5.83 ¥7.85 5.3% ¥300,000 ¥6.46 ¥0.96 -0.4%

India $150,000 $1.94 $0.94 4.5% $50,000 $1.15 $0.12 3.0%

Mexico $300,000 $2.92 $2.17 2.4% $130,000 $2.03 $0.09 0.8%

Parameters such as direct labor cost and capacity

retaining cost are highly time-sensitive. They are

adjusted based on constant dollars according to

historical trends from 2000 to 2008 [20]. Data in 2008

are used for the first period. For manufacturing

operations, these costs are categorized in table 3 and

the rates of increase per year are given. For the

headquarters in Hong Kong, its fixed operating cost

tFHQ is $100,000 and unit capacity retaining cost

tCHQ is $0.13 in the first period. Both values

decrease by 0.7% every year. Unit supply chain costs

mtSCC are $7.8, $7.4, and $7.1 respectively for the

US, EU and Japan markets in the first period, with an

annual increase of 1.3% per year. Raw material costs

are stable at $2.35 per unit at all locations.

Key operational attributes of this representative

company are based on a leading global footwear

manufacturer in the PRD region [21]. Supplementary

data were collected from industrial practitioners, Hong

Kong Trade Development Council (HKTDC),

Investment Commission of India, ProMexico, Werner

International, State Administration of Foreign

Exchange (China), Ministry of Finance (China),

Guangdong Municipal Labor & Social Security

Bureau, United States Department of Labor, Japan

Customs, Shenzhen Container Trailer Association, two

major shipping lines, and two international freight

forwarders.

4.2 Experimental scenarios

Parameter values presented above do not

include RMB exchange rate and oil price, which both

demonstrated a high level of uncertainty in recent

years. The RMB has been under pressure to appreciate,

but it is difficult to predict its rate of appreciation. Oil

price has risen and fluctuated wildly in the past five

years. The rising trend is generally expected to

continue. However, its future movement may still be

very volatile. To incorporate these uncertainties, three

experimental scenarios are designed for these two

business factors, and they are illustrated in figure 2(a)

and (b).

For RMB exchange rate, the stable scenario

defines that RMB to USD exchange rate will be stable

at 0.143. The modest appreciation scenario assumes

that RMB will appreciate by 2% per year against USD,

while the dramatic appreciation scenario represents a

higher ratio of 4% per year. For oil price, a 25%

fluctuation is incorporated into each scenario in

consideration of its historical volatility. Dashed lines

in figure 2(b) represent moving averages. The stable

scenario sets a constant moving average of $80 per

barrel. The modest rise scenario assumes that oil price

will increases by 5% each year from the average of $80

per barrel as in the first period. The dramatic rise

scenario presumes an increase of 10% each year.

0.13

0.15

0.17

0.19

0.21

0 1 2 3 4 5 6 7 8 9 10

(a)

RM

B to U

SD

Stable

Modest appreciation

Dramatic appreciation

0

50

100

150

200

250

0 1 2 3 4 5 6 7 8 9 10

(b)

Oil

price $

/barr

el

Stable

Modest rise

Dramatic rise

Stable

Modest rise

Dramatic rise

Figure 2: Experimental scenarios on RMB exchange rate and oil price

Table 4: Optimal capacity transfer (in 1000 units) and profits (in $million) in the base scenario

Period 1 2 3 4 5 6 7 8 9 10

PRD -2,160 -4,320 -4,320

O-PRD 0 0 3,408

India 2,160 4,320 912

Mexico

Profit -$2.6 -$3.4 $4.1 $9.5 $9.0 $9.7 $10.6 $9.8 $8.9 $9.5

Table 5: Modeling results in all experimental scenarios (profit in $million)

Facility status after

the transition period Production allocation

RMB

scenario

Oil price

scenario Profit PRD O-PRD India Mexico

US

market

EU

market

Japan

market

Stable Stable $93.9 0 1 1 0 O-PRD India O-PRD

Stable Modest $87.3 0 1 1 0 O-PRD India O-PRD

Stable Dramatic $78.3 0 1 1 0 O-PRD India O-PRD

Modest Stable $72.4 0 1 1 0 India, O-PRD India O-PRD

Modest Modest $65.1 0 1 1 0 India, O-PRD India O-PRD

Modest Dramatic $56.4 0 1 1 1 Mexico, O-PRD India O-PRD

Dramatic Stable $66.3 0 0 1 0 India India India

Dramatic Modest $58.0 0 1 1 0 India India India, O-PRD

Dramatic Dramatic $48.0 0 1 1 1 Mexico, India India India, O-PRD

4.3 Results and findings

Table 4 presents modeling results in the base

scenario, in which both RMB exchange rate and oil

price will rise modestly. All transferrable capacity is

suggested to relocate out of the PRD region. The

optimal capacity transfer schedule is to first set up in

India to produce for the EU market, and then for the US

market. The last step is to transfer remaining capacity

to O-PRD in the third year to produce for the Japan and

US markets. After the capacity relocation out of the

PRD region, demand in the US market will be met by

production from both O-PRD and India. Production

allocation between these two facilities will vary in

periods to minimize total cost as a response to changes

in business factors especially oil price. In the first two

years of the transition period, operating loss is

expected due to high relocation expenditures.

However, after-tax profits will be much improved after

the transition.

Optimal relocation decisions are also obtained

for alternative scenarios. The combination of 3

scenarios for both RMB exchange rate and oil price

leads to 9 scenarios in total with the inclusion of the

base scenario. Scenario definition and optimization

results are given in table 5.

Modeling results show that the EU market

should mostly be served from production in India.

Besides the labor cost advantage in India, favorable

tariffs play an important role. Footwear products of

China origin suffer from the antidumping tariff rate of

16.9% in the EU market, while those of India origin

enjoy the preferential tariff rate of 11.9%. In

comparison with China, manufacturing in India to

serve the EU market also benefits from lower freight

costs due to a shorter shipping distance.

Demand in the US should be fulfilled from

O-PRD if the RMB exchange rate stays stable. If the

RMB appreciates 2% or 4% per year against the USD,

India would become most cost competitive as long as

oil price does not rise dramatically to drive up freight

costs. If oil price increases by 10% per year as in the

dramatic scenario, the effect of high oil price would

become dominant to make Mexico most attractive to

serve the US market. The North American Free Trade

Agreement (NAFTA) is also crucial for the potential

shift of manufacturing to Mexico. As can be seen from

table 1, labor-intensive footwear products from

Mexico incur zero tariffs in the US market, while those

from China or India are imposed with very high tariff

rates of 20% on average.

The Japan market should be served by

production in O-PRD in most cases. If the RMB

exchange rate is stable or appreciates modestly at 2%

per year, O-PRD will maintain its comparative

advantage over India. If the RMB appreciates 4% per

year as in the dramatic scenario, India will become

more favorable. However, even if that is the case, a

portion of demand should still be fulfilled from O-PRD

if oil price rises modestly or dramatically. This is

because the logistics advantage of O-PRD at higher oil

prices partially offsets its disadvantage from the

dramatic RMB appreciation.

These above findings are expected to be valid in

general for labor-intensive global manufacturers in the

PRD region whose supply chains and cost structures

are similar to the representative company. Varying

degrees of labor-intensiveness and

freight-intensiveness may lead to differences in

optimal relocation decisions. However, the general

cause-and-effect relationships do not change.

5. CONCLUSIONS AND FUTURE

WORK

This paper deals with the facility relocation

problem of global manufacturing. The research is

motivated by the changing business conditions in the

Pearl River Delta of China, known as “The World’s

Factory” since the 1990s. Rising operating costs in the

region have triggered global manufacturers to plan for

relocation. A multi-period mixed integer programming

facility relocation model is developed for global

manufacturers in the region. Modeling results suggest

optimum relocation decisions.

This paper makes several contributions. First, it

identifies research opportunities on the relocation of

labor-intensive global manufacturing out of the Pearl

River Delta of China. The phenomenon is significant

and warrants further study. Second, a multi-period

facility relocation model is presented for the industrial

problem, and its application is illustrated through a

representative case. The model employs multiple

planning periods to addresses dynamic aspects of

timing, including potential developments in business

factors and the need of a gradual capacity transfer in

order not to disrupt demand fulfilment. Third,

modeling results offer managerial insights on

labor-intensive global manufacturing location and

relocation decisions. In general, a stable RMB

exchange rate would make lower-cost areas of China

more competitive. Dramatic RMB appreciation would

enhance the comparative advantage of manufacturing

in Asian lower-cost countries, which are represented

by India in the numerical example. A rapid hike in oil

prices would cause global manufacturing to move near

major markets, for example, Mexico in relation to the

US market.

The research has its limitations. First, as most

products from the PRD region compete mainly on cost

in international markets, the modeling work focuses on

cost. Modeling results may not be applicable for global

manufacturers with different competitive strategies

like marketing, product design and development, etc.

Second, the quantitative analysis does not consider

intangible factors, for example, political stability and

cultural differences. In addition, suggested relocation

decisions are subject to future uncertainties. The

research does not exclude the possibility that it may be

altered by unexpected factors.

An immediate extension of the multi-period

model will be to address uncertainties through

stochastic programming. Uncertainties in demand and

business operating costs will be considered.

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ABOUT THE AUTHORS

Abraham Zhang is a Ph.D. candidate in the

Department of Industrial and Manufacturing Systems

Engineering, The University of Hong Kong. He

obtained his Dual Master Degrees in Industrial

Engineering from Georgia Institute of Technology

(USA) and in Logistics and Supply Chain Management

from National University of Singapore. His research

activities include global manufacturing, supply chain

management, mathematical modeling.

George Q. Huang is a professor in the Department of

Industrial and Manufacturing Systems Engineering,

The University of Hong Kong. He obtained BEng and

PhD degrees from Southeast University (China) and

Cardiff University (UK) respectively. He has

conducted extensive research in collaborative product

development, ubiquitous manufacturing and

cross-border logistics with substantial financial

supports from the university, government and

industrial funding bodies.

(Received March 2010; revised June 2010; accepted

July 2010)

針對全球化製造工廠搬遷問題的多階混合整數規劃模型

張錫平*，黃國全

香港大學工業與製造系統工程系

香港薄扶林道

摘要

最近幾年，營商環境的變化導致勞動密集型的全球化製造商考慮搬離

享有“世界工廠”聲譽的中國珠江三角洲。本文提出一個針對全球化

製造工廠搬遷問題的多階混合整數規劃模型。該模型的目標函數實現

稅後利潤的最大化。該模型考慮與時間相關的動態因素，包括營商環

境的變化趨勢以及分階段的產能轉移以避免擾亂供應鏈管理。應用該

模型可以制定最優的產能轉移計劃並預測稅後利潤。總體而言，穩定

的人民幣匯率有利於提高中國内陸低成本地區的競爭力。人民幣快速

升值則會導致亞洲更低成本國家獲得比較競爭優勢。為避免高昂的運

輸成本，油价高漲有可能使靠近主要國際市場的地區獲益。

關鍵詞：選址，全球化製造，供應鏈管理，混合整數規劃，

珠江三角洲

（*聯絡人：abraham.zhang@hkusua.hku.hk）