Is Reshoring Better than Offshoring?The Effect of Offshore Supply Dependence

Li ChenSamuel Curtis Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853

li.chen@cornell.edu

Bin HuKenan-Flagler Business School, University of North Carolina, Chapel Hill, NC 27599

bin hu@unc.edu

In this paper we investigate the effect of offshore supply dependence (OSD) on offshoring-reshoring profit

comparisons. We find that OSD hampers a reshoring manufacturer’s responsiveness to demand information

updates and may significantly affect offshoring-reshoring comparisons, such that reshoring may yield lower

profits than offshoring in many cases, including when offshoring has no baseline-cost advantage. We then

show that OSD also affects how salient costs such as customs duties and shipping costs influence offshoring-

reshoring profit comparisons. We further identify common-component designs as a mitigating measure to

make reshoring more appealing under OSD, and numerically confirm the robustness of our results.

Key words : offshoring, reshoring, offshore supply dependence, responsiveness, demand update, pooling

History : file version July 30, 2016

1. Introduction

For nearly three decades, offshoring has been the predominant trend of the US manufacturing

industry. The top driver of this trend is the substantially lower labor costs in emerging economies.

Recently, this labor arbitrage has been gradually tapering off as wages in developing economies

such as China and India increase by 10-20% annually, putting a spotlight on the drawbacks of

offshoring, including shipping costs and lead-times, lost manufacturing expertise, potential intel-

lectual property leakage, increased disruption risks, and political pressure (The Economist 2013).

Accordingly, a growing number of US-based companies started to consider bringing factories back

to the US—dubbed reshoring—and some have taken actions. In December 2013, Apple announced

that they had started producing the Mac Pro computers in a Texas plant as part of a US$100

million Made-in-the-USA push (Burrows 2013). Google also assembled its Moto X smartphones in

the US and heavily advertised this initiative (King 2013). However, the adoption of reshoring has

1

2

been slower than many have hoped, generating much discussion (Schoenberger 2013). Practitioners’

views on whether reshoring is viable and scalable are divided (Hertzman 2014, Wang 2014).

Despite rapidly shrinking cost differences between offshoring and reshoring, labor costs are still

the top driver of manufacturers’ global supply chain re-structuring decisions, according to recent

surveys by Chen et al. (2015) of a large number of multi-national companies. Taking the cost

consideration one step further, a Boston Consulting Group (BCG) report argues that when making

supply chain re-structuring decisions, “companies should undertake a rigorous, product-by-product

analysis of their global supply networks that fully accounts for total costs, rather than just factory

wages” (Sirkin et al. 2011). Indeed, researchers have rigorously analyzed issues beyond direct cost

comparisons. A notable example is responsiveness (Donohue 2000, Wang et al. 2014, Wu and Zhang

2014). The common notion is that reshoring reduces the products’ shipping lead-times and allows

production decisions to be postponed based on more accurate demand information.

However, the above notion about reshoring’s superior responsiveness ignores the potential issue

of limited onshore supply availability—which makes frequent appearances in practitioners’ discus-

sions about reshoring. Chen et al. (2015) and Cohen et al. (2016)’s survey respondents rate supply

availability to be among top drivers of multi-national companies’ supply chain re-structuring deci-

sions. The BCG report by Sirkin et al. (2011) lists well-developed supply networks as one of China’s

strengths as an offshoring destination. A New York Times article (Duhigg and Bradsher 2012)

also depicts the superior supply availability in China’s iPhone supply chain: “You need a thousand

rubber gaskets? That’s the factory next door. You need a million screws? That factory is a block

away.” On the other hand, during the long-lasting offshoring movement, onshore supply bases have

gradually withered as manufacturing moved overseas (The Economist 2014). Shih (2014) summa-

rizes, “Over time, China-based manufacturers localized their supply chains...For industries such as

electronics...moving production back to a country such as the United States therefore often means

a manager will face a hollowed-out supply base.” In fact, Google’s “made in the USA” Moto X

smartphone was revealed to contain components that mostly came from overseas (King 2013).

The above evidence suggests that many firms, should they choose to reshore manufacturing,

would continue depending on offshore suppliers until the reemergence of full-fledged onshore supply

bases. Such offshore supply dependence (OSD) may potentially undermine a reshoring manufac-

turer’s responsiveness. We explained earlier that, assuming perfect onshore supply availability,

reshoring reduces product shipping lead-times and allows production decisions to be postponed

based on more accurate demand information. However, under OSD, while reshoring can reduce

3

finished product shipping lead-times, it would at the same time increase material and compo-

nent shipping lead-times; therefore, while production decisions are postponed, component purchase

decisions are not. As a result, OSD hampers a reshoring manufacturer’s responsiveness to demand

information updates. In addition, OSD also implies that a reshoring manufacturer still needs to

engage in cross-border transactions for components. Accordingly, expenses such as customs duties

and shipping costs remain relevant to reshoring manufacturer under OSD.

In this paper, we seek to answer three main research questions. First, how does OSD affect a

reshoring manufacturer’s responsiveness to demand information updates and impact offshoring-

reshoring profit comparisons? Second, how do salient costs of cross-border transactions such as

customs duties and shipping costs influence offshoring-reshoring profit comparisons under OSD?

Third, what mitigating measures could one take to make reshoring more appealing under OSD?

To address these research questions, we consider a manufacturer whose factory converts com-

ponents sourced offshore into finished goods to meet random onshore demands. The factory may

be either close to the supplier under offshoring or close to the market under reshoring. There are

two decision stages. Under offshoring, the offshore production decision precedes the finished good

shipping decision, whereas under reshoring with OSD, the components shipping decision is followed

by the onshore production decision. We assume that more accurate demand information will be

revealed between the two decision stages through certain marketing events (Fisher and Raman

1996). Note that demand information updates typically come from marketing departments and

thus are not affected by where products are manufactured; what is different between offshoring

and reshoring is how the manufacturer can respond to such information updates. In particular,

an offshoring manufacturer may either adjust the inventory level upward by rushing a production

order before shipping (without worrying about component supply), or adjust it downward by not

shipping all finished goods. By contrast, a reshoring manufacturer under OSD may either adjust

the inventory level upward by expediting more components from offshore before production begins,

or adjust it downward by not processing all shipped components into finished goods.

To demonstrate the effect of OSD, we first introduce a benchmark case where OSD is ignored,

namely the reshoring manufacturer has access to unlimited onshore component supply with negli-

gible lead-time. Reflecting the current industry reality, we analyze the benchmark model (as well as

all other models throughout this paper) on the premise that offshoring has equal or lower“baseline-

cost” than reshoring, namely offshoring’s unit cost of goods sold under regular operations is equal

to or lower than reshoring. Our analysis reveals a basic tradeoff between offshoring’s baseline-cost

advantage and reshoring’s responsiveness advantage which is well documented in the literature

4

(Wang et al. 2014, Wu and Zhang 2014). In particular, when offshoring has no baseline cost advan-

tage, reshoring ignoring OSD dominates offshoring due to its responsiveness advantage.

We then show how OSD significantly cripples reshoring’s responsiveness advantage, revealing

new insights into the cost-responsiveness tradeoff between offshoring and reshoring. Under OSD,

reshoring’s responsiveness advantage is determined by the costs of (OSD-related) inventory adjust-

ments after demand information updates. Specifically, the upward and downward-adjustment costs

under OSD are the costs of expedited shipping and discarded components, respectively. We show

that when the expedited shipping cost (upward-adjustment cost) is relatively low, the offshoring-

reshoring comparison retains the same structure as when OSD is ignored, with a shrinking reshoring

region (as one would expect). However, when the expedited shipping cost is relatively high, OSD

drastically alters the structure of the offshoring-reshoring comparison. In particular, if the discarded

component cost is also relatively high, reshoring under OSD can be dominated by offshoring, yield-

ing the most striking contrast to when OSD is ignored. In this case, reshoring’s upward and down-

ward adjustments are both costly, which completely wipe out reshoring’s responsiveness advantage

over offshoring. Therefore, ignoring OSD may exaggerate reshoring’s responsiveness advantage,

leading to misguided favorable predictions about reshoring, while in fact the opposite may be true

should OSD be properly accounted for.

We next investigate how salient costs of cross-border transactions such as customs duties and

shipping costs affect offshoring-reshoring profit comparisons under OSD. We find that increasing

customs duties may or may not make reshoring more appealing, and higher shipping costs for both

finished goods and components can make reshoring less appealing when compared with offshoring.

Both observations are more nuanced than the common notions formed without accounting for

OSD, signifying the importance of considering OSD when comparing offshoring and reshoring.

To help mitigate OSD’s hampering effect on reshoring’s responsiveness, we propose a simple

approach, namely common-component designs. If a reshoring manufacturer implements common-

component designs in its product family, it can pool component purchases for multiple products and

later allocate the components among products after learning more accurate demand information,

thus improving its responsiveness. By contrast, an offshoring manufacturer would benefit little

from such an approach, because it already has unlimited component supply due to being close to

its supplier. As a result, common-component designs make reshoring under OSD more appealing.

In addition, we numerically confirm the robustness of our results through two model extensions.

In the first extension, we generalize the two-point demand prior considered in our main model to

a continuous demand prior. In the second extension, we allow for using existing components or

5

finished goods to satisfy unmet demand after demand realization, via rush production or expedited

shipping. In both extensions the main model’s predictions remain structurally unchanged.

In summary, to our knowledge, this paper is the first to rigorously model and investigate the

effect of OSD on reshoring manufacturing. We show that OSD hampers reshoring’s responsiveness,

reshaping the cost-responsiveness tradeoff between offshoring and reshoring and significantly affect-

ing offshoring-reshoring profit comparisons. Failing to account for OSD may lead to false optimism

about reshoring, and thus OSD deserves careful attention of relevant stakeholders in the consid-

eration of reshoring. In fact, the recent empirical study by Cohen et al. (2016) finds that firms

which choose to reshore tend to have less concerns about supply-related factors including supply

availability and raw material and logistics costs, which is consistent with our model predictions.

The rest of this paper is organized as follows. A literature review is provided in Section 2. We

model and formulate the offshoring and reshoring problems in Section 3, and compare them to

reveal main insights about the effect of OSD in Section 4. We then discuss the influence of customs

duties and shipping costs, a mitigating measure for OSD, as well as two robustness checks in Section

5. Finally, we conclude the paper in Section 6. Online Appendix A contains additional analyses,

and Online Appendix B contains all proofs.

2. Literature review

In this paper we compare reshoring to offshoring. A related concept to offshoring is outsourcing.

Tsay (2014) provides a lucid delineation between offshoring and outsourcing. Here is an excerpt

from p. 129 of his monograph: “The hazards of both offshoring and outsourcing can be interpreted

as losing proximity, i.e., the creation of distance. In the case of outsourcing, the distance is organi-

zational in nature. An intervening corporate boundary obstructs visibility and communication and

causes divergence of incentives... With offshoring, the distance is geographic. This increases the

difficulty of moving materials, funds, information, knowledge, and workers.” Accordingly, the out-

sourcing literature focuses on decentralized decision-making and the need for coordination (see the

reviews by Elmaghraby 2000 and Cachon 2003), whereas we focus on how the geographic distance

between an offshore supplier and an onshore market impacts a firm’s operations.

At the core of our model is responsiveness, namely the ability to adjust inventory after receiving

demand information updates. Therefore, our work is related to the literature on production man-

agement with demand updating. This literature can be loosely divided into two main categories.

The first category focuses on optimal responsiveness strategies and their benefits. For example,

Fisher and Raman (1996) study how to dynamically allocate production capacity in response to

6

information updates in a Quick Response system. Iyer and Bergen (1997) study the benefits of

Quick Response in a manufacturer-retailer supply chain. Gurnani and Tang (1999) further consider

optimal ordering policies with additional cost uncertainties under a similar setting. The second

category revolves around the tradeoff between cost and responsiveness. Donohue (2000) studies

efficient contract design with forecast updating between two production modes, one less costly

and the other with a shorter lead-time. Two particularly related papers are by Wang et al. (2014)

and Wu and Zhang (2014), who, in the context of offshoring, study the interplay between cost,

responsiveness, competition, and information. A commonality of these papers is that they all model

two-tier supply chains each consisting of a manufacturer and a market, without considering sup-

pliers. By contrast, we focus on OSD and explicitly model a three-tier supply chain consisting of

an offshore supplier, a manufacturer, and an onshore market. To the best of our knowledge, this

paper is the first to do so in the study of reshoring.

Our problem is related to the newsvendor network design literature. Van Mieghem and Rudi

(2002) offer an excellent review of this literature; here we focus on the two most relevant papers by

Lu and Van Mieghem (2009) and Dong et al. (2010). Their basic setting can be described as that

a firm sells a product in two separate markets, and needs to decide whether to build a centralized

production facility for both markets or a dedicated facility in each market. In short, the focus

is on placing a factory between two separate markets. Our reshoring problem under OSD, on the

other hand, can be described as placing a factory between an offshore supplier and an onshore

market. Also, the main tradeoff of Lu and Van Mieghem (2009) and Dong et al. (2010) is between

risk-pooling benefits and production and shipping costs, whereas in our reshoring problem under

OSD the decision is made balancing offshoring and reshoring’s baseline-cost difference as well as

their costs to adjust inventories upward and downward.

Finally, several papers have studied Quick Response and postponement in competitive environ-

ments, including Van Mieghem and Dada (1999), Anand and Girotra (2007), Goyal and Netessine

(2007), Caro and Martınez-de-Albeniz (2010), Wang et al. (2014), and Wu and Zhang (2014). As

a first attempt to study OSD’s impact on reshoring manufacturing, we restrict our attention to a

monopolistic setting. The insights from our paper will serve as a stepping stone to understanding

this problem in more complex settings such as competitive environments.

3. Model setup and formulation

Our main objective in this paper is to investigate the effect of OSD on offshoring-reshoring profit

comparisons. To do so, we first introduce a two-stage information updating model, based on which

7

we analyze and compare a manufacturer’s optimal profits in different production modes (i.e., off-

shoring or reshoring). Specifically, we consider an expected-profit-maximizing manufacturer selling

its product in an onshore market at exogenous retail price p. The demand for the product is a

random variable Ψ with a normal distribution N(µ,σ). We assume that the standard deviation σ

is known, but the mean µ can be µH (High demand) with prior probability γ or µL (Low demand)

with prior probability 1−γ. (In Section 5.3 we show that the main insights remain unchanged with

a continuous demand prior distribution.) We assume that µH > µL� σ, so that the probability

of a negative demand is negligible, and define ∆.= (µH − µL)/σ as a measure of the difference

between high and low demands relative to the demand uncertainty. At the beginning of Stage 1, the

manufacturer only knows γ but not the exact demand type (i.e., whether µ= µH or µL). A large

(small) γ means that the demand is more likely to be high (low), which we refer to as a high (low)

demand prospect. After Stage 1, the manufacturer learns the demand type µ through a marketing

event, which is incorporated in its Stage-2 decisions. The demand type revelation captures how a

firm may learn additional demand information through market studies prior to the selling season.

In the above two-stage information updating model, offshoring and reshoring manufacturers

face different production and shipping costs and decision-making scenarios. Below we introduce

and formulate the production problem of an offshoring manufacturer, and that of a reshoring

manufacturer under OSD. For benchmarking, we also formulate a reshoring manufacturer’s problem

ignoring OSD. The timelines of the three models are illustrated in Figure 1.

3.1. Offshoring

An offshoring manufacturer sources components and produces goods offshore before shipping the

goods onshore to satisfy demands (Figure 1 Case (a)). At the beginning of Stage 1, the manufacturer

sources components from an offshore supplier at unit cost c and produces one unit of finished good

from one unit of the component in its offshore factory at regular production cost m0 per unit (we

use super/subscript 0 to denote offshoring). We assume that the supplier has no capacity limit or

order lead-time, and the regular production lasts through Stage 1. After Stage 1, the manufacturer

learns the demand type (high or low).

At the beginning of Stage 2, if necessary, the offshoring manufacturer resorts to rush production

to increase its inventory on short notice with an associated cost premium of r per unit (in addition

to the regular production cost m0). It then insures and ships finished goods onshore at unit cost

sg (we use subscript g to denote finished goods). Shipping lasts through Stage 2 and the goods

arrive onshore just in time for the selling season when demand is realized. Staying true to the

newsvendor framework, we assume that unmet demand is lost and leftover inventory has no salvage

8

Regularproduction

Rush production/Hold back shipping

Finished goodsin stock

Demand update Demand realization

Finished goodsin shipping

Componentsourcing

Expedite shipping/Hold back production

Finished goodsin stock

Demand update Demand realization

Componentsin shipping

(a) Offshoring

(b) Reshoring under offshore supply dependence

time

time

ComponentProduct

Productionin progress

Productionin progress

Regularproduction

Finished goodsin stock

Demand update Demand realization

time

Productionin progress(c) Reshoring ignoring

offshore supply dependence (benchmark)

Stage 1 Stage 2

Figure 1 Sequences of events

value. (In Section 5.4 we show that our main insights remain unchanged even if the manufacturer

can respond after demand realization and capture some unmet demand.) Note that if the demand

update after Stage 1 reveals a lower demand than the manufacturer has initially produced for, it

may choose to hold back shipping of some finished goods to save shipping costs. This is essentially

the offshoring manufacturer adjusting the inventory downward in response to the demand update

(whereas it can also adjust the inventory upward using rush production).

In addition, an offshoring manufacturer needs to pay customs duties on imported finished goods.

We denote the duty rate for finished goods by tg as a fraction of the cost base. There are two

common International Commerce Terms (Incoterms) for determining the cost base for customs

duties. One is called FOB (Free on Board), under which customs duties are levied on purchase

prices but not shipping and insurance costs. The other one is called CIF (Cost Insurance Freight),

where customs duties are levied on purchase prices as well as shipping and insurance costs. Among

major importers, the US adopts FOB1 whereas Europe adopts CIF.2 We adopt FOB in this paper,

1 https://help.cbp.gov/app/answers/detail/a_id/324/~/duty---cost.-insurance-and-freight-(cif)

2 http://www.export.gov/logistics/eg_main_018140.asp

9

but have also confirmed that all of our structural results remain unchanged under CIF.

An offshoring manufacturer’s decisions can be characterized by two quantities: Stage 1’s regular

production quantity x0m before learning the demand type, and Stage 2’s finished good shipping

quantity x0s after learning the demand type. If x0

s > x0m, it means the manufacturer uses rush

production to increase inventory, and if x0s < x0

m, it means the manufacturer holds back shipping

some finished goods to decrease inventory, upon learning the demand type. The formulation of the

offshoring manufacturer’s problem is

Π0m

.= max

x0m≥0{−(c+m0)x

0m + γΠ0

s(µH , x0m) + (1− γ)Π0

s(µL, x0m)}, (1)

where Π0s(µ,x

0m) is the optimal profit due to adjusting inventory after learning the mean demand

µ (= µH or µL), given the regular production quantity x0m:

Π0s(µ,x

0m)

.= max

x0s≥0{−(c+m0 + (1 + tg)r)(x

0s−x0

m)+− (tg(c+m0) + sg)x0s + pE[min{Ψ, x0

s}|µ]}. (2)

The full analysis of (1)-(2) and optimal profit expressions can be found in Online Appendix A;

here we only briefly describe the result. Depending on ∆(= (µH −µL)/σ) and γ (the prior proba-

bility of a high demand), the manufacturer may play three different strategies. With a sufficiently

small ∆, the manufacturer does not adjust inventory upon learning the demand type because the

value cannot justify the cost of such adjustments. When ∆ is larger, the manufacturer may adjust

inventory upon learning the demand type. With a low demand prospect (small γ), the manu-

facturer plans the initial production quantity anticipating a low demand, and makes an upward

adjustment using rush production in the event that the demand turns out to be high. With a high

demand prospect (large γ), the manufacturer plans the initial production quantity anticipating a

high demand, and makes a downward adjustment by holding back shipping finished goods onshore

in the event that the demand turns out to be low.

3.2. Reshoring under OSD

A reshoring manufacturer under OSD must source components from an offshore supplier even

though production takes place onshore (Figure 1 Case (b)). At the beginning of Stage 1, the

manufacturer sources components from an offshore supplier at unit cost c and ships the components

onshore at unit cost sc (we use subscript c to denote components). Shipping lasts through Stage

1. After Stage 1, the manufacturer learns the demand type.

At the beginning of Stage 2, if necessary, the reshoring manufacturer resorts to expedited shipping

to increase its component inventory on short notice with an associated cost premium of e per unit

(in addition to the regular shipping cost sc). It also needs to pay customs duties on imported

10

components. We denote the duty rate for components by tc (recall that under CIF customs duties

are not levied on shipping costs sc or e). The manufacturer then processes available components into

finished goods in its onshore factory at unit cost m1 (we use super/subscript 1 to denote reshoring).

Production lasts through Stage 2 and the goods are ready just in time for the selling season when

demand is realized. Note that if the demand update after Stage 1 reveals a lower demand than the

manufacturer has initially sourced components for, it may choose to hold back processing some

available components into finished goods to save production costs. This is essentially the reshoring

manufacturer adjusting the inventory downward in response to the demand update (whereas that

it can also adjust the inventory upward using expedited shipping). Since the production decision

is made after the demand update, no rush production is needed onshore.

A reshoring manufacturer’s decisions can be characterized by two quantities: Stage 1’s component

purchase quantity x1c before learning the demand type, and Stage 2’s regular production quantity

x1m after learning the demand type. If x1

m >x1c, it means the manufacturer uses expedited shipping

to increase inventory, and if x1m < x1

c, it means the manufacturer holds back processing some

available components into finished goods to decrease inventory, upon learning the demand type.

The formulation of the reshoring manufacturer’s problem is

Π1c

.= max

x1c≥0{−((1 + tc)c+ sc)x

1c + γΠ1

m(µH , x1c) + (1− γ)Π1

m(µL, x1c)}, (3)

where Π1m(µ,x1

c) is the optimal profit due to adjusting the final inventory level after learning the

mean demand µ (= µH or µL), given the component purchase quantity x1c:

Π1m(µ,x1

c).= max

x1m≥0{−((1 + tc)c+ sc + e)(x1

m−x1c)

+−m1x1m + pE[min{Ψ, x1

m}|µ]}. (4)

The full analysis of (3)-(4) and optimal profit expressions can be found in Online Appendix A.

Depending on ∆ and γ, the manufacturer may play three different strategies. With a sufficiently

small ∆, the manufacturer does not adjust inventory upon learning the demand type. When ∆ is

larger, the manufacturer may adjust inventory upon learning the demand type. With a low demand

prospect (small γ), the manufacturer plans the initial component purchase quantity anticipating

a low demand, and makes an upward adjustment using expedited shipping in the event that the

demand turns out to be high. With a high demand prospect (large γ), the manufacturer plans

the initial component purchase quantity anticipating a high demand, and makes a downward

adjustment by holding back processing components into finished goods in the event that the demand

turns out to be low. As one can see, a reshoring manufacturer’s problem and optimal strategies

under OSD are structurally similar to those of an offshoring manufacturer.

11

3.3. Benchmark: reshoring ignoring OSD

In order to demonstrate the effect of OSD on reshoring, we also analyze a benchmark reshoring

model ignoring OSD, namely a reshoring manufacturer can source locally (onshore) for required

components (Figure 1 Case (c)). In other words, the reshoring manufacturer has unlimited access

to onshore component supply with no lead-time at the beginning of Stage 2, and can make an

integrated component purchase and production decision after learning the demand type. Clearly,

depending on the realized demand type, the manufacturer faces one of two simple newsvendor

problems. Specifically, given the mean demand µ, it is easy to show that the manufacturer’s Stage-

2 optimal profit has the following expression (throughout this paper we use Φ(·) and φ(·) to

respectively denote the cumulative distribution function (CDF) and probability density function

(PDF) of a standard normal distribution):

Π(µ).= max

x≥0{−((1 + tc)c+ sc +m1)x+ pE[min{Ψ, x}|µ]}= (p− (1 + tc)c− sc−m1)µ− pσφ(z1),

where z1 = Φ−1(p−(1+tc)c−sc−m1

p

)is the newsvendor critical ratio. Consequently, the manufacturer’s

Stage-1 ex ante optimal profit in this benchmark case is simply

γΠ(µH) + (1− γ)Π(µL) = (p− (1 + tc)c− sc−m1)(µL + γσ∆)− pσφ(z1). (5)

The above reshoring model ignoring OSD has a two-tier (manufacturer-market) supply chain

structure, which has been commonly adopted in the literature (e.g., Wang et al. 2014, Wu and

Zhang 2014). By contrast, accounting for OSD necessitates a three-tier (supplier-manufacturer-

market) reshoring model as described in Section 3.2 and illustrated in Figure 1 Case (b). In the

next section we will demonstrate how OSD alters offshoring-reshoring profit comparisons.

4. The effect of offshore supply dependence

In this section, we first analyze the benchmark comparison between a manufacturer’s offshoring

profit and its reshoring profit ignoring OSD, and then analyze the profit comparison under OSD

to shed light on the effect of OSD on such comparisons.

The current industry reality is that, without considering issues such as responsiveness, offshoring

has equal or lower “baseline-costs” than reshoring. In our model, the baseline-costs, i.e., the unit

costs of goods sold without responding to demand information updates, are (c+m0)(1 + tg) + sg

under offshoring and c(1 + tc) + sc + m1 under reshoring. Accordingly, we assume (c + m0)(1 +

tg) + sg ≤ c(1 + tc) + sc +m1, or equivalently δ.=m1 −m0(1 + tg) + (tc − tg)c+ sc − sg ≥ 0, in all

comparisons. It is worth noting that our approach to the comparisons does not depend on this

assumption, and can be easily extended to the case of δ < 0.

12

4.1. Benchmark: offshoring-reshoring comparison ignoring OSD

Utilizing the expected profit expressions of (1) and (5), we obtain the following proposition. (All

proofs are found in Online Appendix B.)

Proposition 1. Suppose δ≥ 0 and ignore OSD. There exists a threshold γB = c+m0c+m0+δ

. For any

γ ≥ γB, reshoring yields lower profits than offshoring. For any 0<γ < γB, there exists ∆∗B(γ) such

that reshoring yields higher profits than offshoring if and only if ∆>∆∗B(γ). In particular, if δ= 0,

reshoring always yields higher profits than offshoring.

The offshoring-reshoring profit comparison ignoring OSD reveals a basic baseline-cost versus

responsiveness tradeoff. Specifically, offshoring has a baseline-cost advantage over reshoring, namely

offshoring without adjusting inventory after learning the demand type is cheaper than reshoring.

On the other hand, reshoring has a responsiveness advantage over offshoring: if one ignores OSD,

then a reshoring manufacturer can postpone all decisions until after learning the demand type,

whereas an offshoring manufacturer has to make its regular production decision before learning the

demand type (see Figure 1 Cases (a) and (c)). In the extreme case, if offshoring ceases to have a

baseline-cost advantage (δ= 0), then reshoring would dominate offshoring due to its responsiveness

advantage (see Proposition 1).

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

γ

Δ

��#

Offshoring

Reshoring

Figure 2 Illustration of Proposition 1 with δ > 0

When offshoring has a baseline-cost advantage (δ > 0), the outcome of the tradeoff depends on

the demand prior parameters ∆ and γ (see Figure 2 for an illustration). With small ∆ (high and

13

low mean demands being close) or γ close to 0 or 1 (mostly predictable demand type), reshoring’s

responsiveness has little value, thus offshoring yields higher profits than reshoring. In particular,

a threshold γB related to offshoring’s baseline-cost advantage δ exists such that for γ > γB, off-

shoring’s baseline-cost advantage dominates reshoring’s responsiveness advantage, and offshoring

yields higher profits than reshoring for any ∆; as δ diminishes, the threshold γB approaches 1. On

the other hand, with moderate γ and sufficiently large ∆, reshoring’s responsiveness has significant

value and reshoring yields higher profits.

4.2. Offshoring-reshoring comparison under OSD

As we showed earlier, when considering OSD, a reshoring manufacturer’s model has a three-tier

(supplier-manufacturer-market) supply chain structure instead of a two-tier (manufacturer-market)

structure when OSD is ignored. The manufacturer’s optimal strategies and profits accordingly differ

as well. Utilizing the expected profit expressions of (1) and (3), we obtain the following proposition.

The full analysis and the detailed version of this proposition are found in Online Appendix A as

Propositions A3-A4.

Proposition 2. Suppose δ≥ 0 and consider OSD.

(a) If e ≤ (1 + tg)r − δ, there exists a threshold γ ≤ γB. For any γ ≥ γ, reshoring yields lower

profits than offshoring. For any 0 < γ < γ, there exists ∆∗(γ) ≥ ∆∗B(γ) such that reshoring

yields higher profits than offshoring if and only if ∆>∆∗(γ).

(b) If e > (1 + tg)r− δ and (1 + tc)c+ sc <(c+m0)((1+tg)r−δ)

(1+tg)r, there exist two thresholds γ < γ ≤ γB.

For any γ ≤ γ or γ ≥ γ, reshoring yields lower profits than offshoring. For any γ < γ < γ, there

exists ∆∗(γ) ≥∆∗B(γ) such that reshoring yields higher profits than offshoring if and only if

∆>∆∗(γ).

(c) If e > (1 + tg)r − δ and (1 + tc)c+ sc ≥ (c+m0)((1+tg)r−δ)(1+tg)r

, reshoring always yields lower profits

than offshoring.

The three cases of Proposition 2 are illustrated in Figure 3. The same cases (parameters) with

OSD ignored (as in Section 4.1 and Proposition 1) are also illustrated for comparison. Clearly,

accounting for OSD results in much smaller parameter regions where reshoring yields higher profits

than offshoring. This is expected; on a high level, OSD constrains a reshoring manufacturer’s

operational flexibility and hampers its responsiveness. However, to fully understand how exactly

OSD leads to such changes, we need to carefully examine and compare the tradeoffs a manufacturer

faces between offshoring and reshoring with or without OSD.

14

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

γ

Δ

��

Offshoring

Reshoring

Case (a) under OSD

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

γ

Δ

��#

Offshoring

Reshoring

Case (a) ignoring OSD

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

γ

Δ

��

Offshoring Reshoring

𝛾$

Case (b) under OSD

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

γ

Δ

��#Offshoring

Reshoring

Case (b) ignoring OSD

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

γ

Δ

Offshoring

Case (c) under OSD

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

γ

Δ

��#

Offshoring

Reshoring

Case (c) ignoring OSD

Figure 3 Comparison between Proposition 2 and Proposition 1 with δ > 0

15

In Section 4.1 we pointed out that, when ignoring OSD, the offshoring-reshoring comparison

boils down to a basic tradeoff between offshoring’s baseline-cost advantage and reshoring’s respon-

siveness advantage, the latter due to that a reshoring manufacturer postpones all decisions until

after learning the demand type whereas an offshoring manufacturer has to make the regular pro-

duction decision before learning the demand type. Under OSD, however, reshoring no longer enjoys

the same level of responsiveness (see Figure 1 Case (b)). Because of the component shipping lead-

time from the offshore supplier, a reshoring manufacturer needs to make the component purchase

decision before learning the demand type. In fact, our analyses in Sections 3.1 and 3.2 reveal that

a reshoring manufacturer under OSD faces decision-making scenarios similar to those of an off-

shoring manufacturer: the reshoring manufacturer needs to make the component purchase decision

(corresponding to the regular production decision under offshoring) in Stage 1 before learning the

demand type; in Stage 2 after learning the demand type, the manufacturer can respond to it by

adjusting its inventory upward by expedited shipping (corresponding to rush production under

offshoring) or downward by holding back production (corresponding to holding back shipping of

finished goods under offshoring). In short, OSD hampers a reshoring manufacturer’s responsiveness

and forces the manufacturer to face a two-stage decision problem similar to that under offshoring.

As a result, the costs of inventory adjustments after learning the demand type determine

reshoring’s responsiveness under OSD. The unit upward and downward-adjustment costs intro-

duced by OSD are the expedited shipping cost e and the discarded component cost (1 + tc)c+

sc, respectively. (By comparison, a reshoring manufacturer without OSD postpones component

purchases until after learning the demand type, which is equivalent to having zero upward and

downward-adjustment costs.) When the expedited shipping cost (upward-adjustment cost) is rel-

atively low (e≤ (1 + tg)r− δ, Proposition 1 Case (a)), the offshoring-reshoring comparison retains

the same structure as when OSD is ignored, with a shrinking reshoring region as one would expect

(see Figure 3 Case (a)). When the expedited shipping cost is relatively high (e > (1 + tg)r − δ),

however, accounting for OSD begins to alter the structure of the offshoring-reshoring compari-

son. In cases where the discarded component cost (downward-adjustment cost) are relatively low

((1 + tc)c+ sc <(c+m0)((1+tg)r−δ)

(1+tg)r, Proposition 1 Case (b)), the reshoring region further shrinks, and

a new threshold γ emerges such that offshoring dominates reshoring for any γ ≤ γ (see Figure

3 Case (b)). This is because low demand prospects (small γ) require more often upward inven-

tory adjustments, and reshoring’s high expedited shipping cost (upward-adjustment cost) leads to

offshoring dominating reshoring under OSD in this region. If the discarded component cost also

becomes relatively high ((1 + tc)c+ sc ≥ (c+m0)((1+tg)r−δ)(1+tg)r

), the reshoring region completely vanishes

16

under OSD, yielding the most striking contrast to when OSD is ignored (see Figure 3 Case (c)). In

this case, reshoring’s upward and downward adjustments are both costly, which completely wipe

out reshoring’s responsiveness advantage over offshoring. In fact, in today’s environment where

offshoring’s baseline-cost advantage δ is relatively large and/or the offshoring’s rush production

premium r is relatively small (see Section 1), the conditions for Proposition 2 Case (c) are likely to

hold. Clearly, failing to account for OSD in this case may lead to misguided favorable predictions

about reshoring, while offshoring actually completely dominates reshoring under OSD.

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

γ

Δ

Offshoring

��Indifferent

Reshoring

Case (a)

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

γ

Δ

�� = 1

Reshoring

Indifferent𝛾

Offshoring

Case (b)

Figure 4 Illustration of Proposition 2 with δ= 0

The distinction in the offshoring-reshoring comparison with and without OSD is even more evi-

dent in the special case where offshoring’s baseline-cost advantages approaches zero (a full analysis

and complete characterization of this special case are included in Online Appendix A as Propo-

sition A5). Ignoring OSD would predict that reshoring dominates offshoring due to the former’s

responsiveness advantage (Proposition 1). By contrast, accounting for OSD yields drastically dif-

ferent outcomes. To illustrate, we provide two examples accounting for OSD in Figure 4. In these

examples, we choose parameters such that the baseline-cost difference δ = 0, thus for small ∆

where the manufacturer does not adjust inventory after learning the demand type it is indifferent

between offshoring and reshoring. We separate the indifferent and offshoring regions with dotted

lines to indicate that the indifferent regions will merge into the offshoring regions for an arbitrar-

ily small δ > 0. The first example corresponds to Proposition 2 Case (a) and Figure 3 Case (a)

where reshoring’s upward-adjustment cost is low. The second example corresponds to Proposition

17

2 Case (b) and Figure 3 Case (b) where reshoring’s upward-adjustment cost is high and downward-

adjustment cost is low; in this example due to δ= 0 the threshold γ becomes 1. One can see that in

both examples reshoring does not dominate offshoring, contrasting the prediction of Proposition 1

ignoring OSD. In fact, Proposition A5 in Online Appendix A indicates that in some cases offshoring

may even dominate reshoring, similar to Proposition 2 Case (c).

To summarize, when ignoring OSD, one would conclude that because a reshoring manufacturer

can postpone production (without being constrained by component supplies), reshoring always

has a responsiveness advantage over offshoring, and the only way offshoring may be preferable is

when it possesses a baseline-cost advantage. Our analysis however shows that, when accounting for

OSD, although a reshoring manufacturer can postpone production, it cannot postpone component

purchases, which makes the manufacturer’s inventory adjustments in response to demand updates

costly (like under offshoring). These costs determine whether reshoring has a responsiveness advan-

tage over offshoring. When the costs are relatively small, the offshoring-reshoring comparison under

OSD behaves similarly to that in the case ignoring OSD; however, when the costs are relatively

large (as is often the case in practice), OSD substantially changes the outcome of the comparison,

and offshoring may dominate reshoring even when the former has no baseline-cost advantage. This

signifies the importance of taking into account OSD for a manufacturer considering reshoring, as

failing to do so may lead to misguided profitability predictions.

5. Further discussions

In this section we offer additional discussions and robustness checks about offshoring-reshoring

profit comparisons under OSD.

5.1. Customs duties and shipping costs

Both offshoring and reshoring under OSD involve cross-border transactions. Below we analyze the

impacts of salient costs of cross-border transactions, such as customs duties and shipping costs,

on offshoring-reshoring comparisons under OSD. For Propositions 2 Cases (a) and (b), conducting

sensitivity analysis on ∆∗(γ) is intractable, so we resort to analyzing the sensitivity of the limit

thresholds to gain insights in the next proposition. The proof is straightforward and thus omitted.

Proposition 3. Suppose δ≥ 0 and consider OSD.

(1) In Proposition 2 Case (a), γ is decreasing in tc and sc and increasing in tg and sg.

(2) In Proposition 2 Case (b), γ is decreasing in tc and sc and increasing in tg and sg, and γ is

increasing in tc and sc and decreasing in tg and sg.

18

(3) Between Proposition 2 Cases (b) and (c), Case (c) where offshoring dominates reshoring

becomes more likely as tc and sc increase and as tg and sg decrease.

Proposition 3 suggests that when customs duties and shipping costs for components increase or

when those for finished goods decrease, reshoring may become less appealing or even dominated

when compared with offshoring. (For cases (1) and (2), although the proposition shows this trend for

limit thresholds, we numerically verify that the same trend holds in general.) This trend is intuitive,

as a reshoring manufacturer needs to incur customs duties and shipping costs for components,

whereas an offshoring manufacturer needs to incur those costs for finished goods.

We further note that customs duties and shipping costs of finished goods and components often

do not move independently; many events may simultaneously affect such costs for both finished

goods and components. For example, trade treaties such as the Trans-Pacific Partnership (TPP)

lower or eliminate customs duties across the board, whereas trade wars and protectionist move-

ments such as Britain leaving the European Union (Brexit) may increase customs duties across

the board. Similarly, shipping costs of both finished goods and components are highly correlated

with commodity prices which can be highly volatile; for example, oil prices have climbed above

$120 per barrel in 2008 and 2012 and dropped below $50 per barrel in 2009 and 2015.3 A feature

of such scenarios is that customs duties and shipping costs of finished goods and components move

in the same direction, thus the cost differences between finished goods and components tend to

change much less than the costs themselves. To understand the impacts of such correlated changes

in customs duties and shipping costs of both finished goods and components, we approximate the

scenarios by fixing tg− tc and sg− sc, and investigate the threshold limits’ sensitivity with respect

to changes in tc and sc in the next proposition. The proof is straightforward and thus omitted.

Proposition 4. Suppose δ≥ 0 and consider OSD. Set tg ≡ tc+ tδ and sg ≡ sc+sδ, where tδ and

sδ are kept constant.

(1) In Proposition 2 Case (a), γ may be increasing or decreasing in tc, but is decreasing in sc.

(2) In Proposition 2 Case (b), γ may be increasing or decreasing in tc, but is decreasing in sc; γ

may be increasing or decreasing in tc, but is increasing in sc.

(3) Between Proposition 2 Cases (b) and (c), Case (c) where offshoring dominates reshoring may

become less likely as tc increases or decreases, but will become less likely as sc decreases.

Proposition 4 suggests that when customs duties for both finished goods and components increase

in a correlated manner, their influence on the offshoring-reshoring profit comparison may go either

3 http://www.macrotrends.net/1369/crude-oil-price-history-chart

19

way. This ambiguity is more nuanced than popular arguments, such as that TPP would stall the

reshoring movement (Semuels 2015, Nash-Hoff 2015), or that Brexit may help reshoring gain more

traction (Kondej 2016). A more careful inspection of these popular arguments reveal that they are

mainly based on how tariffs impact imported finished goods without considering similar impacts

on imported materials and components, which are not negligible under OSD. Our inconclusive sen-

sitivity analysis suggests that, under OSD, the impact of trade treaties such as TPP or movements

such as Brexit on reshoring manufacturing may be more subtle than one’s first intuition, and begs

for more thorough investigations.

On the other hand, when shipping costs for both finished goods and components increase in a

correlated manner, Proposition 4 suggests that reshoring may become less appealing or even dom-

inated when compared with offshoring (in Cases (1) and (2), although the proposition shows this

trend for limit thresholds, we numerically verify that the same trend holds in general). The intuition

is as follows. Under offshoring, production takes place before shipping (of finished goods), whereas

under reshoring with OSD, shipping (of components) takes place before production. Therefore,

when shipping costs increase, offshoring gains additional advantage over reshoring (with OSD) due

to its ability to make the shipping decision after learning more accurate demand information.

5.2. Mitigating measure

We have shown that OSD hampers a reshoring manufacturer’s responsiveness. In the long run,

onshore supply bases may gradually grow, relieving reshoring manufacturers’ dependence on off-

shore suppliers. However, onshore suppliers are unlikely to rapidly develop before reshoring reaches

a critical mass, whereas large-scale reshoring is unlikely to take place before onshore supply bases

become full-fledged, creating a chicken-and-egg dilemma. Until this dilemma is resolved, manu-

facturers under OSD will continue to face the problem of remaining offshore to be close to their

suppliers versus reshoring to be close to their markets. Under this circumstance, mitigating mea-

sures that can make reshoring more appealing under OSD would be highly valuable, as they can

help resolve the dilemma and accelerate reshoring as well as onshore supply base development.

We argue that common-component designs is one such mitigating measure. To elaborate this

idea, consider the following modifications to the offshoring model and reshoring model under OSD.

Suppose now the manufacturer makes two different products a and b for the onshore market, which

require separate manufacturing processes, but share a component sourced from an offshore supplier.

Suppose their demand type priors are not perfectly correlated. Figure 5 illustrates the sequence of

events with common-component designs.

20

Regularproduction

Finished goodsin stock

Demand update Demand realization

Finished goodsin shipping

Componentsourcing

Finished goodsin stock

Demand update Demand realization

Componentsin shipping

Offshoring

Reshoring under offshore supply

dependence

time

time

Product a Component for products a and bProduct b

Rush production/Hold back shipping

Expedite shipping/Hold back production

Productionin progress

Productionin progress

Stage 1 Stage 2

Figure 5 Sequence of events with a common-component design

This modification has different implications for the manufacturer under offshoring and reshoring.

Under offshoring, the two products are manufactured separately from the very beginning. As a

result, common-component designs do not affect the base model’s optimal strategy or profit. By

contrast, under reshoring, the manufacturer sources components for both products in Stage 1 and

allocates the components between them in Stage 2 after learning each product’s demand type,

which improves its responsiveness. As a result, the profit comparison is shifted in favor of reshoring.

It is straightforward to prove this conclusion, which we do not include in the paper for brevity.

To summarize, common-component designs make reshoring more appealing under OSD, thus is

a potential approach to break the dilemma between reshoring manufacturing and onshore supply

base development. At its core, this approach resembles delayed product differentiation (Lee and

Tang 1997) in that it improves reshoring’s responsiveness through the well-known inventory pooling

effect, but also notably does not generate similar pooling benefits under offshoring.

5.3. Robustness check: continuous demand prior

For tractability, we have assumed a two-point distribution for the mean demand prior in our

analyses. It is important to confirm that the offshoring-reshoring comparison structure depicted in

Figure 3 is not driven by this specific demand prior distribution. To do so, we modify the offshoring

model (1)-(2) and the reshoring model under OSD (3)-(4) by replacing the two-point mean demand

prior distribution with a continuous beta distribution.

Recall that in the original model, the mean demand prior µ may be µH with probability γ and

µL with probability 1 − γ, where ∆ = (µH − µL)/σ captures the normalized range. To capture

21

similar demand features, we consider a shifted and scaled beta distribution for the mean demand

prior; i.e., we assume µ.= µL + (µH − µL)B where µH > µL � 0 and B has a Beta(α,2 − α)

distribution with α∈ (0,2). A Beta(α,2−α) distribution has support (0,1); for α∈ (0,1) its PDF

is decreasing from ∞ to 0, and for α ∈ (1,2) its PDF is increasing from 0 to ∞. When α= 1, the

beta distribution reduces to a Uniform(0,1) distribution. Hence, small α (close to 0) values imply

that demands are more likely to be low, whereas large α values (close to 2) imply that demands

are more likely to be high. Clearly, this beta prior distribution is a continuous generalization of

the original two-point distribution; in particular, the parameter ∆ = (µH −µL)/σ serves the same

role, and the parameter α∈ (0,2) serves a similar role as the original γ ∈ (0,1). The modifications

to the formulations involve simply replacing the two-point distribution expectations in (1) and

(3) with beta distribution expectations and are omitted. We numerically evaluate the modified

models and find that the basic structure under OSD in Figure 3 are preserved with the beta prior.

One example is provided in Figure 6 with the x-axis representing ∆ and the y-axis representing

α∈ (0,2), generated with the same cost parameters as Figure 3 Case (a).

0

0.4

0.8

1.2

1.6

2

0 2 4 6 8 10 12 14 16 18 20

α

Δ

Offshoring

Reshoring

Beta mean demand prior

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7 8 9 10

γ

Δ

��

Offshoring

Reshoring

Two-point mean demand prior

Figure 6 Illustration of Figure 3 Case (a) under OSD, beta versus two-point mean demand prior

5.4. Robustness check: instantaneous response after demand realization

In our main models, we assumed that rush production or expedited shipping are not fast enough

to satisfy unmet demands after demand realization. We made this assumption to stay true to the

newsvendor framework, which models scenarios where the selling season is much shorter than the

production or shipping lead-times, such that the selling season is modeled as being instantaneous.

22

It also ensures that our model is consistent with the literature (Fisher and Raman 1996) in that the

manufacturer faces and responds to one demand information update during the lead-time. Still, one

might wonder whether the profit comparison between offshoring and reshoring under OSD would

change if instantaneous responses are allowed after demand realization (which essentially allows the

manufacturer to respond to two demand updates). To be specific, consider the scenario where an

offshoring manufacturer had decided to hold back shipping of some of its finished goods following

the post-Stage-1 demand update, yet after demand realization cannot satisfy all demands. What

if the manufacturer could expedite the shipping of the remaining finished goods to satisfy unmet

demands? Similarly, when a reshoring manufacturer had decided to hold back processing some of

its shipped components following the post-Stage-1 demand update, yet after demand realization

cannot satisfy all demand, what if the manufacturer could use rush production to process the

remaining shipped components to satisfy unmet demands? We investigate such an extension below.

First consider an offshoring manufacturer. Let e′ denote the cost premium associated with expe-

dited shipping of finished goods to satisfy unmet realized demands. With this change, the offshoring

problem (1) and (2) become

Π0m

.= maxx0m≥0{−(c+m0)x

0m + γΠ0

s(µH , x0m) + (1− γ)Π0

s(µL, x0m)},

Π0s(µ,x

0m)

.=max

x0s≥0{−(c+m0 + (1 + tg)r)(x

0s−x0

m)+− (tg(c+m0) + sg)x0s + pE[min{Ψ, x0

s}|µ]

+ (p− tg(c+m0)− sg − e′)+E[(min{Ψ, x0

m}−x0s

)+ |µ]}.

The last term in Π0s(µ,x

0m) captures the potential profit generated by expediting held-back finished

goods to satisfy unmet realized demands. When e′ is sufficiently large, i.e., e′ ≥ p− tg(c+m0)− sg,

the last term becomes zero and the formulation is reduced to (1) and (2).

Similarly, consider a reshoring manufacturer under OSD. Let r′ denote the cost premium asso-

ciated with onshore rush production of shipped components to satisfy unmet realized demands.

With this change, the reshoring problem (3) and (4) become

Π1c

.=max

x1c≥0{−((1 + tc)c+ sc)x

1c + γΠ1

m(µH , x1c) + (1− γ)Π1

m(µL, x1c)},

Π1m(µ,x1

c).= maxx1m≥0{−((1 + tc)c+ sc + e)(x1

m−x1c)

+−m1x1m + pE[min{Ψ, x1

m}|µ]

+ (p−m1− r′)+E[(min{Ψ, x1

c}−x1m

)+ |µ]}.

The last term in Π1m(µ,x0

m) captures the potential profit generated by rush-producing finished

goods from held-back components to satisfy unmet realized demands. When r′ is sufficiently large,

i.e., r′ ≥ p−m1, the last term becomes zero and the formulation is reduced to (3) and (4).

23

Allowing for instantaneous responses after demand realization implies that the manufacturer can

respond to two demand information updates, which complicates the problems significantly and ren-

ders them analytically intractable (see Online Appendix A for details). We thus resort to numerical

evaluations. Figure 7 contains nine cases for comparison. All previously existing parameters are

kept identical to Figure 3 Case (a). The two new parameters are e′ (expedited shipping premium

under offshoring) and r′ (onshore rush production premium). Three representatives values ranging

from high (H) to medium (M) to low (L) are evaluated for each of the two new parameters, with

H high enough such that the manufacturer would never use instantaneous responses after demand

realization and the problems are reduced to their counterparts in Section 3. Consistent with Figure

3, the x- and y-axes are respectively ∆∈ [0,10] and γ ∈ [0,1]. We omit the axis labels to save space.

A few observations are immediate from Figure 7. First, offshoring-reshoring profit comparisons

with instantaneous responses after demand realization remain structurally similar to those without

instantaneous responses. Second, a lower e′ (expedited shipping premium under offshoring) favors

offshoring, and a lower r′ (onshore rush production premium) favors reshoring, which are intuitive.

The two effects can also offset each other; for example, the case of e′ = L,r′ = L is qualitatively

similar to the case of e′ =H,r′ =H. In general, our investigation confirms that the results from

the original models are robust with instantaneous responses after demand realization.

6. Concluding remarks

In this paper, we rigorously model and investigate the issue of offshore supply dependence (OSD)

and its effect on reshoring manufacturing. We build our models around the key notion that, under

OSD, reshoring reduces a manufacturer’s distance to the market at the expense of increasing

its distance to the supplier. We find that the increased distance to the supplier and the result-

ing component shipping lead-time hamper a reshoring manufacturer’s responsiveness to demand

information updates. Specifically, under OSD, the reshoring manufacturer still has to make the

component purchase decision based on early, less accurate demand information, which limits its

ability to take advantage of more accurate demand information in the postponed onshore pro-

duction decision. This effect of OSD reshapes the cost-responsiveness tradeoff between offshoring

and reshoring and significantly affects offshoring-reshoring profit comparisons. Therefore, ignoring

OSD may exaggerate reshoring’s responsiveness advantage, leading to misguided favorable predic-

tions about reshoring, while in fact the opposite may be true should OSD be properly accounted

for. Consequently, OSD deserves careful attention of relevant stakeholders in the consideration of

reshoring. In fact, the recent empirical study by Cohen et al. (2016) finds that firms which choose

24

Offshoring

Reshoring

e′ =H,r′ =H

Offshoring

Reshoring

e′ =H,r′ =M

Offshoring

Reshoring

e′ =H,r′ =L

Offshoring

Reshoring

e′ =M,r′ =H

Offshoring

Reshoring

e′ =M,r′ =M

Offshzoring

Reshoring

e′ =M,r′ =L

Offshoring

Reshoring

e′ =L,r′ =H

Offshoring

Reshoring

e′ =L,r′ =M

Offshoring

Reshoring

e′ =L,r′ =L

Figure 7 Illustration of Figure 3 Case (a) under OSD with instantaneous response

to reshore tend to have less concerns about supply-related factors including supply availability and

raw material and logistics costs, which is consistent with our model predictions.

Our models also capture salient costs of cross-border transactions such as different customs duties

and shipping costs for finished goods and components. This allows us to investigate how these

costs influence offshoring-reshoring profit comparisons under OSD. We find that trade treaties or

protectionist movements that increase or decrease customs duties in a correlated manner may or

may not make reshoring more appealing, and that increased shipping costs for both finished goods

25

and components may actually make reshoring less appealing when compared with offshoring. Both

observations are more nuanced than the common notions formed without accounting for OSD,

signifying the importance of OSD when comparing offshoring and reshoring.

By rigorously modeling OSD and showing its importance in the reshoring consideration, our

work provides a theoretical support for many practitioners’ views on this issue; e.g., Shih (2014)

summarizes, “the big picture is shifting away from the centrality of labor-cost arbitrage as a driver

of location decisions. Instead, it is moving to the supplier ecosystems as a key complementary

asset.” To this end, we recommend the near-term approach of common-component designs to make

reshoring more appealing under OSD. In the long run, we believe that fostering onshore supply base

development will be key to creating a viable environment for sustainable and scalable reshoring.

References

Anand, K., K. Girotra. 2007. The strategic perils of delayed differentiation. Management Sci. 53(5) 697–712.

Burrows, P. 2013. Apple’s Cook kicks off ‘Made in USA’ push with Mac Pro. http://www.bloomberg.com/ne

ws/2013-12-18/apple-s-cook-kicks-off-made-in-usa-push-with-mac-pro.html. Retrieved on

May 1, 2016.

Cachon, G. 2003. Supply chain coordination with contracts. Handbooks in Operations Research and Man-

agement Science 11 227–339.

Caro, F., V. Martınez-de-Albeniz. 2010. The impact of quick response in inventory-based competition.

Manufacturing Service Oper. Management 12(3) 409–429.

Chen, Y., M. Cohen, S. Cui, M. Dong, S. Liu, D. Simchi-Levi. 2015. Global oper. sourcing strategy: A

Chinese perspective. Available at SSRN 2623770 .

Cohen, M. A, S. Cui, E. Ricardo, A. Huchzermeier, P. Kouvelis, H. Lee, H. Matsuo, M. Steuber, A. Tsay.

2016. Benchmarking global production sourcing decisions: Where and why firms offshore and reshore.

Available at SSRN 2791373 .

Dong, L., P. Kouvelis, P. Su. 2010. Global facility network design with transshipment and responsive pricing.

Manufacturing Service Oper. Management 12(2) 278–298.

Donohue, K. 2000. Efficient supply contracts for fashion goods with forecast updating and two production

modes. Management Sci. 46(11) 1397–1411.

26

Duhigg, C., K. Bradsher. 2012. How the U.S. lost out on iPhone work. http://www.nytimes.com/2012/

01/22/business/apple-america-and-a-squeezed-middle-class.html. Retrieved on May 1, 2016.

Elmaghraby, W. 2000. Supply contract competition and sourcing policies. Manufacturing Service Oper.

Management 2(4) 350–371.

Fisher, M., A. Raman. 1996. Reducing the cost of demand uncertainty through accurate response to early

sales. Oper. Research 44(1) 87–99.

Goyal, M., S. Netessine. 2007. Strategic technology choice and capacity investment under demand uncertainty.

Management Sci. 53(2) 192–207.

Gurnani, H., C. Tang. 1999. Note: Optimal ordering decisions with uncertain cost and demand forecast

updating. Management Sci. 45(10) 1456–1462.

Hertzman, E. 2014. Made in the USA is more hype than reality. http://www.businessoffashion.com/

2014/06/op-ed-made-usa-hype-reality.html. Retrieved on May 1, 2016.

Iyer, A., M. Bergen. 1997. Quick response in manufacturer-retailer channels. Management Sci. 43(4) 559–

570.

King, I. 2013. Google’s all-American Moto X phone contains few U.S.-made parts. http:

//www.bloomberg.com/news/2013-08-30/google-s-all-american-moto-x-phone-contains-fe

w-u-s-made-parts.html. Retrieved on May 1, 2016.

Kondej, Magdalena. 2016. Fashion industry post-Brexit referendum: is it all that bad? http://blog.eurom

onitor.com/2016/07/fashion-industry-post-brexit-referendum-bad.html. Retrieved on Aug 1,

2016.

Lee, H., C. Tang. 1997. Modelling the costs and benefits of delayed product differentiation. Management

Sci. 43(1) 40–53.

Lu, L., A. Van Mieghem. 2009. Multimarket facility network design with offshoring applications. Manufac-

turing Service Oper. Management 11(1) 90–108.

Nash-Hoff, M. 2015. How would the Trans-Pacific Partnership Agreement affect the reshoring

trend? http://www.industryweek.com/trade/how-would-trans-pacific-partnership-agreeme

nt-affect-reshoring-trend. Retrieved on May 1, 2016.

27

Schoenberger, R. 2013. Reshoring: Are manufacturing jobs coming back to United States? http://www.cl

eveland.com/business/index.ssf/2013/03/reshoring_conference_to_study.html. Retrieved on

May 1, 2016.

Semuels, A. 2015. How the Trans-Pacific Partnership threatens America’s recent manufacturing resur-

gence. http://www.theatlantic.com/business/archive/2015/10/trans-pacific-partnership-

tpp-manufacturing/409591/. Retrieved on May 1, 2016.

Shih, W. 2014. What it takes to reshore manufacturing successfully. Sloan Management Review .

Sirkin, H., M. Zinser, D. Hohner. 2011. Made in America, again: Why manufacturing will return to

the U.S. https://www.bcgperspectives.com/Images/made_in_america_again_tcm80-84471.pdf.

Retrieved on May 1, 2016.

The Economist. 2013. Here, there and everywhere. http://www.economist.com/news/special-report/

21569572-after-decades-sending-work-across-world-companies-are-rethinking-their-off

shoring. Retrieved on May 1, 2016.

The Economist. 2014. Reshoring: hardly reshoring. http://www.economist.com/news/britain/21635615-

david-cameron-tries-bring-back-manufacturing-jobs-britain-hardly-reassuring. Retrieved

on May 1, 2016.

Tsay, A. 2014. Designing and controlling the outsourced supply chain. Foundations and Trends in Technology,

Information and Operations Management 1-2 1–160.

Van Mieghem, J., M. Dada. 1999. Price versus production postponement: Capacity and competition. Man-

agement Sci. 45(12) 1639–1649.

Van Mieghem, J., N. Rudi. 2002. Newsvendor networks: Inventory management and capacity investment

with discretionary activities. Manufacturing Service Oper. Management 4(4) 313–335.

Wang, J. 2014. Reshoring garment manufacturing is viable and scalable. http://www.businessoffashio

n.com/2014/08/op-ed-reshoring-garment-manufacturing-viable-scalable.html. Retrieved on

May 1, 2016.

Wang, T., D. Thomas, N. Rudi. 2014. The effect of competition on the efficient–responsive choice. Production

Oper. Management 23(5) 829–846.

28

Wu, X., F. Zhang. 2014. Home or overseas? an analysis of sourcing strategies under competition. Management

Sci. 60(5) 1223–1240.

1

Online Appendices to “Is reshoring better than offshoring?The effect of offshore supply dependence”’

Appendix A: Additional Analyses

Offshoring analysis

We define z0.= Φ−1

(p−(1+tg)(c+m0)−sg

p

)where Φ is the cumulative distribution function of a stan-

dard normal distribution, and z0 is the critical fractile for the newsvendor problem with regular

production only. It follows that the optimal solution x0∗m to problem (1) must satisfy µL + σz0 ≤

x0∗m ≤ µH +σz0.

Now consider the manufacturer’s decision after learning the demand type. Suppose that the

manufacturer adjusts the final inventory level downward when demand is high, then it must also

adjust the final inventory level downward when demand is low. Such a strategy cannot be optimal

as one can improve it by simply reducing the initial production quantity. Hence, in the event that

the demand type is revealed to be high, the manufacturer would either adjust the final inventory

level upward or do nothing, and the resulting profit function is

Π0s(µH , x

0m)

.= max

x0s≥x0m

{−(1 + tg)(c+m0 + r)(x0

s−x0m)− tg(c+m0)x

0m− sgx0

s + pE[min{Ψ, x0s}|µH ]

}.

(A1)

The above problem is a standard newsvendor problem. We define z0U.= Φ−1

(p−(1+tg)(c+m0+r)−sg

p

)which is the critical fractile for the upward adjustment (rush production). The optimal shipped

quantity to problem (A1) is given by x0∗sH = max{x0

m, µH +σz0U}, where subscript H denotes relation

to high demand.

Similarly, the manufacturer would either adjust production downward or do nothing in the event

that the demand type is revealed to be low, and the resulting profit function is

Π0s(µL, x

0m)

.= max

x0s≤x0m

{−(tg(c+m0) + sg)x

0s + pE[min{Ψ, x0

s}|µL]}. (A2)

We define z0D.= Φ−1

(p−tg(c+m0)−sg

p

)which is the critical fractile for the downward adjustment

(holding back shipping finished goods). The optimal solution to (A2) is given by x0∗sL = min{x0

m, µL+

σz0D}, where subscript L denotes relation to the low demand. Clearly, z0U < z0 < z0D. Recall ∆.=

(µH − µL)/σ as a measure of the difference between the high and low demands relative to the

demand uncertainty. One can verify that µH + σz0U ≤ µL + σz0D if and only if ∆ = (µH − µL)/σ ≤

z0D− z0U . It is also useful to define the following two thresholds for γ:

γ0U(∆)

.=

Φ(z0U + ∆)−Φ(z0)

Φ(z0U + ∆)−Φ(z0U), γ0

D(∆).=

Φ(z0D)−Φ(z0)

Φ(z0D)−Φ(z0D−∆). (A3)

The following lemma characterizes these two thresholds (all proofs are in Appendix B):

2

Lemma A1. The threshold γ0U(∆) is increasing in ∆, with γ0

U(∆) = 0 for ∆ ≤ z0 − z0U . The

threshold γ0D(∆) is decreasing in ∆, with γ0

D(∆) = 1 for ∆≤ z0D− z0. Thresholds γ0U(∆) and γ0

D(∆)

intersect at (∆0, γ0), where ∆0 .= z0D − z0U and γ0 .

= c+m0c+m0+(1+tg)r

. For ∆ ≤∆0, µH + σz0U ≤ x0∗m ≤

µL +σz0D if and only if γ0U(∆)≤ γ ≤ γ0

D(∆).

For ease of exposition, we define two more critical fractiles:

z0mU.= Φ−1

(γ(1 + tg)r+ (1− γ)(p− (1 + tg)(c+m0)− sg)

(1− γ)p

), for γ ≤ γ0 =

c+m0

c+m0 + (1 + tg)r,

where it can be shown that z0mU increases from z to z0D as γ increases from 0 to γ0; and

z0mD.= Φ−1

(γ(p− sg)− (1 + γtg)(c+m0)

γp

), for γ ≥ γ0 =

c+m0

c+m0 + (1 + tg)r,

where it can be shown that z0mD decreases from z to z0U as γ decreases from 1 to γ0. The next

proposition characterizes an offshoring manufacturer’s optimal strategies and profits.

Proposition A1. The offshoring manufacturer’s optimal strategies and profits are as follows:

Case N (neither): ∆≤∆0 and γ0U(∆)≤ γ ≤ γ0

D(∆). The optimal solution is x0∗m = x0∗

sH = x0∗sL = x,

where x uniquely solves γΦ(x−µHσ

)+ (1− γ)Φ

(x−µLσ

)= Φ(z0). In other words, the manufacturer

makes neither upward nor downward adjustments. The optimal profit is −((1+tg)(c+m0)+sg)x0∗m +

pE[min{Ψ, x0∗m}].

Case U (upward): ∆≤∆0 and γ < γ0U(∆), or ∆>∆0 and γ ≤ γ0. The optimal solution is x0∗

m =

x0∗sL = µL +σz0mU , x0∗

sH = µH +σz0U . In other words, the manufacturer makes an upward adjustment

if the demand turns out to be high. The optimal profit is pσγΦ(z0U)∆−pσ[γφ(z0U)+(1−γ)φ(z0mU)]+

pΦ(z0)µL.

Case D (downward): ∆ ≤∆0 and γ > γ0D(∆), or ∆ > ∆0 and γ > γ0. The optimal solution is

x0∗m = x0∗

sH = µH + σz0mD, x0∗sL = µL + σz0D. In other words, the manufacturer makes a downward

adjustment if the demand turns out to be low. The optimal profit is pσγΦ(z0mD)∆− pσ[γφ(z0mD) +

(1− γ)φ(z0D)] + pΦ(z0)µL.

Reshoring analysis under OSD

Similar to the offshoring model, we define

z1.= Φ−1

(p− (1 + tc)c−m1− sc

p

), z1U

.= Φ−1

(p− (1 + tc)c−m1− sc− e

p

), z1D

.= Φ−1

(p−m1

p

),

γ1U(∆)

.=

Φ(z1U + ∆)−Φ(z1)

Φ(z1U + ∆)−Φ(z1U), γ1

D(∆).=

Φ(z1D)−Φ(z1)

Φ(z1D)−Φ(z1D−∆).

Due to the different timelines, these expressions do not exactly mirror the offshoring expressions,

however similar analysis could still be carried out, which leads to the following lemma that mirrors

Lemma A1 for the offshoring model. The proof is similar to that of Lemma A1 and is thus omitted.

3

Lemma A2. The threshold γ1U(∆) is increasing in ∆, with γ1

U(∆) = 0 for ∆ ≤ z1 − z1U . The

threshold γ1D(∆) is decreasing in ∆, with γ1

D(∆) = 1 for ∆≤ z1D− z1. Thresholds γ1U(∆) and γ1

D(∆)

intersect at (∆1, γ1), where ∆1 .= z1D − z1U and γ1 .

= (1+tc)c+sc(1+tc)c+sc+e

. For ∆ ≤ ∆1, µH + σz1U ≤ x1∗c ≤

µL +σz1D if and only if γ1U(∆)≤ γ ≤ γ1

D(∆).

We define two more critical fractiles:

z1cU.= Φ−1

(γe+ (1− γ)(p− (1 + tc)c−m1− sc)

(1− γ)p

), for γ ≤ γ1 =

(1 + tc)c+ sc(1 + tc)c+ sc + e

,

where it can be shown that z1cU increases from z to z1D as γ increases from 0 to γ1; and

z1cD.= Φ−1

(γ(p−m1)− (1 + tc)c− sc

γp

), for γ ≥ γ1 =

(1 + tc)c+ sc(1 + tc)c+ sc + e

,

where it can be shown that z1cD decreases from z to z1U as γ decreases from 1 to γ1. The next

proposition characterizes a reshoring manufacturer’s optimal strategies and profits. The proof is

structurally similar to that of Proposition A1 and is thus omitted.

Proposition A2. The reshoring manufacturer’s optimal strategies and profits are as follows:

Case N (neither): ∆≤∆1 and γ1U(∆)≤ γ ≤ γ1

D(∆). The optimal solution is x1∗c = x1∗

mH = x1∗mL =

x, where x uniquely solves γΦ(x−µHσ

)+(1−γ)Φ

(x−µLσ

)= Φ(z1). In other words, the manufacturer

makes neither upward nor downward adjustments. The optimal profit is −((1+ tc)c+m1 +sc)x1∗c +

pE[min{Ψ, x1∗c }].

Case U (upward): ∆≤∆1 and γ < γ1U(∆), or ∆>∆1 and γ ≤ γ1. The optimal solution is x1∗

c =

x1∗mL = µL+σz1cU , x1∗

mH = µH +σz1U . In other words, the manufacturer makes an upward adjustment

if the demand turns out to be high. The optimal profit is pσγΦ(z1U)∆−pσ[γφ(z1U)+(1−γ)φ(z1cU)]+

pΦ(z1)µL.

Case D (downward): ∆ ≤∆1 and γ > γ1D(∆), or ∆ > ∆1 and γ > γ1. The optimal solution is

x1∗c = x1∗

mH = µH + σz1cD, x1∗mL = µL + σz1D. In other words, the manufacturer makes a downward

adjustment if the demand turns out to be low. The optimal profit is pσγΦ(z1cD)∆− pσ[γφ(z1cD) +

(1− γ)φ(z1D)] + pΦ(z1)µL.

Offshoring-reshoring profit comparison under OSD

We define b0 = (1 + tg)(c + m0) + sg, b1 = (1 + tc)c + sc + m1 to be the baseline-costs (without

adjusting inventory after learning the demand type), u0 = (1 + tg)r, u1 = e to be the cost of a unit

upward inventory adjustment, and d0 = c+m0, d1 = (1+ tc)c+sc to be the cost of a unit downward

inventory adjustment, of offshoring and reshoring respectively. We then rewrite all z terms:

z0.= Φ−1

(p− b0p

), z0U

.= Φ−1

(p− b0−u0

p

), z0D

.= Φ−1

(p− b0 + d0

p

),

4

z1.= Φ−1

(p− b1p

), z1U

.= Φ−1

(p− b1−u1

p

), z1D

.= Φ−1

(p− b1 + d1

p

),

z0mU.= Φ−1

(γu0 + (1− γ)(p− b0)

(1− γ)p

), for γ ≤ γ0 =

d0d0 +u0

,

z0mD.= Φ−1

(γ(p− b0)− (1− γ)d0

γp

), for γ ≥ γ0 =

d0d0 +u0

,

z1cU.= Φ−1

(γu1 + (1− γ)(p− b1)

(1− γ)p

), for γ ≤ γ1 =

d1d1 +u1

,

z1cD.= Φ−1

(γ(p− b1)− (1− γ)d1

γp

), for γ ≥ γ1 =

d1d1 +u1

.

The following useful lemma is straightforward to verify, thus we omit the proof.

Lemma A3. Below are the Π terms’ derivatives with respect to ∆ and the conditions for their

comparisons:

dΠ0U

d∆= pσγΦ(z0U),

dΠ0D

d∆= pσγΦ(z0mD),

dΠ1U

d∆= pσγΦ(z1U),

dΠ1D

d∆= pσγΦ(z1cD).

dΠ0U

d∆≥ dΠ1

U

d∆⇔ b0 +u0 ≤ b1 +u1.

If b0 +u0 ≥ b1− d1 thendΠ0

U

d∆≥ dΠ1

D

d∆⇔ γ ≤ d1

b0 +u0− b1 + d1.

If b0 +u0 ≤ b1− d1 thendΠ0

U

d∆≥ dΠ1

D

d∆.

dΠ0D

d∆≥ dΠ1

U

d∆⇔ γ ≥ d0

b1 +u1− b0 + d0(b1 ≥ b0 implies b1 +u1 ≥ b0− d0).

If d0 ≥ d1 thendΠ0

D

d∆≥ dΠ1

D

d∆⇔ γ ≥ d0− d1

d0− d1 + b1− b0.

If d0 ≤ d1 thendΠ0

D

d∆≥ dΠ1

D

d∆.

We then present the complete versions of Propositions 2 as Propositions A3 and A4. The proofs

are in Appendix B.

Proposition A3. Under OSD, suppose δ= b1− b0 ≥ 0 and u1 ≤ u0−δ. There exists a threshold

γ =

d0

d0 +u1 + δif d0 ≤ d1, or d0 >d1 and γ0 ≤ γ1 and δ≥ (d0− d1)u1/d1;

d0− d1d0− d1 + δ

otherwise,

where γ ≤ γB. For any γ ≥ γ, reshoring yields lower profits than offshoring. For any 0 < γ < γ,

there exists ∆∗(γ)≥∆∗B(γ) such that reshoring yields higher profits than offshoring if and only if

∆>∆∗(γ).

5

Proposition A4. Under OSD, suppose δ = b1 − b0 ≥ 0 and u1 > u0 − δ. If d1 < d0(u0 − δ)/u0,

there exist two thresholds γ = d1/(d1 +u0− δ) and γ = (d0−d1)/(d0−d1 + δ), with γ < γ ≤ γB. For

any γ ≤ γ or γ ≥ γ, reshoring yields lower profits than offshoring. For any γ < γ < γ, there exists

∆∗(γ)≥∆∗B(γ) such that reshoring yields higher profits than offshoring if and only if ∆>∆∗(γ).

Otherwise, if d1 ≥ d0(u0− δ)/u0, reshoring always yields lower profits than offshoring.

Offshoring-reshoring profit comparison under OSD with equal baseline-costs

For simplicity, we assume m0 = m1 = m, sg = sc = s, tc = tg = 0, which leads to baseline-cost

c+m+ s for both offshoring and reshoring. Note that our analysis and structural results do not

depend on this particular parameter configuration, and hold true for any parameter configurations

that yield equal baseline-costs. The full characterization of the offshoring-reshoring comparison in

this special case is presented in the following proposition, where γ0U , γ

0D, γ

1U , γ

1D and z0U , z

0D, z

1U , z

1D

are defined earlier in this Appendix.

Proposition A5. Suppose m0 =m1 =m, sg = sc = s, tc = tg = 0, so δ= 0, and consider OSD.

(a) When m≤ s and r≤ e, reshoring always yields lower profits than offshoring.

(b) When m>s and r > e, reshoring always yields higher profits than offshoring.

(c) When m>s and r≤ e, thresholds γ0U(∆) and γ1

D(∆) intersect at (∆∗, γ∗).= (z1D− z0U , c+s

c+s+r).

• If ∆≤∆∗ and γ0U(∆)≤ γ ≤ γ1

D(∆), reshoring and offshoring yield equal profits.

• If ∆≤∆∗ and γ < γ0U(∆), or ∆>∆∗ and γ ≤ γ∗, reshoring yields lower profits than offshoring.

• If ∆ ≤ ∆∗ and γ > γ1D(∆), or ∆ > ∆∗ and γ > γ∗, reshoring yields higher profits than off-

shoring.

(d) When m≤ s and r > e, thresholds γ0D(∆) and γ1

U(∆) intersect at (∆†, γ†).= (z0D− z1U , c+m

c+m+e).

• If ∆≤∆† and γ1U(∆)≤ γ ≤ γ0

D(∆), reshoring and offshoring yield equal profits.

• If ∆≤∆† and γ < γ1U(∆), or ∆>∆† and γ ≤ γ†, reshoring yields higher profits than offshoring.

• If ∆≤∆† and γ > γ0D(∆), or ∆>∆† and γ > γ†, reshoring yields lower profits than offshoring.

Offshoring analysis with instantaneous responses

The offshoring formulation with instantaneous responses after demand realization is

Π0m

.= maxx0m≥0{−(c+m0)x

0m + γΠ0

s(µH , x0m) + (1− γ)Π0

s(µL, x0m)},

Π0s(µ,x

0m)

.=max

x0s≥0{−(c+m0 + (1 + tg)r)(x

0s−x0

m)+− (tg(c+m0) + sg)x0s + pE[min{Ψ, x0

s}|µ]

+ (p− tg(c+m0)− sg − e′)+E[(min{Ψ, x0

m}−x0s

)+ |µ]}.

If the manufacturer uses rush production (which implies no holding back shipping of finished

goods) after the Stage 1 demand information update, the Stage 2 formulation is

Π0s(µ,x

0m) = max

x0s≥x0m

{− (c+m0 + (1 + tg)r)(x

0s−x0

m)− (tg(c+m0) + sg)x0s

6

+p

[−(x0

s−µ)Φ

(x0s−µσ

)−σφ

(x0s−µσ

)+x0

s

]}.

If the manufacturer holds back shipping of finished goods (which implies no rush production) or

do nothing after the Stage 1 demand information update, the Stage 2 formulation is

Π0s(µ,x

0m)

= max0≤x0s≤x0m

{−(tg(c+m0) + sg)x

0s +

∫ x0s

−∞pψφµ(ψ)dψ +

∫ x0m

x0s

[pψ− (tg(c+m0) + sg + e′)(ψ−x0s)]φµ(ψ)dψ

+

∫ ∞x0m

[px0m− (tg(c+m0) + sg + e′)(x0

m−x0s)]φµ(ψ)dψ

}

= max0≤x0s≤x0m

{−(tg(c+m0) + sg)x

0s + p

∫ x0s

−∞ψφµ(ψ)dψ+ (p− tg(c+m0)− sg − e′)

∫ x0m

x0s

ψφµ(ψ)dψ

+x0s(tg(c+m0) + sg + e′)

∫ x0m

x0s

φµ(ψ)dψ+ [px0m− (tg(c+m0) + sg + e′)(x0

m−x0s)]

∫ ∞x0m

φµ(ψ)dψ

}

= max0≤x0s≤x0m

{−(tg(c+m0) + sg)x

0s + p

[µΦ

(x0s−µσ

)−σφ

(x0s−µσ

)]+ (p− tg(c+m0)− sg − e′)

[µΦ

(x0m−µσ

)−σφ

(x0m−µσ

)−µΦ

(x0s−µσ

)+σφ

(x0s−µσ

)]+x0

s(tg(c+m0) + sg + e′)

[Φ

(x0m−µσ

)−Φ

(x0s−µσ

)]+[px0

m− (tg(c+m0) + sg + e′)(x0m−x0

s)]

[1−Φ

(x0m−µσ

)]}.

The last equation is due to the relationship that∫ x

−∞ψφµ(ψ)dψ= µΦ

(x−µσ

)−σφ

(x−µσ

).

The above closed-form formulations are then numerically evaluated to solve for the offshoring

manufacturer’s optimal strategies and profits.

Reshoring analysis under OSD with instantaneous responses

The reshoring formulation with instantaneous responses after demand realization is

Π1c

.=max

x1c≥0{−((1 + tc)c+ sc)x

1c + γΠ1

m(µH , x1c) + (1− γ)Π1

m(µL, x1c)},

Π1m(µ,x1

c).= maxx1m≥0{−((1 + tc)c+ sc + e)(x1

m−x1c)

+−m1x1m + pE[min{Ψ, x1

m}|µ]

+ (p−m1− r′)+E[(min{Ψ, x1

c}−x1m

)+ |µ]}

If the manufacturer expedites components (which implies no holding back production) after the

Stage 1 demand information update, the Stage 2 formulation is

Π1m(µ,x1

c).= maxx1m≥x1c

{− ((1 + tc)c+ sc + ec)(x

1m−x1

c)−m1x1m

7

+ p

[−(x1

m−µ)Φ

(x1m−µσ

)−σφ

(x1m−µσ

)+x1

m

]}.

If the manufacturer holds back production (which implies no expedited components) or do noth-

ing after the Stage 1 demand information update, the Stage 2 formulation is

Π1m(µ,x1

c)

= max0≤x1m≤x1c

{−m1x

1m +

∫ x1m

−∞pψφµ(ψ)dψ+

∫ x1c

x1m

[pψ− (m1 + r′)(ψ−x1m)]φµ(ψ)dψ

+

∫ ∞x1c

[px1c − (m1 + r′)(x1

c −x1m)]φµ(ψ)dψ

}

= max0≤x1m≤x1c

{−m1x

1m + p

[µΦ

(x1m−µσ

)−σφ

(x1m−µσ

)]+ (p−m1− r′)

[µΦ

(x1c −µσ

)−σφ

(x1c −µσ

)−µΦ

(x1m−µσ

)+σφ

(x1m−µσ

)]+x1

m(m1 + r′)

[Φ

(x1c −µσ

)−Φ

(x1m−µσ

)]+ [px1

c − (m1 + r′)(x1c −x1

m)]

[1−Φ

(x1c −µσ

)]}.

The derivation is similar to the offshoring case. The above closed-form formulations are then

numerically evaluated to solve for the reshoring manufacturer’s optimal strategies and profits, and

comparing the offshoring and reshoring optimal profits yields Figure 7.

Appendix B: Proofs

Proof of Proposition 1. The general result with δ ≥ 0 follows from Propositions A3 with e= 0

(ignoring OSD is equivalent to having free expedited shipping). The special result with δ= 0 follows

from the argument that a reshoring manufacturer can replicate any offshoring production quantity

at no higher costs. �

Proof of Proposition 2. Case (a) follows from Proposition A3. Cases (b) and (c) follow from

Proposition A4. �

Proof of Lemma A1. By (A3), it is straightforward to verify that γ0U(∆) is increasing in ∆,

γ0D(∆) is decreasing in ∆, γ0

U = 0 for ∆≤ z0 − z0U , and γ0D = 1 for ∆≤ z0D − z0. Therefore, γ0

U(∆)

and γ0D(∆) intersect at most once. Since when ∆0 = z0D−z0U , γ0

U(∆0) = γ0D(∆0) = γ0 = c+m0

c+m0+(1+tg)r,

(∆0, γ0) characterizes the intersection.

Recall that ∆ ≤ ∆0 = z0D − z0U implies µH + σz0U ≤ µL + σz0D. From the anal-

ysis preceding the lemma, when x0m ∈ [µH + σz0U , µL + σz0D], the manufacturer

would do nothing after learning the demand type. The problem thus becomes

maxx0m≥0 {−((1 + tg)(c+m0) + sg)x0m + pE[min{Ψ, x0

m}]} . It is straightforward to show that the

optimal solution solves the FOC: γΦ((x− µH)/σ) + (1− γ)Φ((x− µL)/σ) = Φ(z0). Note that the

8

left-hand-side of the FOC is increasing in x and decreasing in γ. Therefore, x≥ µH + σz0U if and

only if γ ≤ γ′, where γ′ is determined by

γ′Φ((µH +σz0U −µH)/σ) + (1− γ′)Φ((µH +σz0U −µL)/σ) = Φ(z0)⇒ γ′ =Φ(z0U + ∆)−Φ(z0)

Φ(z0U + ∆)−Φ(z0U)

which is the same as the threshold γ0U(∆) defined in (A3).

Symmetrically, x≤ µL +σz0D if and only if γ ≤ γ, where γ is determined by

γΦ((µL +σz0D−µH)/σ) + (1− γ)Φ((µL +σz0D−µL)/σ) = Φ(z0)⇒ γ =Φ(z0D)−Φ(z0)

Φ(z0D)−Φ(z0D−∆)

which is the same as the threshold γ0D(∆) defined in (A3). Therefore, we conclude that µH +σz0U ≤

x0∗m ≤ µL +σz0D if and only if γ0

U(∆)≤ γ ≤ γ0D(∆). �

Proof of Proposition A1. We first introduce a relation that follows straightforward integration

by parts. Recall that Φ and φ denote the standard normal cumulative distribution and probability

density functions, respectively. Suppose Ψ follows a normal distribution with mean µ and standard

deviation σ. Then ∫ x

−∞

ψ√2πσ

e− (ψ−µ)2

2σ2 dψ= µΦ

(x−µσ

)−σφ

(x−µσ

). (B1)

Case I: ∆≤∆0 and γ0U ≤ γ ≤ γ0

D. Due to Lemma A1, we know that the manufacturer would do

nothing after learning the demand type. Therefore, the optimal solution is x0∗m = x0∗

sH = x0∗sL = x,

where x uniquely solves γΦ((x − µH)/σ) + (1 − γ)Φ((x − µL)/σ) = Φ(z0). The optimal profit is

−((1 + tg)(c+m0) + sg)x0∗m + pE[min{Ψ, x0∗

m}].

Case II: ∆≤∆0 and γ < γ0U , or ∆>∆0 and γ ≤ γ0. First consider the subcase of ∆≤∆0 and

γ < γ0U . Due to Lemma A1, we know that x0∗

m < µH + σz0U ≤ µL + σz0D, hence it is optimal for the

manufacturer to adjust the final inventory level upward to µH +σz0U if the demand type turns out

to be high and do nothing if it turns out to be low. The problem becomes the following:

Π0m

.= max

x0m≥0{−(c+m0)x

0m + γΠ0

s(µH , x0m) + (1− γ)Π0

s(µL, x0m)}, (B2)

where Π0s(µH , x

0m) =−(1 + tg)(c+m0 + r)(x0∗

sH −x0m)− tg(c+m0)x

0m− sgx0∗

sH +pE[min{Ψ, x0∗sH}|µH ]

with x0∗sH = µH +σz0U , Π0

s(µL, x0m) =−(tg(c+m0) +sg)x

0m+pE[min{Ψ, x0

m}|µL]. One can show that

the optimal x0∗m solves the following FOC: Φ((x0

m−µL)/σ)) = [γ(1 + tg)r+ (1− γ)(p− (1 + tg)(c+

m0)− sg)]/[(1− γ)p]. Therefore, x0∗m = µL + σz0mU . Plugging x0∗

m into Π0m and utilizing (B1), we

obtain the optimal profit

Π0m = pσγΦ(z0U)∆− pσ[γφ(z0U) + (1− γ)φ(z0mU)] + pΦ(z0)µL. (B3)

9

Now consider the subcase of ∆>∆0 and γ ≤ γ0. Recall that ∆>∆0 implies µL+σz0D <µH+σz0U ,

hence if x0m ≤ µL+σz0D, then the manufacturer would adjust the final inventory level upward if the

demand type turns out to be high and do nothing if it turns out to be low. The problem becomes

the same as (B2), and it follows that x0∗m = µL + σz0mU . It is straightforward to verify that z0mU

increases from z to z0D as γ increases from 0 to γ0 = c+m0c+m0+(1+tg)r

. Therefore, when ∆ > ∆0 and

γ ≤ γ0, the optimal solution is x0∗m = µL +σz0mU and the optimal profit is given by (B3).

Case III: ∆≤∆0 and γ > γ0D, or ∆>∆0 and γ > γ0. Following an argument symmetric to Case

II, we can show that in this case, it is optimal for the manufacturer to adjust the final inventory

level downward to µL + σz0D if the demand type turns out to be low and do nothing if it turns

out to be high. The problem becomes the following: Π0m

.= maxx0m≥0{−(c+m0)x

0m+γΠ0

s(µH , x0m)+

(1 − γ)Π0s(µL, x

0m)}, where Π0

s(µH , x0m) = −((1 + tg)(c + m0) + sg)x

0∗ψ + pE[min{Ψ, x0∗

ψ }|µH ], and

Π0s(µL, x

0m) =−((1+tg)(c+m0)+sg)x

0∗sL+pE[min{Ψ, x0∗

sL}|µL] with x0∗sL = µL+σz0D. Similar to Case

II, the optimal x0∗m solves the following FOC: Φ((x0

m−µH)/σ)) = [γ(p−sg)−(1+γtg)(c+m0)]/(γp).

Therefore, the optimal solution is x0∗m = x0∗

sH = µH + σz0mD, x0∗sL = µL + σz0D. Plugging x0∗

m into Π0m

and utilizing (B1), we obtain the optimal profit Π0m = pσγΦ(z0mD)∆−pσ[γφ(z0mD)+(1−γ)φ(z0D)]+

pΦ(z0)µL. �

Proof of Proposition A3. We show the proof in four parts. First we show that the manufacturer

prefers to remain offshoring for sufficiently small ∆. Second we show the manufacturer’s limit

preference for sufficiently large ∆. Third we show that if the manufacturer’s preference for ∆→ 0

and ∆→∞ differs, then as ∆ increases, the manufacturer’s preference changes exactly once. Finally

we show that if the manufacturer’s preference for ∆→ 0 and ∆→∞ is the same, then as ∆

increases, the manufacturer’s preference never changes.

We use short-hand notations ΠiX(∆, γ) to denote the offshoring (i = 0) or reshoring (i = 1)

manufacturer’s profit expressions in the three cases (X =N,U,D) presented in Propositions A1 and

A2. For example, Π0N(∆, γ) =−b0x0∗

m + pE[min{Ψ, x0∗m}] and Π1

N(∆, γ) =−b1x1∗c + pE[min{Ψ, x1∗

c }].

We also denote the inverse functions of γiX(∆) by ∆iX(γ).

I. When ∆ < min(∆0U(γ),∆1

U(γ),∆0D(γ),∆0

D(γ)), both offshoring and reshoring are in Case N ,

namely the manufacturer uses neither flexibility regardless of the demand type. Since b0 ≤ b1, in

this case an offshoring manufacturer could mimic the reshoring strategy at no higher costs and

receive the same revenue, thus the manufacturer prefers to remain offshoring.

II. When ∆→∞, each of offshoring and reshoring will be either in Case U or Case D, and the Π

terms’ derivatives with respect to ∆ determine the limit profit comparisons. The conditions in the

proposition follow straightforwardly from Lemma A3.

10

III. We make an important observation that for any γ, the manufacturer’s profit is concave in ∆.

We already know in Cases U and D the profits are linear in ∆. For Case N , take the example of

offshoring and γ < γ0 so as ∆ increases the solution case shifts from N to U (the proof for the

other cases are similar). Consider any ∆<∆0U(γ), and we know Π0

U(∆, γ)< Π0N(∆, γ). Since Π0

U

is decreasing in u0, there must exist a u′0 < u0 such that Π0U(∆, γ, u′0) = Π0

N(∆, γ, u0). Therefore,

we know that dΠ0N(u0)/d∆ = dΠ0

U(u′0)/d∆ = pσγ(p− b0− u′0). Such u′0 must increase in ∆. As a

result, we know that Π0N is concave in ∆. Finally note that Π0

U(∆, γ)< Π0N(∆, γ)⇔∆<∆0

U(γ),

which guarantees that the left- and right-derivatives at ∆0U(γ) are equal, and thus Π0 is first concave

then linear, and is generally concave. The proof for the other cases are similar.

Using this property, we show that if the manufacturer’s preference for ∆→ 0 and ∆→∞ differs,

then as ∆ increases, the manufacturer’s preference changes exactly once. When both offshoring

and reshoring are in Case N , we know that the manufacturer’s preference does not change in ∆.

When one production mode is out of Case N , for example offshoring is in Case U , then Π0U(∆) is

linear and Π1(∆) is generally concave and increasing. When Π0U(0)<Π1(0) and Π0

U(∞)>Π1(∞),

or vice versa, it follows that they intersect exactly once.

IV. Take the example of a small γ such that as ∆ increases, both offshoring and reshoring shift

from Case N to Case U (the proof for the other cases are similar). We need to show that if

Π0N(0)>Π1

N(0) and Π0U(∞)>Π1

N(∞), then Π0N/U(∆) and Π1

N/U(∆) do not intersect.

We already know from Bullet I that for ∆ ≤ min(∆0U(γ),∆1

U(γ)), Π0N(∆) and Π1

N(∆) do not

intersect, and only need to prove they do not intersect for ∆>min(∆0U(γ),∆1

U(γ)). First consider

∆1U(γ)<∆0

U(γ). In this case, we know for ∆>∆1U(γ), reshoring is always in Case U , and offshoring

shifts from Case N to Case U at ∆0U(γ). We also know from Bullet III that in this region Π1

U(∆) is

linear and Π0N/U(∆) is concave. Recall that Π0

N(∆1U(γ))>Π0

U(∆1U(γ)), and Π0

U(∞)>Π1U(∞). One

can easily see graphically that they do not intersect in this region.

Next consider ∆0U(γ) < ∆1

U(γ). In this case, we know for ∆ > ∆0U(γ), offshoring is always in

Case U , and reshoring shifts from Case N to Case U at ∆1U(γ). For ∆∈ [∆0

U(γ),∆1U(γ)], we know

that Π0U(∆)>Π0

N(∆)≥Π1N(∆) (the latter due to b0 ≤ b1). Therefore, Π0

U(∆) and Π1N(∆) do not

intersect in this region. For ∆>∆1U(γ), note that Π0

U(∆1U(γ))>Π1

U(∆1U(γ)), and Π0

U(∆)′ >Π1U(∆)′.

Therefore, Π0U(∆) and Π1

U(∆) do not intersect in this region. This concludes the proof that in

generally, Π0N/U(∆) and Π1

N/U(∆) do not intersect.

Finally, γ ≤ γB and ∆∗(γ)≥∆∗B(γ) are due to the following argument: a reshoring manufacturer

ignoring OSD can always replicate the optimal decisions of a reshoring manufacturer under OSD

at no higher costs, and that an offshoring manufacturer’s profit is not affected by OSD, thus

accounting for OSD reduces the reshoring region. �

11

Proof of Proposition A4. For the case of d0 ≥ d1, the proof is similar to that of Proposition A3

and omitted. For the case of d0 < d1, we provide a sample-path proof. Note that under either off-

shoring or reshoring, the manufacturer’s strategy can be described by three decisions: the inventory

obtained regularly; the inventory obtained with expedition; and the components/finished goods

discarded before the selling season (not including inventory discarded after the selling season, which

is out of the manufacturer’s control). The costs associated with the three decisions are bi, bi + ui,

and bi, where i= 0,1 respectively represent offshoring and reshoring. Since b0 ≤ b1, b0 +u0 < b1 +u1,

and d0 < d1, an offshoring manufacturer could mimic any reshoring strategy at no higher costs

and receive the same revenue, thus the manufacturer prefers to remain offshoring. Finally, γ ≤ γBand ∆∗(γ) ≥∆∗B(γ) are due to the following argument: a reshoring manufacturer ignoring OSD

can always replicate the optimal decisions of a reshoring manufacturer under OSD at no higher

costs, and that an offshoring manufacturer’s profit is not affected by OSD, thus accounting for

OSD reduces the reshoring region. �

Proof of Proposition A5. Cases (a) follows from the fact that m ≤ s and r ≤ e respectively

ensure that reshoring has higher downward and upward inventory adjustment costs than offshoring.

Cases (b) follows from the fact that m> s and r > e respectively ensure that reshoring has lower

downward and upward inventory adjustment costs than offshoring. In Case (c) we have m>s and

r≤ e. Due to Lemmas A1 and A2, we know that γ0U(∆) is increasing in ∆ and γ1

D(∆) is decreasing

in ∆. It is easy to verify that γ0U(∆) and γ1

D(∆) intersect at (∆∗, γ∗), where ∆∗ = z1D − z0U and

γ∗ = c+sc+s+r

. It is also easy to verify that γ0U(∆)> γ1

U(∆), γ0D(∆)> γ1

D(∆), ∆∗ <min{∆0,∆1}, and

γ1 <γ∗ <γ0, hence when ∆≤∆∗, µH +σz1U ≤ µH +σz0U ≤ µL +σz1D ≤ µL +σz0D.

We first consider Case 1: ∆≤∆∗ and γ0U(∆)≤ γ ≤ γ1

D(∆). Due to Lemmas A1 and A2, we know

that µH + σz0U ≤ x0∗m ≤ µL + σz1D and µH + σz0U ≤ x1∗

c ≤ µL + σz1D. In this case, the manufacturer

would do nothing after learning the demand type, and the offshoring and reshoring problems

become identical, hence x0∗m = x1∗

c and the manufacturer is indifferent toward reshoring.

We next consider Case 2: ∆ ≤∆∗ and γ < γ0U(∆), or ∆> ∆∗ and γ ≤ γ∗. The first subcase is

∆≤∆∗ and γ < γ0U(∆), which has two possible scenarios: 1) γ1

U(∆)<γ < γ0U(∆), and 2) γ ≤ γ1

U(∆).

In Scenario 1), due to Propositions A1 and A2, we know that if the demand type turns out to be

high, an offshoring manufacturer would adjust the final inventory level upward, but a reshoring

manufacturer would do nothing. Because an offshoring manufacturer always has the option of doing

nothing, offshoring must yield higher profits than reshoring. In Scenario 2), due to Propositions

A1 and A2, we know that if the demand type turns out to be high, both an offshoring and a

reshoring manufacturer would adjust the final inventory level upward, which incurs r per unit

12

under offshoring and e per unit under reshoring. Since r ≤ e, offshoring yields higher profits than

reshoring. Therefore, the manufacturer prefers to remain offshoring in this subcase.

The second subcase is ∆>∆∗ and γ ≤ γ∗. Recall that γ1 < γ∗ < γ0. Due to Proposition A1, we

know that an offshoring manufacturer would adjust the final inventory level upward if the demand

type turns out to be high. On the other hand, due to Proposition A2, a reshoring manufacturer

may do nothing, adjust the final inventory level upward if the demand type turns out to be high, or

adjust the final inventory level downward if it turns out to be low. When a reshoring manufacturer

does nothing or adjusts the final inventory level upward if the demand type turns out to be high,

offshoring yields higher profits than reshoring following similar arguments as the first subcase.

It remains to compare offshoring and reshoring profits with ∆>∆∗ and max{γ1D(∆), γ1}< γ <

γ∗, when an offshoring manufacturer adjusts production upward if the demand type turns out to be

high, and a reshoring manufacturer adjusts the component inventory level downward if the demand

type turns out to be low. Due to Propositions A1 and A2, the optimal offshoring profit is given by

Π0m = pσγΦ(z0U)∆− pσ[γφ(z0U) + (1− γ)φ(z0mu)] + pΦ(z)µL = (p− c−m− s− r)γσ∆− pσ[γφ(z0U) +

(1 − γ)φ(z0mu)] + pΦ(z)µL, whereas the optimal reshoring profit is given by Π1c = pσγΦ(z1cd)∆ −

pσ[γφ(z1cd) + (1 − γ)φ(z1D)] + pΦ(z)µL = [(p − m)γ − (c + s)]σ∆ − pσ[γφ(z1cd) + (1 − γ)φ(z1D)] +

pΦ(z)µL.. The difference between the two expressions is Π0m −Π1

c = σ[(c+ s)− γ(c+ s+ r)]∆−

pσ[γφ(z0U) + (1− γ)φ(z0mu)− γφ(z1cd)− (1− γ)φ(z1D)]. Note that for any γ′ ∈ (max{γ1D(∆), γ1}, γ∗)

where γ∗ = (c+ s)/(c+ s+ r), the above expression is strictly increasing in ∆. Define ∆ as the

solution to γ1D(∆) = γ′. We know that at the point (∆, γ′), the reshoring manufacturer would do

nothing regardless of the revealed demand type. Therefore, offshoring yields higher profits than

reshoring. It then follows that offshoring yields strictly higher profits than reshoring for all ∆> ∆

and γ′ ∈ (max{γ1D(∆), γ1}, γ∗). Combining the above cases, we conclude that the manufacturer

prefers to remain offshoring in Case 2.

This leaves Case 3: ∆≤∆∗ and γ > γ1D(∆), or ∆>∆∗ and γ > γ∗. The proof is similar to Case

2 and omitted.

The proof of Case (d) mirrors that of Case (c) and is omitted. �