32
Reshoring Manufacturing: Supply Availability, Demand Updating, and Inventory Pooling Li Chen Samuel Curtis Johnson Graduate School of Management, Cornell University, Ithaca, NY 14853 [email protected] Bin Hu Kenan-Flagler Business School, University of North Carolina, Chapel Hill, NC 27599 bin [email protected] Reshoring refers to the emerging industry movement of once-offshoring manufacturers moving their factories back onshore. Existing literature emphasizes reshoring’s demand responsiveness due to market proximity. We however note that limited onshore supply availability may force reshoring manufacturers to remain dependent on offshore suppliers for component sourcing. As a result, the advantages due to improved market proximity may be offset by the disadvantages due to lost supply proximity. By accounting for the supply availability issue, we show that manufacturers’ preferences toward reshoring boil down to trade-offs between operational flexibilities under offshoring and reshoring. We characterize cost and demand scenarios wherein manufacturers prefer reshoring, and further identify operational strategies that can swing such preferences. Key words : newsvendor with demand updating, commonality, risk pooling History : file version August 16, 2015 1. Introduction For nearly three decades, manufacturing offshoring has been a predominant industry trend, espe- cially in the United States. The top driver of this trend has been the substantially lower labor costs in emerging economies. However, the previous labor “arbitrage” gradually tapers off as wages in developing economies such as China and India have increased by 10-20% annually for the past decade, putting a spotlight on the drawbacks of offshoring, including shipping costs and lead-times, lost manufacturing expertise, potential intellectual property leakage, increased disruption risks, and political pressure (The Economist 2013). Accordingly, a growing number of US-based com- panies 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). Nevertheless, the adoption of reshoring has been slower than many have hoped, gen- erating much discussion (Schoenberger 2013). Divided views are abundant among practitioners on whether reshoring is viable and scalable (Hertzman 2014, Wang 2014). 1

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Reshoring Manufacturing: Supply Availability,Demand Updating, and Inventory Pooling

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

[email protected]

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

bin [email protected]

Reshoring refers to the emerging industry movement of once-offshoring manufacturers moving their factories

back onshore. Existing literature emphasizes reshoring’s demand responsiveness due to market proximity.

We however note that limited onshore supply availability may force reshoring manufacturers to remain

dependent on offshore suppliers for component sourcing. As a result, the advantages due to improved market

proximity may be offset by the disadvantages due to lost supply proximity. By accounting for the supply

availability issue, we show that manufacturers’ preferences toward reshoring boil down to trade-offs between

operational flexibilities under offshoring and reshoring. We characterize cost and demand scenarios wherein

manufacturers prefer reshoring, and further identify operational strategies that can swing such preferences.

Key words : newsvendor with demand updating, commonality, risk pooling

History : file version August 16, 2015

1. Introduction

For nearly three decades, manufacturing offshoring has been a predominant industry trend, espe-

cially in the United States. The top driver of this trend has been the substantially lower labor

costs in emerging economies. However, the previous labor “arbitrage” gradually tapers off as wages

in developing economies such as China and India have increased by 10-20% annually for the past

decade, putting a spotlight on the drawbacks of offshoring, including shipping costs and lead-times,

lost manufacturing expertise, potential intellectual property leakage, increased disruption risks,

and political pressure (The Economist 2013). Accordingly, a growing number of US-based com-

panies 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). Nevertheless, the adoption of reshoring has been slower than many have hoped, gen-

erating much discussion (Schoenberger 2013). Divided views are abundant among practitioners on

whether reshoring is viable and scalable (Hertzman 2014, Wang 2014).

1

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Most existing literature on this topic emphasizes onshore manufacturing’s cost disadvantage

compared with offshoring (Wu and Zhang 2014, Wang et al. 2014). However, practitioners’ discus-

sions about reshoring have not always been around costs. Chen et al. (2015) survey multi-national

companies operating in China about their recent supply chain re-structuring decisions and moti-

vations. The survey results indicate that manufacturing jobs are generally not coming back to the

US, and supply availability is among the top non-cost considerations. An article in The Economist

(2014) also quotes, “the biggest problem with reshoring is that the decline in manufacturing over

the decades means that the supply chain has all but disappeared.” In fact, an analysis of the

Google Moto X smartphone that we mentioned above revealed that nearly all of its parts came from

overseas (King 2013). On the other hand, Duhigg and Bradsher (2012) depict the convenience and

flexibility of the iPhone supply chain in Shenzhen, China: “You need a thousand rubber gaskets?

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

that screw made a little bit different? It will take three hours.” These articles highlight the reality

faced by many offshoring manufacturers contemplating reshoring: as they extensively sourced from

local (offshore) suppliers, onshore supply bases have gradually withered. The limited onshore sup-

ply availability may force them to continue sourcing from offshore suppliers even if they reshore

manufacturing, until the reemergence of full-fledged onshore supply bases.

How does a manufacturer’s dependence on offshore suppliers impact its consideration of

reshoring? A widely-perceived advantage of reshoring is that it allows a manufacturer to be closer

to the market, potentially making it easier to adjust production in response to demand changes.

However, the dependence on offshore suppliers means that a reshoring manufacturer also moves

away from its suppliers, which may make it more challenging to procure components in response

to demand changes. This is not a straightforward trade-off, prompting several research questions.

Under what conditions do the disadvantages of losing supply proximity outweigh the advantages

of obtaining market proximity? What are the underlying operational drivers? And what strategies

may influence the trade-off in favor of or against reshoring?

To answer these questions, we consider the following model. An expected-profit-maximizing

manufacturer sources components from an offshore supplier and converts the components into

finished goods to meet random onshore demands. Production takes place in the manufacturer’s

(or its strategic partner’s) factory, which may be placed close to the supplier in the offshoring

mode (the as-is case), or close to the market in the reshoring mode (the to-be case). The supply

chain operates in two sequential stages. Under offshoring, the two stages are (offshore) production

followed by shipping (of finished goods), whereas under reshoring, the two stages are shipping (of

components) followed by (onshore) production. We assume all common costs under offshoring and

reshoring to be identical to isolate non-cost drivers.

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To capture potential demand information updates during the production-shipping (or shipping-

production) process, we assume that the onshore demand may have two different types—high and

low, which is initially unknown to the manufacturer. At certain time before the selling season, the

manufacturer learns the demand type through a marketing event such as a trade show (Fisher

and Raman 1996). We assume that the demand update occurs before the second stage in both

production modes so that the manufacturer can always respond to it (otherwise the comparison

of the two modes would become trivial). As such, the manufacturer faces a newsvendor problem

with demand updating in either production mode.

One can see that the most crucial distinction between offshoring and reshoring in our model

is in the sequence of events. Under offshoring production takes place before shipping, whereas

under reshoring shipping takes place before production. The different sequences of events entail

different operational flexibilities in response to the demand update before the second decision

events. Upon receiving new demand information, an offshoring manufacturer may either adjust

the final inventory level upward by rushing a production order before shipping (without worry-

ing about component supply), or adjust the final inventory level downward by not shipping all

finished goods. By contrast, a reshoring manufacturer may either adjust the final inventory level

upward by expediting more components from offshore before production begins, or adjust the final

inventory level downward by not processing all shipped components into finished goods. While the

manufacturer has both upward and downward flexibilities to adjust the final inventory level in each

mode, the costs of these flexibilities differ in nature. Under offshoring, utilizing the upward flexi-

bility (rushing production) incurs rush production costs, whereas utilizing the downward flexibility

(discarding finished goods) is at the expense of component sourcing and regular production costs.

Under reshoring, utilizing the upward flexibility (expediting component shipping) incurs expedited

shipping costs, whereas utilizing the downward flexibility (discarding shipped components) is at

the expense of component sourcing and regular shipping costs. Therefore, despite the identical cost

structure in each production mode, the costs of flexibilities may differ.

Since in our model offshoring and reshoring mainly differ in their operational flexibilities, when

a production mode has both the cheaper upward and downward flexibilities, we find that it always

outperforms the other (see Table 1’s diagonal quadrants). On the other hand, the comparison when

one production mode has the cheaper upward flexibility while the other has the cheaper downward

flexibility is less straightforward. Our analysis shows that in this case, whether reshoring is preferred

to offshoring depends on the prior probability of a high demand, or the demand prospect. The

intuition is as follows. Suppose a product has a low (high) demand prospect. This means that the

manufacturer is likely to plan a low (high) initial production quantity, which calls for an upward

(downward) flexibility in case demand turns out to be high (low). Therefore, for this product, the

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manufacturer prefers the production mode with the cheaper upward (downward) flexibility. The

specific preferences depend on the cost parameters (see Table 1’s off-diagonal quadrants). In short,

the demand prospect determines which type of flexibility is needed, and the needed flexibility

then determines whether reshoring is preferred to offshoring. These results reveal insights about

reshoring with limited onshore supply availability. First, reshoring is advantageous for products

that are expensive to make but cheap to ship (in terms of both regular and rushed/expedited

costs), and disadvantageous otherwise. Second, when the regular production and shipping cost

comparison differs from that between the rushed/expedited costs, the manufacturer’s preference

toward reshoring goes beyond cost parameter comparisons, and demand prospects come into play.

r < e r > e

m< s Offshoring

Reshoring for products withlow demand prospects

Offshoring for products withhigh demand prospects

m>s

Offshoring for products withlow demand prospects

Reshoring for products withhigh demand prospects

Reshoring

m= regular production cost s= regular shipping costr= rush production premium e= expedited shipping premium

Table 1 A manufacturer’s preferred production mode in different cost scenarios

We further investigate operational strategies that can swing manufacturers’ preferences for

reshoring. We find that, due to the different sequences of production and shipping under offshoring

and reshoring, when a manufacturer makes two products that share a common component, it

enjoys component-pooling benefits only under reshoring and not under offshoring, which makes

reshoring more attractive. On the other hand, when a manufacturer makes a product for two sep-

arate markets, it enjoys product-pooling benefits only under offshoring and not under reshoring,

which makes reshoring less attractive. The above two effects, when coexisting, can offset each other

to some extent. These results make a connection between the classic inventory pooling strategy

and the emerging reshoring movement.

Our findings confirm many practitioners’ intuition that offshoring manufacturers’ dependence on

local (offshore) suppliers leads to operational trade-offs regarding reshoring, and that even under

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identical cost structures, reshoring does not always provide operational advantages. The product

and operational characteristics that we identify as favoring reshoring can help policy makers deter-

mine which industries to target for promoting reshoring. In the long run, our study suggests that

policy makers should focus on promoting and fostering onshore supply base developments, so as

to reduce reshoring manufacturers’ dependence on offshore suppliers.

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

and analyze offshoring and reshoring in §3, and compare them in §4. This lays the foundation for

the investigation of common-component designs and serving multiple markets in §5. Finally, we

conclude the paper in §6. All proofs are found in the Appendix.

2. Literature review

In this paper we study offshoring manufacturers’ considerations of reshoring. A related concept

to offshoring is outsourcing. Tsay (2014) provides a lucid delineation between offshoring and out-

sourcing. 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 organizational 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, studies of outsourcing focus on the impact of decentralized decision-making

and the need for coordination (see Elmaghraby 2000 and Cachon 2003 for comprehensive reviews

of this literature), whereas we study how the geographic distance between offshore suppliers and

onshore markets impact offshoring manufacturers’ preferences toward reshoring.

At the core of our models are operational flexibilities, namely the ability to adjust final inventory

levels after receiving updated demand information. Therefore, our work is related to the literature

on production management with demand updating. This literature can be loosely divided into two

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

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

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 trade-offs between costs 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 common feature of the above papers is that they

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all model two-tier supply chains, each consisting of a manufacturer and a market, and consider one

operational flexility, either investigating its benefits or trading it off against costs. By contrast, we

model a three-tier supply chain consisting of a supplier, a manufacturer, and a market, and consider

two operational flexibilities. In our model, trade-offs between these operational flexibilities can drive

manufacturers’ preferences toward reshoring without any direct cost advantages for offshoring.

Therefore, both the premise and the insights of our paper are different from the above papers.

In our model extensions, we study common-component designs as well as serving multiple mar-

kets in the context of reshoring. The former strategy resembles delayed product differentiation

(Lee and Tang 1997), whereas the latter is essentially demand pooling (Eppen 1979). While such

strategies are widely studied and well understood, we make a contribution by recognizing that

common-component designs generate risk-pooling benefits only for reshoring manufacturers, and

serving multiple markets generates risk-pooling benefits only for offshoring manufacturers, thus

connecting the classic inventory pooling strategy and the emerging topic of reshoring.

Our problem is also 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

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

a centralized production facility for both markets, or build a dedicated facility in each market. In

short, the decision is about where to place a factory between two separate markets. Our research

problem, on the other hand, can be described as about where to place a factory between an offshore

supplier and an onshore market. Clearly, these research problems are different. Also, the basic

trade-off of Lu and Van Mieghem (2009) and Dong et al. (2010) is that between risk-pooling

benefits and production and shipping costs. Our base model considers a manufacturer making one

product for one market, thus does not involve risk pooling. In our extensions, as discussed above,

we study multiple products and/or multiple markets, which offers insights that are related to, but

different from those shown by Lu and Van Mieghem (2009) and Dong et al. (2010).

Recently, several papers have studied Quick Response and postponement in competitive envi-

ronments; examples include 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 operational flexibilities intrinsic to offshoring and reshoring, 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. Base model and analyses

Our goal is to compare a currently-offshoring manufacturer’s profits before and after reshoring in

otherwise identical settings. We assume that an expected-profit-maximizing manufacturer depends

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on an offshore supplier for sourcing components at unit cost c. The manufacturer can make one unit

of finished good from one unit of the component to meet a random onshore demand at retail price p

in a short selling season. The offshore supplier has no capacity limit or supply lead-time. Production

takes place in the manufacturer’s (or its strategic partner’s) factory, which may be placed close

to the supplier (offshoring), or close to the market (reshoring). Regardless of the location, regular

production costs m per unit. An offshoring manufacturer needs to ship finished goods, and a

reshoring manufacturer needs to ship components, from offshore to onshore. Regardless of what is

being shipped, the regular shipping cost is s per unit. We assume away cost differences between

offshoring and reshoring in order to isolate non-cost drivers. (The impacts of unequal costs are

straightforward: if offshore production is cheaper, then reshoring is less attractive; and if shipping

components is cheaper than shipping finished goods, then reshoring is more attractive.)

We assume the demand D to have a normal distribution N(µ,σ), where σ is the publicly known

standard deviation, and the mean µ can be µH (High demand) with prior probability γ, or µL (Low

demand) with prior probability 1− γ. We assume that µH > µL� σ, so that the probability of

having a negative demand is negligible. At the beginning of the decision horizon, the manufacturer

knows γ but not the 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.

Both regular production and shipping can require significant lead-times. For example, ocean

freight between Asia and America takes up to a month (Arnold 2009); Foxconn had to start

mass-producing iPhone 6 two months before the selling season (Culpan and Burrows 2014). We

do not quantitatively model lead-times, but rather treat production and shipping as two discrete

stages. For an offshoring manufacturer, the manufacturing process consists of (offshore) production

followed by shipping (of finished goods), whereas for a reshoring manufacturer, the manufacturing

process consists of shipping (of components) followed by (onshore) production.

At certain time before the selling season, the manufacturer learns the demand type through a

marketing event such as a trade show (Fisher and Raman 1996). We assume that the demand

update occurs before the second stage of the manufacturing process regardless of offshoring or

reshoring, so that the manufacturer can always respond to the updated information (otherwise the

comparison between the two modes would become trivial). The specific sequences of events under

offshoring and reshoring are illustrated in Figure 1.

Under offshoring, the manufacturer begins regular production in the offshore factory without

knowing the demand type. The regular production, once scheduled, cannot be changed. Once the

demand type is revealed, the manufacturer can adjust the production quantity upward by rushing

an order at additional cost r (on top of the regular production cost m) per unit, without delaying

shipping. (Component supply is not a constraint because production takes place in the proximity

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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

Offshoring:

Reshoring:

time

time

ComponentProduct

Productionin progress

Productionin progress

Figure 1 Sequences of events when offshoring and reshoring

of the supplier.) Alternatively, the manufacturer can adjust its final inventory level downward by

holding back shipping and discarding some finished goods. As the shipped goods arrive onshore,

the actual demand realizes, and the manufacturer satisfies the demand subject to available stock.

Under reshoring, the manufacturer orders components to be delivered to the onshore factory

using regular shipping without knowing the demand type. Once the demand type is revealed, the

manufacturer can adjust the component inventory level upward by obtaining components using

expedited shipping at additional cost e (on top of the regular shipping cost s) per unit, without

delaying production. Alternatively, the manufacturer can adjust the final inventory level downward

by holding back production and discarding some shipped components. As the production is finished,

the actual demand realizes, and the manufacturer satisfies the demand subject to available stock.

In summary, we employ a newsvendor model with demand updating, wherein the sequence

of events differs based on the production mode (production-shipping when offshoring, shipping-

production when reshoring). In each mode, the manufacturer has the flexibilities to adjust the final

inventory level upward or downward in response to a demand update through different means.

Newsvendor models with demand updating are generally difficult to analyze, and closed-form char-

acterizations are often elusive (Fisher and Raman 1996, Iyer and Bergen 1997). Nevertheless, we are

able to analyze two newsvendor models with demand updating, and provide a simple, closed-form

characterization of their comparison.

To proceed, we formulate and analyze the offshoring and reshoring models in the rest of this

section, before comparing the manufacturer’s profits in both modes in the next section. Throughout

the paper, we use superscript 0 to denote offshoring, and superscript 1 to denote reshoring.

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3.1. Offshoring

There are two decisions for an offshoring manufacturer: the regular production quantity before

learning the demand type, and the final shipped quantity (which may be higher or lower than the

former) after learning the demand type. We use subscript m to denote relation to regular produc-

tion, and subscript s to denote relation to shipping. Accordingly, the offshoring manufacturer’s

regular production quantity is denoted by x0m, and the shipped quantity by x0

s. Recall that p, c,

m, s, and r denote the retail price, the component sourcing cost, the regular production cost, the

regular shipping cost, and the rush production premium, respectively. An offshoring manufacturer’s

objective is to maximize its expected profit by choosing an optimal regular production quantity:

Π0m

.= max

x0m≥0{−(c+m)x0

m + γΠ0s(µH , x

0m) + (1− γ)Π0

s(µL, x0m)}, (1)

where Π0s(µ,x

0m) is the optimal profit due to adjusting the final inventory level after the mean

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

Π0s(µ,x

0m)

.= max

x0s≥0{−(c+m+ r)(x0

s−x0m)+− sx0

s + pE[min{D,x0s}|µ]}. (2)

We define

z.= Φ−1

(p− c−m− s

p

)where Φ is the cumulative distribution function of a standard normal distribution (we use φ to

denote the corresponding probability density function), and z is the critical fractile for the newsven-

dor problem with regular production only. It follows that the optimal solution x0∗m to problem (1)

must satisfy µL +σz ≤ x0∗m ≤ µH +σz.

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 given by

Π0s(µH , x

0m)

.= max

x0s≥x0m

{−(c+m+ r)(x0

s−x0m)− sx0

s + pE[min{D,x0s}|µH ]

}. (3)

The above problem is a standard newsvendor problem. We define

z0u.= Φ−1

(p− c−m− s− r

p

)which is the critical fractile for the newsvendor problem using the upward flexibility (rush produc-

tion). The optimal shipped quantity to problem (3) is given by x0∗sH = max{x0

m, µH + σz0u}, where

subscript H denotes relation to the high demand.

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By an analogous argument, we can show that 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 given by

Π0s(µL, x

0m)

.= max

x0s≤x0m

{−sx0

s + pE[min{D,x0s}|µL]

}. (4)

We define

z0d.= Φ−1

(p− sp

)which is the critical fractile for the newsvendor problem using the downward flexibility (holding

back shipping finished goods). The optimal solution to (4) is given by x0∗sL = min{x0

m, µL + σz0d},

where subscript L denotes relation to the low demand. Clearly, z0u < z < z0d. We further define

∆.=µH −µL

σ

as a measure of the difference between the high and low demands relative to the demand uncertainty.

It is straightforward to 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(z)

Φ(z0u + ∆)−Φ(z0u), γ0

d(∆).=

Φ(z0d)−Φ(z)

Φ(z0d)−Φ(z0d −∆). (5)

The following lemma characterizes the properties of these two thresholds:

Lemma 1. The threshold γ0u(∆) is increasing in ∆, with γ0

u(∆) = 0 for ∆≤ z−z0u. The threshold

γ0d(∆) is decreasing in ∆, with γ0

d(∆) = 1 for ∆≤ z0d− z. Thresholds γ0u(∆) and γ0

d(∆) intersect at

(∆0, γ0), where ∆0 .= z0d − z0u and γ0 .= c+mc+m+r

. For ∆≤∆0, µH + σz0u ≤ x0∗m ≤ µL + σz0d if and only

if γ0u(∆)≤ γ ≤ γ0

d(∆).

Figure 2 illustrates Lemma 1 with parameters p= 20, c= 2, m= 4, s= 2, e= 5, r= 3 (the same

as for all later figures). We also mark the regions characterized in Proposition 1 below.

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

z0mu.= Φ−1

(γr+ (1− γ)(p− c−m− s)

(1− γ)p

), for γ ≤ γ0 =

c+m

c+m+ 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− s)− c−m

γp

), for γ ≥ γ0 =

c+m

c+m+ 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 1. The offshoring manufacturer’s optimal strategies and profits are as follows:

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11

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

γ

Δ

𝑧"# − 𝑧

𝛾"#(Δ) III

Δ#, 𝛾#Ι

𝛾*#(Δ) II

𝑧 − 𝑧*#

Figure 2 An offshoring manufacturer’s optimal strategies

Case I: ∆≤∆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(z). The optimal profit is

−(c+m+ s)x0∗m + pE[min{D,x0∗

m}].

Case II: ∆ ≤∆0 and γ < γ0u(∆), or ∆ > ∆0 and γ ≤ γ0. The optimal solution is x0∗

m = x0∗sL =

µL +σz0mu, x0∗sH = µH +σz0u. The optimal profit is

pσγΦ(z0u)∆− pσ[γφ(z0u) + (1− γ)φ(z0mu)] + pΦ(z)µL.

Case III: ∆≤∆0 and γ > γ0d(∆), or ∆>∆0 and γ > γ0. The optimal solution is x0∗

m = x0∗sH =

µH +σz0md, x0∗sL = µL +σz0d. The optimal profit is

pσγΦ(z0md)∆− pσ[γφ(z0md) + (1− γ)φ(z0d)] + pΦ(z)µL.

Proposition 1 characterizes an offshoring manufacturer’s optimal strategy in three cases, as

illustrated in Figure 2. In Case I, where the high and low demand types are sufficiently similar

and/or the prior probability of a high demand is relatively moderate, the values of the flexibilities

cannot justify their costs, thus neither flexibility is used following the demand update. When

the two mean demands are further apart, however, the manufacturer may utilize the upward or

downward flexibilities depending on the demand prospect. In Case II with a low demand prospect

(small prior probability of a high demand), the manufacturer plans the initial production quantity

anticipating a low demand, and resorts to the upward flexibility (rush production) in the unlikely

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12

event that the demand turns out to be high. In Case III with a high demand prospect (large prior

probability of a high demand), the manufacturer plans the initial production quantity anticipating

a high demand, and resorts to the downward flexibility (holding back shipping finished goods) in

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

3.2. Reshoring

There are two decisions for a reshoring manufacturer: the component ordering quantity before

learning the demand type, and the regular production quantity (which may be higher or lower than

the former) after learning the demand type. We use subscript c to denote relation to component

ordering. Accordingly, the offshoring manufacturer’s component ordering quantity is denoted by x1c,

and the regular production quantity by x1m. A reshoring manufacturer’s objective is to maximize

its expected profit by choosing an optimal component ordering quantity:

Π1c

.= max

x1c≥0{−(c+ s)x1

c + γΠ1m(µH , x

1c) + (1− γ)Π1

m(µL, x1c)}, (6)

where Π1m(µ,x1

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

demand µ (= µH or µL) is revealed, given the component ordering quantity x1c:

Π1m(µ,x1

c).= max

x1m≥0{−(c+ s+ e)(x1

m−x1c)

+−mx1m + pE[min{D,x1

m}|µ]}. (7)

By comparing (1)-(2) and (6)-(7), one can see that the offshoring and reshoring models struc-

turally identical, only with m and s, r and e switched. The identical structure reflects that in both

modes, the manufacturer has both upward and downward flexibilities. The switched parameters,

on the other hand, reflect the different natures of the flexibilities. To increase the final inventory

level, an offshoring manufacturer incurs extra cost r per unit due to rush production, whereas a

reshoring manufacturer incurs extra cost e per unit due to expedited shipping. To decrease the final

inventory level, an offshoring manufacturer holds back shipping of some finished goods, discarding

the worth of c+m per unit, whereas a reshoring manufacturer holds back processing some shipped

components into finished goods, discarding the worth of c+s per unit. The identical structure and

the switched parameters mean that we can present a reshoring manufacturer’s optimal strategy

without repeating the analysis. Mirroring the offshoring expressions, we define

z1u.= Φ−1

(p− c−m− s− e

p

), z1d

.= Φ−1

(p−mp

),

γ1u(∆)

.=

Φ(z1u + ∆)−Φ(z)

Φ(z1u + ∆)−Φ(z1u), γ1

d(∆).=

Φ(z1d)−Φ(z)

Φ(z1d)−Φ(z1d −∆).

The following lemma mirrors Lemma 1 for the offshoring model:

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13

Lemma 2. The threshold γ1u(∆) is increasing in ∆, with γ1

u(∆) = 0 for ∆≤ z−z1u. The threshold

γ1d(∆) is decreasing in ∆, with γ1

d(∆) = 1 for ∆≤ z1d− z. Thresholds γ1u(∆) and γ1

d(∆) intersect at

(∆1, γ1), where ∆1 .= z1d− z1u and γ1 .= c+sc+s+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− c−m− s)

(1− γ)p

), for γ ≤ γ1 =

c+ s

c+ s+ 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−m)− c− s

γp

), for γ ≥ γ1 =

c+ s

c+ s+ 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 (illustrated in

Figure 3 with the same parameters as for Figure 2):

Proposition 2. The reshoring manufacturer’s optimal strategies and profits are as follows:

Case I: ∆≤∆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(z). The optimal profit is

−(c+m+ s)x1∗c + pE[min{D,x1∗

c }].

Case II: ∆ ≤∆1 and γ < γ1u(∆), or ∆ > ∆1 and γ ≤ γ1. The optimal solution is x1∗

c = x1∗mL =

µL +σz1cu, x1∗mH = µH +σz1u. The optimal profit is

pσγΦ(z1u)∆− pσ[γφ(z1u) + (1− γ)φ(z1cu)] + pΦ(z)µL.

Case III: ∆≤∆1 and γ > γ1d(∆), or ∆>∆1 and γ > γ1. The optimal solution is x1∗

c = x1∗mH =

µH +σz1cd, x1∗mL = µL +σz1d. The optimal profit is

pσγΦ(z1cd)∆− pσ[γφ(z1cd) + (1− γ)φ(z1d)] + pΦ(z)µL.

4. Profit comparison of offshoring and reshoring

In the previous section, we solved the manufacturer’s problem under offshoring and reshoring.

Despite the complexity of the optimal strategies and profit expressions, in this section we provide

a full structural characterization of their profit comparison.

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0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

γ

Δ

𝑧"# − 𝑧

𝛾"#(Δ) III

Δ#, 𝛾#Ι

𝛾*#(Δ) II

𝑧 − 𝑧*#

Figure 3 A reshoring manufacturer’s optimal strategies

4.1. The dominance case

We first show a simple dominance result.

Proposition 3. When m<s and r < e, the manufacturer weakly prefers to remain offshoring.

When m>s and r > e, the manufacturer weakly prefers reshoring.

To understand this result, recall that the offshoring model (1)-(2) and the reshoring model (6)-(7)

are structurally identical, and the unit product cost without using any flexibility is always c+m+s.

The only differences are in the “costs of flexibilities”. As discussed in Section 3.2, under offshoring,

the upward flexibility costs r per unit due to rush production, and the downward flexibility costs

c+m per unit due to discarding a finished good; whereas under reshoring, the upward flexibility

costs e per unit due to expedited shipping, and the downward flexibility costs c+s per unit due to

discarding a shipped component. When m< s and r < e (m> s and r > e), offshoring (reshoring)

has both cheaper upward and downward flexibilities than reshoring (offshoring), thus is preferred.

Let us consider the cost parameters m, s, r, and e. Both m and r are related to production,

whereas both s and e are related to shipping. Therefore, Proposition 3 can be interpreted as that

reshoring is less attractive for those products that are cheap to make but expensive to ship (e.g.,

furniture), and more attractive for those products that are expensive to make but cheap to ship

(e.g., designer apparel). These insights (especially the former) may be counterintuitive. One may

expect that bulky goods are suitable for reshoring due to the eliminated shipping cost. This notion

however neglects the fact that many reshoring firms continue to depend on offshore suppliers for

sourcing, and therefore the finished good shipping costs are merely replaced by component/material

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shipping costs. In fact, if shipping is a dominant cost component, then a firm should make the

shipping decision with more available information, which means offshoring (where shipping takes

place after production) is more favorable than reshoring.

4.2. The conditional case

In the previous subsection, Proposition 3 establishes the comparison between offshoring and

reshoring when m < s, r < e and m > s, r > e, leaving two more cases to be analyzed. In this

subsection, we mainly explore the case of m> s and r < e (the analyses and results for the case

of m < s and r > e mirror those for this case). Recall that the offshoring and reshoring models

each have three solution cases, separated by γid(∆), γiu(∆), and γi, i= 0,1. When m>s and r < e,

one can straightforwardly verify that γ0u(∆)> γ1

u(∆), γ0d(∆)> γ1

d(∆), and γ0 > γ1. These relation-

ships mean that the offshoring and reshoring solution cases are positioned in a particular manner.

As a result, we need to compare the offshoring and reshoring profits in six case combinations in

an overlay of Figures 2 and 3, then “stitch” the preferences together. Despite the complexity of

the analysis, the resulting preference regions are surprisingly clean, as characterized in the next

proposition and illustrated in Figure 4 (generated with the same parameters as for Figure 2).

Proposition 4. Suppose that m > s and r < e. Thresholds γ0u(∆) and γ1

d(∆) intersect at

(∆∗, γ∗), where ∆∗.= z1d−z0u and γ∗

.= c+s

c+s+r. The manufacturer’s preferences toward reshoring are:

1. ∆≤∆∗ and γ0u(∆)≤ γ ≤ γ1

d(∆): the manufacturer is indifferent toward reshoring.

2. ∆≤∆∗ and γ < γ0u(∆), or ∆>∆∗ and γ ≤ γ∗: the manufacturer prefers to remain offshoring.

3. ∆≤∆∗ and γ > γ1d(∆), or ∆>∆∗ and γ > γ∗: the manufacturer prefers reshoring.

Proposition 4 characterizes the case where each mode has an advantaged flexibility. For example,

m>s means that reshoring has the cheaper downward flexibility, and r < e means that offshoring

has the cheaper upward flexibility. When the high and low demand types are sufficiently similar

and/or the prior probability of a high demand is relatively moderate, the manufacturer is indifferent

toward reshoring. Otherwise, the manufacturer prefers reshoring if and only if the demand prospect

is sufficiently high, namely the prior probability of a high demand γ is above a threshold γ∗. It

is interesting to note that besides cost parameters, a product’s demand characteristics may also

influence its manufacturer’s preference toward reshoring. Furthermore, not all cost parameters

directly affect the preference: the threshold γ∗ depends on c, s, and r, but not on m or e.

To understand these results, recall that in our model offshoring and reshoring mainly differ in

their operational flexibilities. In Case 1 of Proposition 4, it is never optimal for the manufacturer to

use any flexibility. As a result, the manufacturer is indifferent toward reshoring. In Case 2 with low

demand prospects (the demand type is more likely to be low), the manufacturer will only commit

to a limited initial production quantity, thus no downward flexibility will be needed. However, if

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0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

γ

Δ

𝛾"#(Δ) 3. Reshoring

1. Indifferent𝛾∗ = )*+

)*+*,

𝛾-.(Δ) 2. Offshoring

Figure 4 A manufacturer’s preferences (solid), relative to the offshoring and reshoring solution cases (dotted)

the demand type turns out to be high, the manufacturer may need to resort to upward flexibilities

(rush production when offshoring, expedited shipping when reshoring). Since rush production is

cheaper than expedited shipping (r < e), offshoring yields higher profits than reshoring. Case 3 is

similar: with high demand prospects, the manufacturer will make to a large initial component order,

and may resort to downward flexibilities if the demand type turns out to be low. Since discarding

finished goods is more expensive than discarding shipped components (c+m> c+ s), offshoring

yields lower profits than reshoring. In short, the manufacturer always prefers the production mode

with the cheaper needed flexibility. This explains why the threshold γ∗ separating Cases 2 and 3

only depends on the costs of the cheaper upward and downward flexibilities, r and c+ s. In fact,

the expression (c+ s)/(c+ s+ r) exactly captures the relative magnitudes of these costs.

For the case of m<s and r > e, the manufacturer’s preferences mirror those of Proposition 4:

Proposition 5. Suppose that m < s and r > e. Thresholds γ0d(∆) and γ1

u(∆) intersect at

(∆†, γ†), where ∆†.= z0d−z1u and γ†

.= c+m

c+m+e. The manufacturer’s preferences toward reshoring are:

1. ∆≤∆† and γ1u(∆)≤ γ ≤ γ0

d(∆): the manufacturer is indifferent toward reshoring.

2. ∆≤∆† and γ < γ1u(∆), or ∆>∆† and γ ≤ γ†: the manufacturer prefers reshoring.

3. ∆≤∆† and γ > γ0d(∆), or ∆>∆† and γ > γ†: the manufacturer prefers to remain offshoring.

Our analyses in this section reveal that when a manufacturer depends on offshore suppliers,

its preferences toward reshoring boil down to trade-offs between operational flexibilities. If both

upward and downward flexibilities are cheaper in one production mode than the other, then the

manufacturer prefers the mode with the cheaper flexibilities. On the other hand, if the upward

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flexibility is cheaper in one mode and the downward flexibility is cheaper in the other, then the

demand prospect comes into play: when it is high, the manufacturer prefers the mode with the

cheaper downward flexibility, otherwise it prefers the one with the cheaper upward flexibility.

5. Operational strategies concerning reshoring

We have shown that limited onshore supply availability may hamper reshoring. In the long run,

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

shore suppliers. However, this process is likely to be slow. In some industries, building and main-

taining production capability is extremely expensive: Taiwan Semiconductor Manufacturing Com-

pany (TSMC)’s annual capital expenditures regularly amount to US$10 billion (Patterson 2014).

In other industries, the onshore environments lack the required resources to sustain their oper-

ations: Foxconn’s facilities in Shenzhen, China alone hire half a million workers—more than the

population of Atlanta (Mack 2011). Additionally, onshore suppliers are unlikely to rapidly develop

before reshoring reach 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, those manufacturers who depend on offshore suppliers will face operational trade-offs

between remaining offshore to be closer to their suppliers and reshoring to be closer to their mar-

kets. If we could identify an operational strategy which, despite a manufacturer’s dependence on

offshore suppliers, improves reshoring’s attractiveness, then it might accelerate reshoring and help

resolve this dilemma. We discuss one such strategy in the following subsection.

5.1. Common-component designs

We argue that a common-component design is an operational strategy that makes reshoring more

attractive. To elaborate this idea, we make the following modifications to the base model. 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. For

simplicity, we assume that both products have the same cost, price, and demand parameters as in

the base model (i.e., symmetric products), but their demand types and realizations are independent.

Figure 5 illustrates the 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, the optimal strategy is identical to that of the base model under offshoring, and the profit

equals twice of Π0m determined by (1)-(2). Therefore, the common-component design brings no

benefit under offshoring. When reshoring, however, the manufacturer initially sources components

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18

Regularproduction

Finished goodsin stock

Demand update Demand realization

Finished goodsin shipping

Componentsourcing

Finished goodsin stock

Demand update Demand realization

Componentsin shipping

Offshoring:

Reshoring:

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

Figure 5 Sequence of events with a common-component design

for both products, and allocates the component inventory between them only after learning each

product’s demand type. The reshoring manufacturer’s problem formulation is

Π1c

.= max

x1c≥0{−(c+ s)x1

c + γ2Π1m(µH , µH , x

1c) + 2γ(1− γ)Π1

m(µH , µL, x1c) + (1− γ)2Π1

m(µL, µL, x1c)},

(8)

Π1m(µa, µb, x

1c).= max

x1a+x1b=x1c

{Π1(µa, x1a) + Π1(µb, x

1b)}, (9)

Π1(µi, x1i ).= max

y1i≥0{−(c+ s+ e)(y1i − x1

i )+−my1i + pE[min{D, y1i }|µi]}, i= a, b, (10)

where subscripts a and b represent the two products. By comparing (8)-(10) to (6)-(7), one can see

that (8) and (10) respectively resemble (6) and (7), whereas the additional equation (9) reflects

a reshoring manufacturer’s additional flexibility of allocating the components between the two

products after learning their demand types, which yields component-pooling benefits. Since a

common-component design generates component-pooling benefits only under reshoring, it improves

reshoring’s attractiveness. This result is formally stated in the following proposition.

Proposition 6. Suppose that the manufacturer prefers or is indifferent toward reshoring in the

base model. Then, when the manufacturer makes two products that share a common component, it

strictly prefers reshoring.

We illustrate Proposition 6 in Figure 6 with a numerical example evaluated on a 20× 20 grid

(with the same parameters as for Figure 2). One can clearly see that, compared with the base

model’s preferences (dotted), when the manufacturer makes two products that share a common

component, the new reshoring region contains the original reshoring and indifferent regions.

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19

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

γ

Δ

Reshoring

Offshoring

Figure 6 A manufacturer’s preferences with a common-component design (solid), compared with the base

model (dotted)

The essence of the common-component design strategy is component inventory pooling. While

inventory pooling is widely studied and well understood, we make a contribution by recognizing that

a common-component design generates risk-pooling benefits only under reshoring, and proposing

it as a strategy to improve reshoring’s attractiveness. This discovery connects the classic inventory

pooling strategy and the emerging topic of reshoring.

5.2. Serving multiple markets

In the previous subsection we identified a common-component design as an operational strategy to

improve reshoring’s attractiveness. Its essence is component inventory pooling. Another common

pooling form is product inventory pooling, which can be achieved with serving multiple markets.

In this subsection, we show that this strategy actually reduces reshoring’s attractiveness.

We make the following modifications to the base model. Suppose now the manufacturer makes

the same product for two separate onshore markets A and B, which are distant from each other and

require separate shipping (e.g., the US and Europe). For simplicity, we assume that both markets

have the same cost, price, and demand parameters as in the base model (i.e., symmetric markets),

but their demand types and realizations are independent. Figure 7 illustrates the sequence of events

with multiple markets. When offshoring, the manufacturer makes the product in its offshore factory

before sending two shipments to both markets. When reshoring, we assume that the manufacturer

has one factory near each market, and ships sourced components to each factory to be processed

into finished goods for their respective markets. (Clearly, two onshore factories require substantially

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more capital investments than a single offshore factory; however, we will follow the convention of

ignoring capital investments, and focus on the operational aspects of the two production modes.

Considering capital investments will put reshoring at a disadvantage.)

Regularproduction

Finished goodsin stock

Demand update Demand realization

Finished goodsin shipping

Componentsourcing

Finished goodsin stock

Demand update Demand realization

Componentsin shipping

Offshoring:

Reshoring:

time

time

Component/product for market AProduct for markets A and B

Component/product for market B

Rush production/Hold back shipping

Expedite shipping/Hold back production

Productionin progress

Productionin progress

Figure 7 Sequence of events with multiple markets

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

Under reshoring, the components for the two markets are sourced and shipped separately to their

respective onshore factories from the very beginning. As a result, the optimal strategy is identical

to that of the base model under reshoring, and the profit equals twice of Π1c determined by (6)-(7).

Therefore, serving multiple markets brings no benefit under reshoring. When offshoring, however,

the manufacturer initially makes products for both markets, and allocates the product inventory

between them only after learning each market’s demand type. The offshoring manufacturer’s prob-

lem formulation is

Π0m

.= max

x0m≥0{−(c+m)x0

m + γ2Π0s(µH , µH , x

0m) + 2γ(1− γ)Π0

s(µH , µL, x0m) + (1− γ)2Π0

s(µL, µL, x0m)},

(11)

Π0s(µA, µB, x

0m)

.= max

x0A+x0

B=x0m

{Π0(µA, x0A) + Π0(µB, x

0B)}, (12)

Π0(µi, x0i ).= max

y0i≥0{−(c+m+ r)(y0i − x0

i )+− sy0i + pE[min{D, y0i }|µi]}, i=A,B (13)

where subscripts A and B represent the two markets. By comparing (11)-(13) to (1)-(2), one can

see that (11) and (13) respectively resemble (1) and (2), whereas the additional equation (12)

reflects an offshoring manufacturer’s additional flexibility of allocating the products between the

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two markets after learning their demand types, which yields product-pooling benefits. Since serving

multiple markets generates product-pooling benefits only under offshoring, it reduces reshoring’s

attractiveness. This result is formally stated in the following proposition.

Proposition 7. Suppose that the manufacturer prefers to remain offshoring or is indifferent

toward reshoring in the base model. Then, when the manufacturer sells its product in two markets,

it strictly prefers to remain offshoring.

We illustrate Proposition 7 in Figure 8 with a numerical example evaluated on a 20× 20 grid

(with the same parameters as for Figure 2). One can clearly see that, compared with the base

model’s preferences (dotted), when the manufacturer sells its product in two markets, the new

reshoring region is contained in the original reshoring region.

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

γ

Δ

Reshoring

Offshoring

Figure 8 A manufacturer’s preferences with multiple markets (solid), compared with in the base model (dotted)

5.3. Common-component designs and serving multiple markets

In the previous two subsections, we studied the impacts of common-component designs and serving

multiple markets on a manufacturers’ preferences toward reshoring, which go in opposite directions.

It is thus natural to ask whether these impacts would offset each other in a model with both a

common-component design and multiple markets.

To answer this question, we make the following modifications to the base model. Suppose now

the manufacturer makes two products a and b for each of two markets A and B. The two products

share a common component but require separate production processes, and the two markets are

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22

distant from each other and require separate shipping. For simplicity, we assume that both products

in both markets have the same cost, price, and demand parameters as in the base model (i.e.,

symmetric products and markets), but their demand types and realizations are independent.

Regularproduction

Finished goodsin stock

Demand update Demand realization

Finished goodsin shipping

Componentsourcing

Finished goodsin stock

Demand update Demand realization

Componentsin shipping

Offshoring:

Reshoring:

time

time

Component/products for market AProducts a, b for markets A and B

Component/products for market B

Rush production/Hold back shipping

Expedite shipping/Hold back production

Productionin progress

Productionin progress

Figure 9 Sequence of events with a common-component design and multiple markets

Figure 9 illustrates the sequence of events with a common-component design and multiple mar-

kets. When offshoring, the manufacturer makes two separate products in its offshore factory before

sending two shipments (each containing both products) to the two markets. When reshoring, the

manufacturer sends out two separate shipments of sourced components to the two onshore factories,

which then make both products for their respective markets.

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

Under offshoring, the two products are made separately from the very beginning, but the manu-

facturer can allocate the product inventory between the two markets after learning each market’s

demand types. As a result, the offshoring profit equals twice of that with multiple markets, Π0m,

determined by (11)-(13). When reshoring, the components for the two markets are sourced and

shipped separately to their respective onshore factories from the very beginning, but each onshore

factory can allocate the component inventory between the two products after learning each prod-

uct’s demand type. As a result, the reshoring profit equals twice of that with a common-component

design, Π1c, determined by (8)-(10). Note that (8)-(10) and (11)-(13) are structurally identical, only

with m and s, r and e switched—similar to (1)-(2) and (6)-(7). This allows us to partially recover

Propositions 3-5 for the case with a common-component design and multiple markets.

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Proposition 8. Suppose that the manufacturer makes two products that share a common com-

ponent for two markets.

1. When m<s and r < e, the manufacturer prefers to remain offshoring. When m>s and r > e,

the manufacturer prefers reshoring.

2. For any γ, the manufacturer is indifferent toward reshoring when ∆ is sufficiently small.

In Figure 10 we present a numerical example evaluated on a 20×20 grid (with the same param-

eters as for Figure 2). One can see that the manufacturer’s preferences with a common-component

design and multiple markets are structurally similar to those of the base model (dotted). This

confirms our intuition that component-pooling benefits due to a common-component design and

product-pooling benefits due to serving multiple markets can offset each other to some extent.

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4

γ

Δ

Reshoring

Indifferent

Offshoring

Figure 10 A manufacturer’s preferences with a common-component design and multiple markets (solid),

compared with the base model (dotted)

6. Concluding remarks

In this paper, we introduce a framework for understanding currently-offshoring manufacturers’

preferences toward reshoring, accounting for their dependence on offshore suppliers due to lim-

ited onshore supply availability. For a manufacturer that depends on offshore suppliers, reshoring

reduces its distance to the market at the expense of increasing its distance to the suppliers. The

market and supply proximities under reshoring and offshoring respectively enable different oper-

ational flexibilities for the manufacturer to adjust the final inventory level upward or downward

when new demand information becomes available. We show that the manufacturer’s preferences

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24

toward reshoring boil down to trade-offs between such flexibilities. When a production mode (off-

shoring or reshoring) has both the cheaper upward and downward flexibilities, the manufacturer

prefers this mode to the other. If the upward flexibility is cheaper in one mode and the downward

flexibility is cheaper in the other, then the demand prospect comes into play: when it is high, the

manufacturer prefers the mode with the cheaper downward flexibility, otherwise it prefers the one

with the cheaper upward flexibility.

The above findings confirm many practitioners’ intuition that offshoring manufacturers’ depen-

dence on local (offshore) suppliers leads to operational trade-offs regarding reshoring, and that even

under identical cost structures, reshoring does not always provide operational advantages. Our anal-

yses can help identify product and operational characteristics that may or may not favor reshoring

given limited onshore supply availability. For example, designer apparels, which are expensive to

make but relatively cheap to ship (in terms of both regular and rushed/expedited costs), may be

suitable for reshoring, whereas furniture, which is bulky and relatively expensive to ship, may not

be suitable for reshoring (the diagonal quadrants in Table 1). Another example is electronics. They

are typically more expensive to make than to ship by sea, but expedited shipping can cost much

more than rush production (The World Bank 2011 estimates air freight to cost 12 to 16 times as

much as ocean freight). For such a product, reshoring is more suitable if the manufacturer has high

confidence that the product will be a hit (the lower-left quadrant in Table 1). These results may

inform policy makers in determining which industries to target for promoting reshoring.

We then investigate operational strategies that may swing manufacturers’ preferences for

reshoring. We show that implementing a common-component design generates component-pooling

benefits only under reshoring, hence improves reshoring’s attractiveness. On the other hand, serv-

ing multiple markets generates product-pooling benefits only under offshoring, hence reduces

reshoring’s attractiveness. These two effects, when coexisting, can offset each other to some extent.

This implies that manufacturers can potentially utilize common-component designs to support

their reshoring initiatives before onshore supply bases become fully-fledged. In fact, this insight is

not limited to one firm; if multiple reshoring firms share a component, they can potentially source

the component via a third-party purchasing agent and share the inventory, which generates similar

component-pooling benefits and improves reshoring’s attractiveness for all firms. In general, lim-

ited onshore supply availability may hamper reshoring, which suggests that in the long run, policy

makers should focus on fostering onshore supply base developments in order to promote reshoring.

Our discrete-period model with a single information update implicitly assumes equal information

quality under offshoring and reshoring. If information is instead continuously updated, then the

information quality for decision-making under offshoring and reshoring may differ based on the

relative lengths of the production and shipping lead-times. In practice, shipping and production

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can both take significant amounts of time: ocean freight between Asia and America takes up to a

month (Arnold 2009); Foxconn had to start mass-producing iPhone 6 two months before the selling

season (Culpan and Burrows 2014). Therefore, each of production and shipping may take longer

than the other. Recall that production takes place before shipping under offshoring, and shipping

takes place before production under reshoring. If shipping takes longer (shorter) than production,

then reshoring allows more (less) accurate information before the production (shipping) decision

than offshoring, which improves (reduces) reshoring’s attractiveness. Aside from this additional

effect, such a model will likely generate the same insights as ours.

In our model, we study a manufacturer’s problem of placing a factory either offshore or onshore.

Therefore, we consider offshoring and onshoring as exclusive production modes. One can also imag-

ine a hybrid mode wherein the manufacturer owns two factories—one offshore and one onshore—

between which it can freely allocate production. The hybrid mode obviously requires substantially

more capital investments than the exclusive modes. We follow the convention of ignoring capital

investments in the following discussion (considering capital investments will put the hybrid mode

at a disadvantage). In the hybrid mode, the manufacturer always has access to the cheaper upward

and downward flexibilities. For example, when m>s and r < e, the manufacturer can use onshore

factory for its downward flexibility (discarding shipped components) and the offshore factory for

its upward flexibility (rush production), thus the hybrid mode performs better than both exclusive

modes in general. However, as we have shown, the manufacturer will need at most one flexibility

for any specific product, thus can choose the exclusive mode that offers the cheaper needed flex-

ibility, which would match the performance of the hybrid mode. Therefore, although the hybrid

mode can always achieve the optimal performance for any products, it performs no better than

the manufacturer’s preferred exclusive mode for a specific product.

Our work presents a first step to understanding the impact of limited onshore supply avail-

ability on reshoring. To isolate the pure operational trade-offs regarding reshoring, we consider a

monopolistic, centralized decision-making setting, and obtain insights into first-best profit com-

parisons between offshoring and reshoring. The insights from studying this setting will serve as a

stepping stone for understanding the problem in more complex settings, such as one with compe-

tition, asymmetric information, and/or decentralized decision-making (outsourcing), all of which

are interesting extensions that merit future research investigation.

Appendix

Offshoring analysis (proof of Lemma 1)

By (5), it is straightforward to verify that γ0u(∆) is increasing in ∆, γ0

d(∆) is decreasing in ∆, γ0u = 0

for ∆≤ z−z0u, and γ0d = 1 for ∆≤ z0d−z. Therefore, γ0

u(∆) and γ0d(∆) intersect at most once. Since

when ∆0 = z0d − z0u, γ0u(∆0) = γ0

d(∆0) = γ0 = c+m

c+m+r, (∆0, γ0) characterizes the intersection.

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Recall that ∆ ≤ ∆0 = z0d − z0u implies µH + σz0u ≤ µL + σz0d. From the analysis 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

{−(c+m+ s)x0

m + pE[min{D,x0m}]}.

It is straightforward to show that the optimal solution solves the FOC:

γΦ((x−µH)/σ) + (1− γ)Φ((x−µL)/σ) = Φ(z).

Note that the 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(z)⇒ γ′ =Φ(z0u + ∆)−Φ(z)

Φ(z0u + ∆)−Φ(z0u)

which is the same as the threshold γ0u(∆) defined in (5).

Symmetrically, x≤ µL +σz0d if and only if γ ≤ γ′′, where γ′′ is determined by

γ′′Φ((µL +σz0d −µH)/σ) + (1− γ′′)Φ((µL +σz0d −µL)/σ) = Φ(z)⇒ γ′′ =Φ(z0d)−Φ(z)

Φ(z0d)−Φ(z0d −∆)

which is the same as the threshold γ0d(∆) defined in (5). Therefore, we conclude that µH + σz0u ≤

x0∗m ≤ µL +σz0d if and only if γ0

u(∆)≤ γ ≤ γ0d(∆). �

Offshoring profit (proof of Proposition 1)

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 ξ follows a normal distribution with mean µ and standard deviation σ. Then∫ x

−∞

ξ√2πσ

e− (ξ−µ)2

2σ2 dξ = µΦ

(x−µσ

)−σφ

(x−µσ

). (14)

Case I: ∆≤∆0 and γ0u ≤ γ ≤ γ0

d . Due to Lemma 1, 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(z). The optimal profit is

−(c+m+ s)x0∗m + pE[min{D,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 1, 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+m)x0

m + γΠ0s(µH , x

0m) + (1− γ)Π0

s(µL, x0m)}, (15)

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where Π0s(µH , x

0m) =−(c+m+ r)(x0∗

sH − x0m)− sx0∗

sH + pE[min{D,x0∗sH}|µH ] with x0∗

sH = µH + σz0u,

Π0s(µL, x

0m) =−sx0

m+pE[min{D,x0m}|µL]. It is straightforward to show that the optimal x0∗

m solves

the following FOC:

Φ((x0m−µL)/σ)) =

γr+ (1− γ)(p− c−m− s)(1− γ)p

.

Therefore, x0∗m = µL +σz0mu. Plugging x0∗

m into Π0m and utilizing (14), we obtain the optimal profit

Π0m = pσγΦ(z0u)∆− pσ[γφ(z0u) + (1− γ)φ(z0mu)] + pΦ(z)µL. (16)

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 (15), 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+mc+m+r

. Therefore, when ∆>∆0 and γ ≤ γ0,

the optimal solution is x0∗m = µL +σz0mu and the optimal profit is given by (16).

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

.= max

x0m≥0{−(c+m)x0

m + γΠ0s(µH , x

0m) + (1− γ)Π0

s(µL, x0m)},

where Π0s(µH , x

0m) =−sx0∗

m + pE[min{D,x0∗m}|µH ]], and Π0

s(µL, x0m) =−sx0∗

sL + pE[min{D,x0∗sL}|µL]

with x0∗sL = µL +σz0d. Similar to Case II, the optimal x0∗

m solves the following FOC:

Φ((x0m−µH)/σ)) =

γ(p− s)− c−mγp

.

Therefore, the optimal solution is x0∗m = x0∗

sH = µH + σz0md, x0∗sL = µL + σz0d. Plugging x0∗

m into Π0m

and utilizing (14), we obtain the optimal profit

Π0m = pσγΦ(z0md)∆− pσ[γφ(z0md) + (1− γ)φ(z0d)] + pΦ(z)µL.

Reshoring analysis (proof of Lemma 2)

The proof mirrors that of Lemma 1, only with m and s, r and e switched, thus is omitted. �

Reshoring analysis (proof of Proposition 2)

The proof mirrors that of Proposition 1, only with m and s, r and e switched, thus is omitted. �

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Profit comparison: the dominance case (proof of Proposition 3)

From Propositions 1 and 2, we know that after learning the demand type, there are three possible

decision cases for the manufacturer: I) do nothing regardless of the demand type; II) 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; and III) adjust the final inventory level downward if the demand type turns out to be

low and do nothing if it turns out to be high. Suppose that m<s and r < e.

In reshoring’s Case I, since the manufacturer does not use any flexibility, the final inventory costs

c+m+ s per unit. An offshoring manufacturer can achieve the same cost by making the same

initial quantity and not using any flexibility. Therefore, offshoring can do no worse than reshoring.

In reshoring’s Case II, when the manufacturer adjusts the final inventory level upward, the initial

production costs c+m+ s per unit and the additional production costs c+m+ s+ e per unit. In

comparison, it would cost an offshoring manufacturer c+m+ s per unit for the initial production

and c+m+ s+ r per unit for the additional production. Since r < e, offshoring incurs lower costs

than reshoring for the same decision quantities, thus generating higher profits.

In reshoring’s Case III, when the manufacturer adjusts the final inventory level downward, the

shipped inventory costs c+m+ s per unit and the discarded inventory costs c+ s per unit. In

comparison, it would cost an offshoring manufacturer c+m+ s per unit for the shipped inventory

and c+m per unit for the discarded inventory. Since m < s, offshoring incurs lower costs than

reshoring for the same decision quantities, thus generating higher profits. Therefore, we conclude

that in general the manufacturer prefers to remain offshoring when m<s and r < e.

The proof for the case of m>s and r > e is similar and omitted. �

Profit comparison: the conditional case (proof of Proposition 4)

Recall that m>s and r < e. Due to Lemmas 1 and 2, we know that γ0u(∆) is increasing in ∆ and

γ1d(∆) is decreasing in ∆. It is easy to verify that γ0

u(∆) and γ1d(∆) 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 1 and 2, 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 ≤

γ1u(∆). In Scenario 1), due to Propositions 1 and 2, we know that if the demand type turns

out to be high, an offshoring manufacturer would adjust the final inventory level upward, but

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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 1 and 2, 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 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 1, 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 2, 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 1 and 2, 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. �

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Profit comparison: the conditional case (proof of Proposition 5)

The proof mirrors that of Proposition 4 and is omitted. �

Common-component designs (proof of Proposition 6)

It is straightforward to see that under reshoring, if the manufacturer sets x1a = x1

b = x1c/2 instead

of allocating the component inventory optimally as in (9), then Π1c = 2Π1

c. Also recall that the

offshoring profit with a common-component design is 2Π0m. Therefore, under this allocation the

manufacturer’s preference toward reshoring would be identical to that in the base model. However,

such an allocation is strictly suboptimal, because in the event that one demand type is high and

the other is low, this allocation does not satisfy the well-known equal-fractile optimality condition.

Thus we know under the optimal allocation, the manufacturer will strictly prefer reshoring where

it prefers or is indifferent toward reshoring in the base model. �

Serving multiple markets (proof of Proposition 7)

The proof mirrors that of Proposition 6 and is omitted. �

Common-component designs and serving multiple markets (proof of Proposition 8)

For Part 1, note that (8)-(10) and (11)-(13) are structurally identical, only with m and s, r and e

switched, hence the conclusion follows from the same argument as for Proposition 3.

For Part 2, consider (8)-(10). First, it is straightforward to see that the optimal allocation of

the component inventory, x1c, after the two products’ mean demands µa and µb are revealed, is

x1∗a = (x1

c+µa−µb)/2 and x1∗b = (x1

c+µb−µa)/2. (This allocation satisfies x1∗a −µa = x1∗

b −µb, which

ensures equal fractiles for the two products.) Also note that when ∆→ 0, the high and low demand

types become indistinguishable, thus the manufacturer never uses any flexibility. By continuity,

we know that for any γ, the manufacturer never uses any flexibility when ∆ is sufficiently small,

namely y1i = x1∗i , i= a, b. In this case, (8)-(10) can be simplified as

Π1c

.= max

x1c≥0{−(c+m+ s)x1

c + γ2Π1m(µH , µH , x

1c) + 2γ(1− γ)Π1

m(µH , µL, x1c) + (1− γ)2Π1

m(µL, µL, x1c)},

Π1m(µa, µb, x

1c).= pE[min{D, (x1

c +µa−µb)/2}|µ= µa] + pE[min{D, (x1c +µb−µa)/2}|µ= µb].

Similarly, for a sufficiently small ∆, (11)-(13) can be simplified as

Π0m

.= max

x0m≥0{−(c+m+ s)x0

m + γ2Π0s(µH , µH , x

0m) + 2γ(1− γ)Π0

s(µH , µL, x0m) + (1− γ)2Π0

s(µL, µL, x0m)},

Π0s(µA, µB, x

0m)

.= pE[min{D, (x0

m +µA−µB)/2}|µ= µA] + pE[min{D, (x0m +µB −µA)/2}|µ= µB].

These formulations are identical. Therefore, we conclude that for a sufficiently small ∆, thus the

manufacturer is indifferent toward reshoring. �

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