End-to-end supply chain models for apparel industry
Dr. Shardul S. Phadnis
Assistant Professor and Director of Research
Malaysia Institute for Supply Chain Innovation
2A, Persiaran Tebar Layar, Bukit Jelutong
40150 Shah Alam, Malaysia
Prof. Charles H. Fine
Chrysler Leaders for Global Operations Professor of Management
Professor of Operations Management and Engineering Systems
Sloan School of Management, Massachusetts Institute of Technology
77 Massachusetts Ave, E62-466
Cambridge, MA 02139 USA
Comments are welcome.
Please do not circulate or cite without the authors’ permission.
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End-to-end supply chain models for apparel industry
ABSTRACT
This paper seeks to answer one of conference theme questions about re-shoring, on-shoring, and
off-shoring of apparel manufacturing from a conceptual lens. It examines the tradeoffs in
sourcing strategies by considering them jointly with sales strategies, as the components of a
firm’s supply chain strategy. We compare four end-to-end strategies—combinations of offshore
vs. near-shore sourcing and online vs. brick-and-mortar retailing—under various scenarios of the
business environment by drawing insights from a numerical exercise. The key finding of this
work is that sourcing and sales strategies are not completely modular—an ideal sales strategy can
be influenced by the parameters of the sourcing strategy—and hence may be beneficial to decide
jointly. Our analyses show that a change in a single dimension of the business environment—
such as, the variation in geographic distribution of demand—can cause a supply chain strategy to
get dominated by one conventionally thought to be its inferior. By identifying such conditions,
our model sheds light on the scenarios in which the successful supply chain strategies pursued by
firms today could become vulnerable to those considered inferior.
Keywords:
Procurement/Sourcing/Purchasing; Offshoring; Demand Chain Management
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End-to-end supply chain models for apparel industry
This paper seeks to answer one of conference theme questions about re-shoring,
on-shoring, and off-shoring of apparel manufacturing from a conceptual lens. It
examines the tradeoffs in sourcing strategies by considering them jointly with
sales strategies, as the components of a firm’s supply chain strategy. We compare
four end-to-end strategies—combinations of offshore vs. near-shore sourcing and
online vs. brick-and-mortar retailing—under various scenarios of the business
environment by drawing insights from a numerical exercise. The key finding of
this work is that sourcing and sales strategies are not completely modular—an
ideal sales strategy can be influenced by the parameters of the sourcing strategy—
and hence may be beneficial to decide jointly. Our analyses show that a change in
a single dimension of the business environment—such as, the variation in
geographic distribution of demand—can cause a supply chain strategy to get
dominated by one conventionally thought to be its inferior. By identifying such
conditions, our model sheds light on the scenarios in which the successful supply
chain strategies pursued by firms today could become vulnerable to those
considered inferior.
INTRODUCTION
The twin forces of globalization and e-commerce have dramatically changed supply chains in the
last two decades. Globalization has provided firms a choice in their sourcing and operations
strategies to either produce close to their home countries and markets or to seek lower costs from
more distant sources. The growth of the internet and widespread connectivity has created a
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powerful new sales channel, where firms can sell goods directly to the consumers through online
stores instead of through brick-and-mortar stores. However, firms around the world still pursue a
range of sourcing as well as sales strategies, so that one cannot assert the emergence of a
dominant design for 21st century’s supply chains (Utterback & Abernathy, 1975).
Nonetheless, firms in the Western countries have outsourced a large share of production
to lower-cost countries in Asia. McKinsey (2014) showed that one-third of all goods produced in
2012 (36 percent of global GDP), crossed national borders. The United States alone imported
$2.3 trillion worth of goods for local consumption. On the other hand, some firms have started
bringing some of their offshored production back into the home country. Boston Consulting
Group (2013) found that 54% of the surveyed executives from firms with revenues of $1 billion
and above were actively considering shifting production back from China to the U.S.; more so,
this number had increased from 37% in a similar survey a year earlier.
On the sales side, e-commerce has grown as an alternative to brick-and-mortar stores.
The share of e-commerce sales in the U.S. retail sector rose to 6.6 percent in the third quarter of
2014, a 16.2 percent growth from a year earlier (U.S. Census Bureau, 2014); this trend is
expected to continue and e-commerce is likely to account for 11 percent of all retail sales in the
U.S. by 2018 (Forrester Research, 2014). Although, the growth in e-commerce channels has been
linked to the demise of established brick-and-mortar stores—such as Borders Book Stores and
Circuit City—this trend does not necessarily spell absolute doom for the brick-and-mortar sales
channels. In fact, the pioneer of online retailing, Amazon.com, opened its first brick-and-mortar
store in New York City in 2014 (WSJ, 2014).
The plurality of supply chain strategies is not observed just at the macroeconomic level,
but can also be seen in numerous industries. The global apparel industry provides one vivid
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example of this apparent state of experimentation in end-to-end supply chain strategies. This
industry is a poster child of globalization: in 2013, apparel manufacturers alone generated $577
billion in revenue, more than 75% of which was generated from goods produced for export
(IBISWorld, 2013). International Apparel Federation, the leading federation of apparel designers,
manufacturers, retailers, and the related companies, boasts a membership of 150,000 companies
employing more than 5 million people in 40 countries. Despite its size, no dominant supply chain
design has yet emerged for the apparel industry. Equally successful apparel brands in the West
have either outsourced the production to low-cost contract manufacturers in Asia or tightly
integrated with producers located close to the market (e.g., Ghemawat & Nueno, 2003; Pisano &
Adams, 2009; Caro, 2011). Similarly, numerous clothing brands have chosen to sell through
brick-and-mortar stores as well as via online stores. This plurality of practices raises two
questions: Why does a multiplicity of supply chain configurations prevail in a competitive
industry? And, under what circumstances do the different configurations outperform others?
The tradeoffs between different sourcing and sales strategies have been examined in the
literature. In general, an offshore source has lower direct, out-of-pocket costs, but may be less
responsive compared to a near-shore source (Farrell, 2005; de Treville & Trigeorgis, 2010).
Firms cite lower cost as the reason for shifting production to or sourcing from an offshore
location; however, there is a tendency to overestimate the cost benefits when the tasks relegated
to an offshore source have a high degree of interdependence with those retained in-house
(Larsen, Manning, & Pedersen, 2013). On the sales side, the online channel can offer lower
prices due to its lower cost structure compared to the brick-and-mortar channel. However, this
comes at the expense of a lack of pre-purchase product experience for the consumer and results
in a higher proportion of returned sales for the online channel (WSJ, 2013)
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Although the tradeoffs between the sourcing and sales strategies have been studied in the
operations and supply chain management literature, the two have not been studied together for
consideration of end-to-end supply chain strategies. This lack of a systemic approach may be due
to the association of these decisions with different functions in firms or academic units in
business schools, or could be a result of the preference for studying parsimonious models of
managerial decisions (Williamson, 2008). Regardless, a joint exploration of the sourcing and
sales strategies is likely to provide novel insights if the two possess a high degree of
interdependence (Larsen, et al., 2013). These two strategies seems to possess such a
complementarity as evidenced from the superior performance of the firms choosing holistic
supply chain strategies (while they suit the business environment), such as Zara (Ghemawat &
Nueno, 2003), Dell (Dell & Fredman, 1999), or Toyota (Womack, Jones, & Roos, 1990).
This paper develops a model of an end-to-end supply chain to explore these
complementarities. The model assumes that a firm chooses its end-to-end supply chain strategy
by defining its sourcing and sales strategy once, and then makes two operational decisions in
each season: it decides the quantity to procure for a particular selling season and allocates the
procured quantity to the store(s). In the model, the firm may source the products from an
offshore or a near-shore supplier; it may sell the products through an online store or a number of
brick-and-mortar stores. We compare the performance of four end-to-end supply chain
configurations under various scenarios as defined by the product’s contribution margin, cost
advantage of offshore supplier, forecast accuracy, change in forecast accuracy over lead time,
geographic variation in demand, product returns rate, and the online returns penalty. The
performance of each end-to-end strategy is defined by the expected profit generated under the
specified scenario.
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The rest of this paper is organized as follows. We begin with a review of the relevant
literature. Following this, we present the end-to-end supply chain model, analyze the model, and
describe the numerical exercise performed to compare profitability of the four end-to-end
strategies. This is followed by the presentation of the results of the numerical exercise. The key
insights obtained from the exercise are codified into a set of propositions. Finally, we conclude
the paper with a discussion of the results and their implications for theory and practice.
LITERATURE REVIEW
This paper studies firms’ end-to-end supply chain strategies, where the factors influencing the
sourcing decisions are considered jointly with those affecting sales performance. The question of
what makes a good supply chain strategy was addressed by Fisher (1997), who noted that
products with different demand characteristics were best served by different supply chain
strategies. Lee (2002) extended Fisher’s argument by explaining how supply side uncertainties
should be considered in developing a supply chain strategy. These two conceptual papers lay the
foundation for studying end-to-end strategies in detail. However, they do not provide analytical
comparisons of the tradeoffs involved in different sourcing and retailing choices.
A large body of literature examines the tradeoffs in sourcing decisions. At least three
different streams can be identified in this literature. One stream studies the topic of supplier
selection using the lens of operations research and economics (Elmaghraby, 2000). The papers in
this domain develop models to explore the tradeoffs between choosing a single vs. multiple
suppliers (e.g., Anton & Yao (1989); Seshadri, et al. (1991)), compare sourcing strategies over
multiple periods in presence of learning and entry costs (e.g., Klotz & Chatterjee, 1995; Li,
2013), and specify auction mechanisms to mitigate the limitations of information asymmetry
(e.g., Klemperer, 1999; Chen, 2007). Typically, these works assume the principal-agent dynamic
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between a buyer and its supplier(s), and explore strategies to overcome its negative impact on the
buyer or the supplier.
A related, and large, body of literature studies the design of contracts to align a buyer’s
and a supplier’s interests (Cachon, 2003). The interactions between a buyer (retailer) and a
supplier are examined using game theoretic models, and contractual mechanisms are prescribed
to coordinate their actions to maximize profit for the entire supply chain. Many of these works
assume that the retailer faces newsvendor demand and suggest contracts that make it optimal for
the retailer to order the quantity that is optimal for the supply chain. Several extensions of the
basic newsvendor models—considering cases of price-setting retailer (Bernstein & Federgruen,
2005), retailer promotions (Krishnan, Kapuscinski, & Butz, 2001; Taylor, 2002), retailer
competition (Lippman & McCardle, 1997; Dana & Spier, 2001), etc.—are studied in this stream.
More recent works extend these models by incorporating the effects of competition for either the
buyer or the supplier (Li, 2013; Wu & Zhang, 2014).
A third stream of research on sourcing strategies examines the strategic reasons and
implications of outsourcing for the buyer firm (e.g., Williamson, 1971; Reitzig & Wagner, 2010;
Larsen, Manning & Pedersen, 2013). In contrast to the research works in the above two streams,
which seek to engineer mechanisms to improve buyer-supplier coordination, the research in this
stream examines the buyer-supplier relationship with a descriptive lens. They examine the
implications of outsourcing in terms of parameters, such as cost, quality, responsiveness, R&D
productivity, and so on (Poppo & Zenger, 1998; Reitzig & Wagner, 2010). One finding from this
stream of empirical research of particular interest to the present work is that the benefits of
offshoring—from lower cost—are overestimated due to the difficulty of understanding the
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interdependence between the tasks offshored and those retained in-house (Larsen, Manning, &
Pedersen, 2013).
A substantial body of research also exists for the other side of the supply chain, i.e., the
sales strategy. Pricing has been studied extensively as a means of revenue optimization.
However, price is only one dimension of a sales strategy. Emergence of the Internet as a strong
alternative to brick-and-mortar stores has made it necessary for retailers to understand
consumers’ reasons for choosing a particular sales channel (Myers, Pickersgill, & Van Metre,
2004). Balasubramaniam (1998) presents the seminal model of inter-channel competition; this
model describes the optimal pricing strategies and their market share implications for one mailorder and multiple brick-and-mortar retailers competing with each other. Subsequent empirical
research shows that increase in the density of local stores significantly reduces the demand for
popular products from the mail-order and the Internet channel; however, the impact of store
density on the Internet-based channel is smaller than that on the mail-order channel
(Brynjolfsson, Hu, & Rahman, 2009). Furthermore, the inter-channel competition is seen as
being limited to popular products and is not observed for niche products (ibid). Another mode of
interaction between multiple channels, besides direct competition, is where the consumers use
one channel to obtain information about a product (i.e., shop or browse) and then use another
channel to purchase it. This is has become an important issue for the brick-and-mortar retailers,
because their stores get treated, in effect, as showrooms for the online channels that sell the same
product for a lower price. This phenomenon, termed ‘showrooming,’ has been linked to the
demise of companies such as Borders Book Stores and Circuit City, and is now seen to affect
luxury fashion retailers as well (Passariello, Kapner, & Mesco, 2014). Balakrishnan, Sundaresan,
and Zhang (2013) model this phenomenon and describe the optimal pricing strategies for the
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competing brick-and-mortar and online retailers under different scenarios based on consumer
characteristics, such as, cost of shopping at a B&M vs. an online store and probability of liking
an unknown product.
The showrooming effect results from the consumers’ desire to experience a product
before deciding whether to purchase it. The remote channels—i.e., the mail-order and the
Internet—seek to mitigate any negative effects of the inability to experience their products before
making the purchase decision by offering lenient returns policies. Experimental evidence shows
that lenient returns policies reduce the amount of conflict in the purchase decision as well as
signal higher product quality (Wood, 2001). However, the optimal returns policies are found to
be the ones that allow for only a moderate amount of product returns (Petersen & Kumar, 2009)
or offer only partial refund (Su, 2009). Insights from mathematical models suggest that the
traditional buyback contracts may no longer coordinate the supply chain between a manufacturer
and a retailer in presence of returns, and need to be modified either by differentiating the unsold
and the returned products bought back by the manufacturer or by giving the manufacturer
visibility of the retailer’s sales (ibid).
This brief overview of the vast literature on the sourcing and retail strategies shows that
the two strategies have largely been studied in isolation. Given the existence of multiple end-toend strategies practiced by firms competing successfully in the same industry, we seek to
understand the conditions under which the different strategies work better than the other. To this
effect, this paper contributes to the literature on supply chain strategy (Fisher, 1997; Lee, 2002)
by examining the tradeoffs between different sourcing and retail strategies by considering them
jointly as the firm’s end-to-end supply chain strategy.
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MODEL
Following the tradition in this literature to build on the newsvendor model structure, consider a
firm that operates in an industry that has distinct selling seasons with known beginnings and
endings. Assume that the aggregate market demand for the product for the entire season is
uncertain (denoted by random variable 𝑋), and follows a normal distribution with of mean 𝑥̅ and
variance of 𝜎𝑋2 , i.e. 𝑋~𝒩 (𝑥̅ , 𝜎𝑋2 ). The product is sold for price 𝑝. Firms have only one
opportunity to buy the product before the selling season begins. If demand for the product
exceeds the quantity purchased, the firm does not have another opportunity to buy additional
quantity and the future demand in that season is not converted into sales. Conversely, if the
season’s demand is lower than the procured quantity, the firm has to salvage the leftover products
for a retail price (𝑠) lower than the product’s total landed cost.
Before the start of each season, the firm has to make a strategic decision about its end-toend value chain regarding how to procure the product and what sales channels to sell it through.
Figure 1 presents the timeline of these decisions. Let’s assume that the firm could choose one of
the two sales channels: 𝑁 brick-and-mortar stores or one online store. For simplicity, assume that
the regular season retail price (𝑝) and the salvage price (𝑠) is identical in both these channels. If
the firm chooses the brick-and-mortar channel, the demand at individual stores (𝑌) is
independently and normally distributed, with average 𝑥̅ /𝑁 and variance of 𝜎𝑋2 /𝑁, i.e.
2
𝑥̅ 𝜎𝑋
𝑌~𝒩 (𝑁 ,
𝑁
). If the firm chooses the Online channel, its demand is identical to the market
demand, i.e. ~𝒩 (𝑥̅ , 𝜎𝑋2 ). Let’s assume that a portion of the consumers who buy the product later
return it for a full refund. This proportion could be different for the products purchased at a
brick-and-mortar store (𝜌𝐵 ) than for those purchased online (𝜌𝑂 ), with the latter likely to be
higher than the former.
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Let’s assume that the firm could choose one of two options for sourcing the product: an
off-shore supplier and a near-shore supplier. The product can be acquired for the total landed
costs of 𝑐𝜔 and 𝑐𝜈 from the off-shore and the near-shore suppliers, respectively. Typically, 𝑐𝜔 is
lower than 𝑐𝜈 . However, the off-shore supplier has a longer lead time—the time between
placement of an order and receipt of the products—than the near-shore supplier. Thus, the firm
would need to order the merchandise for a particular season earlier if it were to acquire the
products from the off-shore supplier than if it chose the near-shore supplier. Let, 𝑋̂𝜈 and 𝑋̂𝜔 be
the random variable denoting forecasts of the aggregate demand made at the time of buying the
merchandise from the near-shore and offshore suppliers, respectively. We assume that the
forecasts are not biased, i.e., they have the same mean as the aggregate market demand, 𝑥̅ . The
forecasts could become more accurate when made closer to the selling season if the firm gets
more reliable signals of the market demand as it gets closer to the selling season. Thus, variance
in the forecast made at the time of ordering the merchandise from the near-shore supplier (𝜎𝜈2 )
cannot be higher than that when ordering it from the offshore supplier (𝜎𝜔2 ).
Insert Figure 1 about here
After defining its end-to-end supply chain strategy by specifying its sourcing and retail
strategies, the firm makes two operational decisions in every season. First, it decides the quantity
of the product to procure from the chosen supplier to satisfy the aggregate market demand for the
entire season. We assume that the firm uses the newsvendor formulation to determine the
quantity to buy to meet the season’s demand.
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∗
Lemma 1: The optimal quantities purchased from the offshore (𝑄𝜔
) or the near-shore
suppliers (𝑄𝜈∗ ) are determined by the supplier’s total landed cost and distribution of the
forecasted demand, and are such that:
𝑃𝑟{𝑋̂𝜔 ≤ 𝑄𝜔∗ } = (
𝑃𝑟{𝑋̂𝜈 ≤ 𝑄𝜈∗ } = (
𝑝 − 𝑐𝜔
)
𝑝−𝑠
𝑝 − 𝑐𝜈
)
𝑝−𝑠
Second, the firm allocates the procured quantity to the stores. If the firm chose the Online
channel, the entire procured quantity will be delivered to the warehouse used to fulfill the online
orders. If the firm chose the brick-and-mortar sales channel, the procured quantity will be
divided evenly among the stores. Since the demand at each store is identically distributed and
independent of the demand at other stores, it is optimal to allocate the procured goods among the
𝑁 stores evenly.
∗
Lemma 2: Let’s assume that the firm procures 𝑄∗ units, where 𝑄∗ equals either 𝑄𝜔
or 𝑄𝜈∗
depending on the choice of supplier. If the firm chooses to sell the goods Online, the total
quantity available for sale is 𝑄∗ . If the firm chooses to sell the goods through 𝑁 brickand-mortar stores, the total quantity available for sale at each store is 𝑞 ∗ = 𝑄∗ /𝑁.
After the goods are allocated to the store(s), the selling season begins. We assume that the
variance of the aggregate market demand (𝜎𝑋2 ) is such that 𝜎𝑋2 ≤ 𝜎𝜈2 ≤ 𝜎𝜔2 . If the firm chooses to
sell the products Online, the channel’s demand is identical to the aggregate market demand:
~𝒩 (𝑥̅ , 𝜎𝑋2 ). If the firm chooses to sell the products through brick-and-mortar stores, the demand
2
𝑥̅ 𝜎𝑋
at each store (𝑌) follows a normal distribution: 𝑌~𝒩 (𝑁 ,
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𝑁
). A portion of the products sold are
returned by the consumers for a full refund (equal to the selling price 𝑝) from the firm. We
assume that the firm is able to salvage all the goods returned for the sale price, 𝑠.
Lemma 3: Let’s assume that the firm procures 𝑄∗ units for a cost of 𝑐 per unit, where 𝑄 ∗
and 𝑐 equal either 𝑄𝜔∗ and 𝑐𝜔 , or 𝑄𝜈∗ and 𝑐𝜈 depending on the firm’s supply strategy. Let
𝐺𝑢 (𝑘) be the unit normal loss function evaluated at 𝑘. The expected profits after all
potential returned products are received and subsequently salvaged by the firm for the
Online (𝛱𝑂 ) and brick-and-mortar (𝛱𝐵 ) channels are given by the following expressions.
𝐸 [𝛱𝑂 ] = (1 − 𝜌𝑂 )(𝑝 − 𝑠) (𝑥̅ − 𝜎𝑋 ∙ 𝐺𝑢 (
𝑄∗ − 𝑥̅
)) − (𝑐 − 𝑠)𝑄∗
𝜎𝑋
𝐸 [𝛱𝐵 ] = (1 − 𝜌𝐵 )(𝑝 − 𝑠) (𝑥̅ − √𝑁𝜎𝑋 𝐺𝑢 (
𝑄∗ − 𝑥̅
√𝑁𝜎𝑋
)) − (𝑐 − 𝑠)𝑄∗
End-to-end Strategies
This section presents a comparison of four end-to-end strategies for different types of products
and for firms with different types of business strategies. The products may either be functional or
innovative (Fisher, 1997): functional products meet basic needs and “have stable, predictable
demand,” whereas innovative products create demand by giving customers additional reasons to
buy making the “demand for them unpredictable.” The firms may pursue the strategy of cost
leadership or differentiation through brand, innovation, or responsiveness (Porter, 1980). Since
supply chains need to be designed to meet product characteristics as well as support the firm’s
strategy, we expect that the ideal end-to-end supply chain would be different for different product
types and for firms with different business strategies. We define the end-to-end supply chain
strategy as where the focal firm simultaneously chooses its sourcing and retail strategies. The
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two options for sourcing the products (Offshore vs. Near-shore) and the two options for selling
them (Online vs. Brick-and-mortar) combine to form four potential end-to-end strategies. The
expected profit of these end-to-end strategies follow directly from Lemma 3.
∗}
Proposition 1: Let, 𝑄𝜔∗ and 𝑄𝜈∗ be such that 𝑃𝑟{𝑋̂𝜔 ≤ 𝑄𝜔
= (𝑝 − 𝑐𝜔 )/(𝑝 − 𝑠) and
𝑃𝑟{𝑋̂𝜈 ≤ 𝑄𝜈∗ } = (𝑝 − 𝑐𝜈 )/(𝑝 − 𝑠). The expected profits of four end-to-end strategies,
denoted by 𝐸[𝛱𝑆𝑜𝑢𝑟𝑐𝑖𝑛𝑔,𝑅𝑒𝑡𝑎𝑖𝑙 ], are as follows.
𝐸[𝛱𝜔,𝑂 ] = (1 − 𝜌𝑂 )(𝑝 − 𝑠) (𝑥̅ − 𝜎𝑋 𝐺𝑢 (
∗
𝑄𝜔
− 𝑥̅
∗
)) − (𝑐𝜔 − 𝑠)𝑄𝜔
𝜎𝑋
𝐸[𝛱𝜔,𝐵 ] = (1 − 𝜌𝐵 )(𝑝 − 𝑠) (𝑥̅ − √𝑁𝜎𝑋 𝐺𝑢 (
𝐸[𝛱𝜈,𝑂 ] = (1 − 𝜌𝑂 )(𝑝 − 𝑠) (𝑥̅ − 𝜎𝑋 𝐺𝑢 (
∗
𝑄𝜔
− 𝑥̅
√𝑁𝜎𝑋
∗
)) − (𝑐𝜔 − 𝑠)𝑄𝜔
𝑄𝜈∗ − 𝑥̅
)) − (𝑐𝜈 − 𝑠)𝑄𝜈∗
𝜎𝑋
𝐸[𝛱𝜈,𝐵 ] = (1 − 𝜌𝐵 )(𝑝 − 𝑠) (𝑥̅ − √𝑁𝜎𝑋 𝐺𝑢 (
𝑄𝜈∗ − 𝑥̅
√𝑁𝜎𝑋
)) − (𝑐𝜈 − 𝑠)𝑄𝜈∗
(1)
(2)
(3)
(4)
From equations (1) through (4), we observe that the expected profit of a particular end-to-end
strategy depends of three factors: the expected revenue from products sold and not returned by
the customers, the expected lost revenue from having insufficient goods to meet the demand, and
the total cost of procuring the products from the supplier. The first is a function of the sales
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channel alone (i.e., proportion of sales returned, 𝜌𝑂 and 𝜌𝐵 ), the second is a function of the sales
∗
channel (i.e., the term √𝑁) as well as the sourcing strategy (i.e., 𝑄𝜈∗ and 𝑄𝜔
, which are
determined by the suppliers’ total landed costs—𝑐𝜈 and 𝑐𝜔 —and the variance in forecast of the
demand at the time of purchase, 𝜎𝜈2 and 𝜎𝜔2 ), and the third is a function of the sourcing strategy
∗
alone (i.e., total landed costs—𝑐𝜈 and 𝑐𝜔 —and procured quantity, 𝑄𝜈∗ and 𝑄𝜔
). As we explain
below, the interactions among these terms through nonlinear functions—such as the normal
cumulative distribution function (𝑋̂𝜔 , 𝑋̂𝜈 ) and the normal loss function (𝐺𝑢 )—make it difficult to
analytically compare the expected profits of the different end-to-end strategies. Therefore, we
use a numerical exercise to derive theoretical propositions.
Reason for analytical intractability. The quantities procured from the near-shore and
∗
offshore sources (𝑄𝜈∗ and 𝑄𝜔
) depend on the costs of the respective sources (𝑐𝜈 and 𝑐𝜔 ) and the
forecasts of aggregate market demand, which are assumed to be unbiased and normally
distributed with variances 𝜎𝜈2 and 𝜎𝜔2 . When the forecast accuracy drops due to an increase in the
order lead time (i.e., 𝜎𝜔2 > 𝜎𝜈2 ), for any offshore cost 𝑐𝜔 ≤ 𝑐𝜈 we find that 𝑄𝜔∗ > 𝑄𝜈∗ if (𝑝 −
𝑐𝜈 )/(𝑝 − 𝑠) > 0.5. However, 𝑄𝜔∗ < 𝑄𝜈∗ when the offshore cost rises to a certain threshold, such
that
𝑝−𝑐𝜔
𝑝−𝑠
𝑝−𝑐
= 𝑋̂𝜔 (𝑋̂𝜈−1 ( 𝑝−𝑠𝜈 )). Thus, the quantity procured from the offshore supplier is not
always greater than that procured from the near-shore supplier, despite the total landed cost for
the former being lower than the latter. Instead the relationship between 𝑄𝜔∗ and 𝑄𝜈∗ is non-linear,
and determined by the distributions of the respective forecasts. The expected profit through a
given sales channel is determined by the total cost of goods procured and expected lost sales for
the given procured quantity. Whether the costs of goods procured is higher or lower for the
∗
offshore source (𝑐𝜔 𝑄𝜔
) compared to the near-shore source (𝑐𝜈 𝑄𝜈∗ ) varies nonlinearly with the
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cost per item. Similarly, the expected lost sales for a given quantity is determined by the unit
∗
normal loss function, 𝐺𝑢 (∙) which has a nonlinear relationship with the procured quantity, 𝑄𝜔
or
𝑄𝜈∗ . As the procured quantity increases, the expected lost sales decrease and the expected
∗
revenues increase, both nonlinearly with the procured quantity 𝑄𝜔
or 𝑄𝜈∗ . However, the effect of
increased procured quantity on the expected profit also depends on the total landed cost of the
procured goods, which is a nonlinear function of the costs and the variance in forecast of the
market demand at the time of procurement. Therefore, the expected profit for a given supply
chain configuration is an intricate nonlinear function of the costs, forecast uncertainty, and
variance in market, and difficult to evaluate analytically.
Numerical Exercise
Given the analytical intractability of comparing the expected profit functions, we choose a
numerical approach to compare the four end-to-end strategies by varying eight attributes:
contribution margin (i.e., price minus the variable cost), offshore cost advantage, predictability of
aggregate market demand, deterioration of forecast accuracy in offshore sourcing, proportion of
products returned, returns penalty for online channel, variation in market demand across stores,
and number of brick-and-mortar stores per market. Since this research was motivated by apparel
supply chains, the numeric values used in the exercise for several attributed are based on the
practices in the apparel industry. However, the qualitative insights obtained from the exercise are
generalizable to other industries with similar attributes as well.
IBISWorld industry reports (2013; 2014a,b) shows that clothing retailers spend an
average of 57.4 and 61.9 percent of the revenue for procuring men’s and women’s clothing items,
respectively. This amounts to about 40 percent contribution margin. Fisher and Raman (2010)
note that the typical gross margins for retailers are between 30 and 50 percent. In the numerical
(17)
exercise, we use two values—10 and 50 percent—for contribution margin for the goods procured
from a near-shore source (i.e., 𝑐𝜈 = 0.9𝑝 and 𝑐𝜈 = 0.5𝑝). We then consider offshore cost
advantage by evaluating the strategies for a range of offshore cost to near-shore cost ratios
(𝑐𝜔 /𝑐𝜈 ) between 0.2 and 1.2, in increments of 0.05. We model the predictability of aggregate
demand by choosing two values of demand uncertainty at the time of purchasing goods from a
near-shore supplier (𝜎𝜈 /𝑥̅ = 0.1 and 1). We then operationalize forecast deterioration for
offshore source by taking a ratio of the standard deviations for the offshore source to the nearshore source (𝜎𝜔 /𝜎𝜈 ). We could not find data related to the deterioration of forecast accuracy
over procurement lead time. Therefore, we chose to use two extreme values—1 (no
deterioration) and 3—for 𝜎𝜔 /𝜎𝜈 to indicate the worsening of forecast accuracy over procurement
lead time.
On the sales side, a study using six years of data (1998-2004) at a large national catalog
retailer of apparel and accessories found that, on average, 16 percent of products sold were
returned (Petersen & Kumar, 2009). Although this study did not name the retailer, a similar
returns rate was found for the items shipped in 2006 by L.L. Bean—a retailer known for one of
the most generous return policies—when eight out of 48 million items shipped in 2006 were
returned (Loudin, 2007). Among the online retailers, about 35 percent of the items ordered from
Zappos.com are returned; this rate rises to 50 percent for the customers who buy some of the
most expensive products from the catalogue (Demery, 2010). Other studies of product returns
have reported returns rates of five-to-nine percent for hard goods and up to 35% for high apparel
(Guide, et al., 2006). We test the end-to-end strategies for the returns rates of 10 and 30 percent
at the brick-and-mortar stores (𝜌𝐵 ), with an addition penalty of 10 or 30 percent for the same
product sold online (i.e., 𝜌𝑂 = 1.1𝜌𝐵 or = 1.3𝜌𝐵 ). We also vary the number of stores served by
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one warehouse where the procured goods may be located and distributed from (𝑁 = 25 and 100,
for the brick-and-mortar channel; 𝑁 = 1 for the online channel). Finally, we consider two values
𝜎
of variation of demand at individual stores ( 𝑦̅𝑌 =
𝜎𝑋 /√𝑁
𝑥̅ /𝑁
= 0.01 and 0.1). These values are chosen
to satisfy two criteria: one, the variance of demand across stores does not exceed the variance of
forecast of the market demand made at the time of procuring the goods from the near-shore
source; two, the likelihood of demand at an individual store, which is normally distributes, being
smaller than zero is minimal.
RESULTS
The combinations of the values of the above attributes provide 2688 different scenarios of
business conditions and the related end-to-end strategies. The expected profit is calculated for
each end-to-end strategy in the given scenario using equations (1) through (4). These results are
grouped into 32 cases, and presented graphically in the Appendix. The chart for each case shows
the expected profits (Y-axis) for several end-to-end strategies, wherein the values of offshore
cost discount (𝑐𝜔 /𝑐𝜈 ) are plotted on the X-axis and four sales strategies—namely, brick-andmortar channel with 25 and 100 stores, and Online channel with 10 percent and 30 percent
returns penalty (i.e., 𝜌𝑂 /𝜌𝐵 = 1.1 and = 1.3)—are plotted as four different data series. The
expected profit of a strategy involving a near-shore source is given by the Y-coordinate of the
appropriate data series at 𝑐𝜔 /𝑐𝜈 = 1; this value is projected along the X-axis using a dotted line
to show its relation to the expected profits under various offshore cost discounts. In the following
section, we draw theoretical insights about the attractiveness of different end-to-end strategies by
comparing multiple cases. They are presented in a series of propositions.
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End-to-end Strategies for Products with Predictable Demand
We first evaluate the four potential end-to-end strategies for ‘functional’ products, which have a
predictable demand. The forecast of the aggregate market demand for such products made close
to the selling season when procuring from a near-shore supplier has a small variance (𝜎𝜈2 ), and
has little deterioration when made in advance when procuring from an offshore supplier (𝜎𝜔2 /
𝜎𝜈2 = 1).
We begin with the examination of cases where the uncertainty in the geographic
distribution of demand (𝜎𝑋2 ) is small. Cases 1 and 2 present the expected profits of end-to-end
strategies for such products when the returns rate is low, which is the case for products in
familiar categories (see hypotheses 3 and 4 in Petersen & Kumar (2009)). The expected profit
rise almost linearly with decrease in the total landed cost of the procured items. The only
difference between a low-margin and a high-margin product is the value of the expected profit
for a given level of offshore discount. The preference ordering between offshore and near-shore
suppliers does not change: offshore supplier remains the dominant source. The difference in
profitability of online and brick-and-mortar channels is almost indistinguishable for a given
source. For functional products with high returns rate (cases 3 and 4), which may be the case for
products from new categories purchased in new channels (ibid), the channel with higher returns
penalty—i.e., the online channel in this case—gets dominated by the other channel. This is the
only case for functional products where near-shore sourcing can dominate offshore sourcing, if
the latter has a small offshore cost discount and is paired with online channel while the former is
paired with brick-and-mortar channel.
Proposition 2: For the products with predictable aggregate market demand (i.e., small
𝜎𝜈2 ), even with a long lead time when procured from an off-shore supplier (i.e., 𝜎𝜔2 /𝜎𝜈2 =
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1), as well as predictable geographic distribution of the demand (i.e., small 𝜎𝑋2 ), the
following is true:
(a) Off-shore supplier is the dominant sourcing choice for a given sales channel
(b) Brick-and-mortar and online channels have similar profitability if online returns
penalty is low
(c) An end-to-end strategy of near-shore supplier and brick-and-mortar stores can
outperform the one with off-shore supplier and online store, if the offshore price
discount is low (i.e., 𝑐𝜔 /𝑐𝜈 close to 1) and online returns penalty (𝜌𝑂 /𝜌𝐵 ) is high.
As the geographic spread of demand becomes more uncertain, the indifference between the
online and brick-and-mortar channels starts vanishing. This phenomenon pertains to high
uncertainty about the demand for a product at a particular physical location, i.e. a particular
brick-and-mortar store; it does not pertain to the cases of high variance in demand across
individual stores but where the demand at each individual store demand has small variance. This
scenario is likely to become more prevalent as consumers increase the use of mobile devices to
make location-based impulse buying decisions. Cases 17 through 20 present the expected profits
of end-to-end strategies for the functional products that experience high uncertainty in physical
location of the demand. They are identical to cases 1 through 4, respectively, with the exception
of the uncertainty in geographic location of demand. The comparison of cases 17-20 with cases
1-4 shows that as variance in demand at individual stores increases, the gap in profitability
between online and brick-and-mortar channels widens, with the former become more profitable.
Proposition 3: For the products with predictable demand, even with a long lead time
when procured from an off-shore supplier, an increase in uncertainty of demand at
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individual brick-and-mortar stores can make the online sales channel superior to brickand-mortar if the online sales returns penalty is sufficiently low.
End-to-end Strategies for Products with Unpredictable Demand
We next consider the end-to-end strategies for products with high uncertainty in the aggregate
market demand. These products are characterized by high variance in demand even when
procured at a relatively small lead time from a near-shore supplier (𝜎𝜈 = 𝑥̅ ). The uncertainty at
the time of near-shore sourcing may be so high that it may not deteriorate much if the products
were sourced from an offshore supplier with even longer lead time (i.e., 𝜎𝜔 /𝜎𝜈 = 1). New
products and fashion good may fall in this category.
Cases 5 and 7 depict the expected profits of end-to-end strategies for such products with
high contribution margin (i.e., small 𝑐𝜈 ). The expected profit rises more slowly, compared with
that for functional products (cases 1 and 2), with an increase in the margin resulting from an
increase in the offshore cost advantage. The relative advantage of the offshore source is
dampened when the product enjoys high contribution margin. In general, the brick-and-mortar
channel is superior to the online channel. The expected profitability of a supply chain with nearshore source and brick-and-mortar stores is comparable to that with an offshore source and an
online store, even when the offshore source offers a moderate cost advantage. The former end-toend model ends up being superior to the latter when the product return rates are high, which is
typically the case with new products (Hypothesis 5, Petersen & Kumar (2009)), even with a high
cost advantage of an offshore source.
Proposition 4: For the products with equally unpredictable aggregate demand when
sourced from either near-shore or offshore suppliers (i.e., large 𝜎𝜈2 and 𝜎𝜔 = 𝜎𝜈 ) and
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high contribution margin (i.e., small 𝑐𝜈 ), if the uncertainty in the geographic distribution
of demand is low (i.e., small 𝜎𝑋2 ) the end-to-end strategy with a near-shore supplier and
brick-and-mortar stores is superior to one with an offshore supplier and online store in
spite of large discounts in the total landed cost afforded by the offshore supplier (i.e.,
small 𝑐𝜔 /𝑐𝜈 ) if the online returns penalty (𝜌𝑂 /𝜌𝑅 ) is high.
However, the end-to-end strategy of near-shore supplier and brick-and-mortar stores for these
products quickly gets dominated by a strategy to source from an offshore supplier and sell
online, if the store-level demand is highly unpredictable. Comparison of cases 21 and 23 with
cases 5 and 7 reveals this complete reversal of preferences of the end-to-end strategies only due
to an increase in the uncertainty of geographic distribution of demand. This is especially true
when the proportion of products returned is low or when the returns penalty for online sales is at
most moderately higher than the brick-and-mortar stores returns. Surprisingly, this superiority of
the offshore-online supply chain strategy is valid when the offshore discount is fairly low (𝑐𝜔 /𝑐𝜈
close to 1). The reason for this result is that newsvendor critical ratio for the offshore source is
only moderately higher than that for the near-shore source resulting in moderately higher order
quantity, which is then placed at one location (warehouse for the online store) instead of being
distributed among multiple brick-and-mortar stores.
Proposition 5: For the products with equally unpredictable aggregate demand when
sourced from either near-shore or offshore suppliers (i.e., large 𝜎𝜈2 and 𝜎𝜔 = 𝜎𝜈 ) and
high contribution margin (i.e., small 𝑐𝜈 ), if the store-level demand has high uncertainty
(i.e., large 𝜎𝑋2 ) the end-to-end strategy with an offshore source and online sales is the
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preferred option, if the proportion of online sales returned is small (because either 𝜌𝐵 or
𝜌𝑂 /𝜌𝐵 or both are low) and offshore cost advantage is moderate.
Effect of Deterioration in Forecast Accuracy
The above propositions compare different end-to-end strategies for function and novel products.
Next, we examine how the utility of end-to-end strategies change if the forecast accuracy
degrades rapidly over the lead time, as one considers the tradeoffs between near-shore and
offshore sourcing in the end-to-end strategy.
We first look at products whose demand is predictable when procured from a near-shore
supplier (𝜎𝜈 /𝑥̅ = 0.1) but harder to predict in advance if procured from an offshore source
(𝜎𝜔 /𝜎𝜈 = 3). Examples of such products include apparel item whose forecast for the season’s
demand has high variability, until some demand signal—such as customer response at a fashion
show, feedback from focus group, etc.—is received, after which the demand can be predicted
with high accuracy. Cases 9 through 12 show the profitability of various end-to-end strategies for
such products, when the geographic distribution of demand has low uncertainty. Regardless of
the deterioration in forecast accuracy, it is still more profitable to source from an offshore
supplier than a near-shore supplier. In general, an offshore source with brick-and-mortar sales
channel is the best end-to-end strategy. Comparing these products to the functional products
(cases 1-4), whose demand can always be predicted fairly accurately, we see that there is no
change in the preference ordering of the end-to-end strategies. Similarly, when the variation in
geographic demand is high, the preference ordering of end-to-end strategies remains unchanged
(compare cases 17-20 with cases 25-28). Generally, it is more advantageous to source from an
offshore supplier. The ideal sales channel is determined by the tradeoff in the loss of profitability
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from high online returns penalty versus dispersion of goods over a larger number of brick-andmortar stores.
Proposition 6: For the products with predictable demand (i.e., small 𝜎𝜈2 ), deterioration in
forecast accuracy over lead time—when the products are procured from an off-shore
source—does not change the preference ordering of end-to-end supply chain strategies.
Next, we consider the high-margin (𝑐𝜈 = 0.5𝑝) products whose demand is unpredictable at the
time of sourcing from a near-shore supplier (𝜎𝜈 = 𝑥̅ ) and become even harder to forecast
accurately when sourcing in advance from an offshore supplier (𝜎𝜔 /𝜎𝜈 = 3). For cases 13, 15,
29, and 31 of this type, the profitability of end-to-end strategies has a distinctly different pattern
from that observed in all the cases until now. Expected profit is a convex function of the total
landed cost: as offshore cost decreases from the near-shore cost, the expected profit of an end-toend strategy also drops and does not start rising again until the offshore cost is significantly
lower than the near-shore cost. If the store-level demand is fairly predictable once the aggregate
market demand is known (𝜎𝑌 = 0.01𝑦̅)—as in cases 13 and 15—the optimal end-to-end strategy
is to source near-shore and sell through brick-and-mortar stores. If the product returns rate is low
(𝜌𝐵 = 0.1), sourcing near-shore and selling online also provides equivalent profits. If the storelevel demand is difficult to predict (𝜎𝑌 = 0.1𝑦̅) even after the aggregate market demand is
known—as in cases 29 and 31—the best end-to-end strategy is to source near-shore and sell
online.
Proposition 7: For high-margin products (i.e., small 𝑐𝜈 ) with unpredictable demand (i.e.,
large 𝜎𝜈2 ), whose forecasts become even less accurate over time when sourced from an
offshore source, the following is true:
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(a) Near-shore sourcing dominates offshore sourcing even when offshore cost
discount is extreme high
(b) If the store-level demand is fairly predictable (i.e., small 𝜎𝑋2 ), the ideal end-to-end
strategy is to source near-shore and sell through the brick-and-mortar channel
(c) If the store-level demand is unpredictable (i.e., large 𝜎𝑋2 ), the ideal end-to-end
strategy is to source near-shore and sell through the online channel.
While the degradation of forecast accuracy of makes near-shore sourcing more attractive for
products with unpredictable demand (𝜎𝜈 = 𝑥̅ ) and high margin (𝑐𝜈 = 0.5𝑝), it has the opposite
effect on the profitability of sourcing strategies if such products have low margin (𝑐𝜈 = 0.9𝑝). In
the latter case, near-shore sourcing is not only not preferred, it may not even be a feasible option.
In fact, for all low-margin products with unpredictable demand—as in cases 6, 8, 14, 16, 22, 24,
30, and 32—a near-shore source as well as any offshore sources with low cost discount are
rendered completely infeasible. This happens because the optimal newsvendor order quantity
from a near-shore source is negative because of the small newsvendor critical ratio (resulting
from the low contribution margin) and high demand uncertainty. If the forecast accuracy worsens
over time (cases 14, 16, 30, and 32), it becomes necessary to have an even higher offshore cost
discount to have a feasible supply chain. Even though the optimal order quantity will not be
negative if a distribution with nonnegative support is used, it still will be too small to make nearshore source profitable.
Proposition 8: For low-margin products (i.e., high 𝑐𝜈 ) with unpredictable demand (i.e.,
large 𝜎𝜈2 ) near-shore sources as well as offshore sources with low cost discount can be
infeasible options.
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DISCUSSION
This paper explores the tradeoffs between different sourcing and sales strategies of one firm in an
end-to-end model of its supply chain. This research contrasts with the vast body of extant
literature that examines sourcing and sales strategies in isolation. The purpose of studying the
sourcing and the sales strategies together is to study the supply chain from a systemic
perspective. The model presented in this paper is designed to do so with the intent to strike the
delicate balance between parsimony and systemic view to gain practicable insights about an endto-end strategy without becoming another model in which “any outcome whatsoever can be
explained … after the fact” (Williamson, 2008). The benefits of taking a systemic approach are
seen in the intriguing insights and the corresponding practical implications provided by some
propositions developed from a comparative analysis of multiple cases.
Proposition 2 reinforces the conventional wisdom that offshore supplier is the dominant
source for functional products regardless of the choice for sales channel; however, it also shows
that an end-to-end supply chain with near-shore supplier and brick-and-mortar stores is more
profitable than one with an offshore supplier and online channel, when the offshore price
discounts are moderate and online returns penalty is high. This provides the intuition for the
attractiveness of Zara’s business model. However, the attractiveness of this business model
diminishes and makes online selling more attractive when the demand at individual store
becomes less predictable (proposition 3). These results suggests that firms using Zara’s supply
chain model will need to change their end-to-end strategies to consolidate the inventory at fewer
physical locations (not necessarily at one warehouse service the online channel), as the demand
at individual stores becomes more uncertain, potentially due to the phenomena such as an
increase in the use of location-based purchases from mobile devices.
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Proposition 4 justifies the practice of sourcing products with high demand uncertainty,
such as fashion items and new products, close to the market. It also shows that it is better to sell
such products through the brick-and-mortar channel where the potential consumers can
experience them before making a purchase decision. This economic advantage of near-shore
source with brick-and-mortar stores for fashion products is another justification of the Zara
model. However, the viability of this end-to-end model requires that the uncertainty in the storelevel demand is low. If the store-level demand had high uncertainty, we see a complete reversal
of the preference for end-to-end strategies: offshore source with online sales becomes the
preferred option (proposition 5), especially if the total landed cost of the offshore supplier is
close to that of the near-shore supplier! Two aspects of this reversal highlight the need for taking
an end-to-end perspective. First, the reversal occurs when offshore cost is high and closer to the
near-shore source, which is counter-intuitive. The reason for this is that less quantity is ordered
and centralized in one (or a few) location. Second, the reversal shows how change in one
attribute of the business environment—namely, predictability of geographic location of demand
in this case—can result into a once eulogized and emulated business model being dethroned by
its polar opposite. If the increase in mobile e-commerce results into an increased uncertainty of
the store-level demand, the revered Zara business model could get deposed by an offshore
source, online sales end-to-end strategy.
Propositions 6 through 8 show that the robustness of end-to-end strategies to any
degradation of forecasts of aggregate demand made when procuring the goods from offshore
suppliers depends on the type of product. For ‘functional’ products (Fisher, 1997), the end-to-end
strategy is robust: surprisingly, it is still preferable to source the products from an offshore source
and sell through brick-and-mortar stores (online) if the store-level demand is (not) predictable
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(proposition 6). However, the strategy is reversed for the ‘innovative’ products with high
margins: near-shore sourcing becomes the dominant strategy (proposition 7). This reversal is
moderated by the product’s contribution margin: reversal to the near-shore sourcing occurs only
if the products have high margin; for the products with low contribution margin, the only feasible
source is an offshore source that offers a significant cost advantage over the near-shore product
(proposition 8). This suggests that firms using the Zara model need to ensure that their products
enjoy a high margin, either by keeping the costs low or by keeping the prices high or both, to
keep the near-shore suppliers a viable source.
In addition to these insights about the robustness of end-to-end strategies, this paper also
highlights some of the hidden costs of outsourcing that result from an increase in the
‘configuration complexity’ of an organization (Larsen, et al., 2013). For instance, the results
suggest that when a firm faces high variation in the market demand, it is ideal to source products
from a near-shore supplier—which has a higher total landed cost than an offshore supplier—
especially if the margins are high. The sourcing and the sales strategies, typically studied in
isolation in the literature, are related in this manner because the newsvendor model suggests a
lower order quantity from the near-shore supplier than the offshore supplier due to the former’s
higher total landed cost as well as higher forecast accuracy, and the firm benefits from having a
fewer unsold items resulting from high variation in demand. Thus, the model presented here
highlights how the cost of information disadvantage in sourcing decisions interacts with the
demand variation in the sales period.
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APPENDIX
Firm receives and allocates goods
to single warehouse for online store
or each brick-and-mortar store
Firm chooses endto-end strategy
Firm orders goods from
offshore supplier at 𝑐𝜔
per forecasted market
demand ~𝒩 (𝑥̅ , 𝜎𝜔2 )
𝑐𝜔 ≤ 𝑐𝜈 ≤ 𝑝
Firm orders goods from Selling season A portion (𝜌𝐵 or 𝜌𝑂 )
near-shore supplier at 𝑐𝜈 (sell price 𝑝) of sales returned by
per forecasted market Market demand customers for full
discount and
demand ~𝒩 (𝑥̅ , 𝜎𝜈2 )
~𝒩 (𝑥̅ , 𝜎𝑀2 )
salvaged by firm
𝜎𝜔2 ≥ 𝜎𝜈2 ≥ 𝜎𝑀2
0 ≤ 𝜌𝐵 ≤ 𝜌𝑂 ≤ 1
Figure 1: Timeline of decisions and events
Proof of Lemma 1
The optimal order quantities are based on newsvendor formulation.
Proof of Lemma 2
If the firm chooses the Online sales channel, the optimal decision is to make the entire procured
quantity available for sale through the online store. If the firm chooses the brick-and-mortar sales
channel with 𝑁 stores, the demand at each store is identically distributed and is independent of
the demand at other stores. Therefore, the optimal decision is to evenly divide the procured
quantity among the 𝑁 stores.
Proof of Lemma 3
Let 𝑄 be the quantity procured at cost 𝑐 per item, where 𝑄 ∗ and 𝑐 take appropriate values
depending on the choice of supplier. The expected sale at the online store is equal to
𝑄∗
∞
∫𝑜 𝑥𝑓𝑋 (𝑥 )𝑑𝑥 + 𝑄 ∗ ∫𝑄 ∗ 𝑓𝑋 (𝑥)𝑑𝑥. A proportion, 𝜌𝑂 , of the sold goods are returned to the retail
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store for a full discount, which are then salvaged for 𝑠 per unit. Therefore, the expected profit
generated by the Online store is equal to,
𝑄∗
𝑄∗
∞
𝐸 [Π𝑂 ] = ((1 − 𝜌𝑂 )𝑝 + 𝜌𝑂 𝑠) [∫ 𝑥𝑓𝑋 (𝑥 )𝑑𝑥 + 𝑄∗ ∫ 𝑓𝑋 (𝑥)𝑑𝑥] + 𝑠 ∫ (𝑄∗ − 𝑥 )𝑓𝑋 (𝑥 )𝑑𝑥 − 𝑐𝑄 ∗
𝑄∗
𝑜
𝑜
∞
This can be simplified to the following by adding and subtracting the term 𝑄 ∗ ∫𝑄 ∗ 𝑓𝑋 (𝑥 )𝑑𝑥 to the
above expression.
𝑄∗
𝑄∗
∞
𝐸 [Π𝑂 ] = (1 − 𝜌𝑂 )𝑝 ∫ 𝑥𝑓𝑋 (𝑥 )𝑑𝑥 + (1 − 𝜌𝑂 )𝑝𝑄∗ ∫ 𝑓𝑋 (𝑥 )𝑑𝑥 + 𝜌𝑂 𝑠 ∫ 𝑥𝑓𝑋 (𝑥 )𝑑𝑥
𝑄∗
𝑜
𝑄∗
∞
𝑜
𝑄∗
+ 𝜌𝑂 𝑠𝑄∗ ∫ 𝑓𝑋 (𝑥 )𝑑𝑥 + 𝑠𝑄 ∗ ∫ 𝑓𝑋 (𝑥 )𝑑𝑥 − 𝑠 ∫ 𝑥𝑓𝑋 (𝑥 )𝑑𝑥 − 𝑐𝑄∗
𝑄∗
∞
𝑜
𝑜
∞
+ 𝑠𝑄∗ ∫ 𝑓𝑋 (𝑥 )𝑑𝑥 − 𝑠𝑄∗ ∫ 𝑓𝑋 (𝑥 )𝑑𝑥
𝑄∗
𝑄∗
Solving this gives
𝑄∗
𝑄∗
∞
𝐸 [Π𝑂 ] = (1 − 𝜌𝑂 )𝑝 ∫ 𝑥𝑓𝑋 (𝑥 )𝑑𝑥 + (1 − 𝜌𝑂 )𝑝𝑄∗ ∫ 𝑓𝑋 (𝑥 )𝑑𝑥 − (1 − 𝜌𝑂 )𝑠 ∫ 𝑥𝑓𝑋 (𝑥 )𝑑𝑥 − (1
𝑄∗
𝑜
𝑜
∞
− 𝜌𝑂 )𝑠𝑄∗ ∫ 𝑓𝑋 (𝑥 )𝑑𝑥 − (𝑐 − 𝑠)𝑄∗
𝑄∗
𝑄∗
∞
𝐸 [Π𝑂 ] = (1 − 𝜌𝑂 )(𝑝 − 𝑠) ∫ 𝑥𝑓𝑋 (𝑥)𝑑𝑥 + (1 − 𝜌𝑂 )(𝑝 − 𝑠)𝑄∗ ∫ 𝑓𝑋 (𝑥 )𝑑𝑥 − (𝑐 − 𝑠)𝑄 ∗
𝑄∗
𝑜
This can be simplified to the following by adding and subtracting the term (1 − 𝜌𝑂 )(𝑝 −
∞
𝑠) ∫𝑄 ∗ 𝑥𝑓𝑋 (𝑥 )𝑑𝑥 to the above expression.
(31)
∞
𝐸 [Π𝑂 ] = (1 − 𝜌𝑂 )(𝑝 − 𝑠) [𝑥̅ − ∫ (𝑥 − 𝑄∗ )𝑓𝑋 (𝑥 )𝑑𝑥 ] − (𝑐 − 𝑠)𝑄∗
𝑄∗
∞
Here, ∫𝑄 ∗ (𝑥 − 𝑄∗ )𝑓𝑋 (𝑥 )𝑑𝑥 represents the expected lost sales. When 𝑋 is distributed normally,
this term equals 𝜎𝑋 𝐺𝑢 (
𝑄∗ −𝑥̅
𝜎𝑋
), where 𝐺𝑢 (𝑘) is the unit normal loss function evaluated at 𝑘.
𝐸 [Π𝑂 ] = (1 − 𝜌𝑂 )(𝑝 − 𝑠) [𝑥̅ − 𝜎𝑋 𝐺𝑢 (
𝑄∗ − 𝑥̅
)] − (𝑐 − 𝑠)𝑄∗
𝜎𝑋
(A1)
Using this expression, the expected profit generated by selling the goods in the brick-and-mortar
channel, where the demand at each store is identically distributed normally with the mean of
𝑥 ̅/𝑁 and variance of 𝜎𝑋2 /𝑁, is given by the following expression.
𝑄∗ ̅
𝑥
−
𝑥̅
𝜎𝑋
𝐸 [Π𝐵 ] = 𝑁(1 − 𝜌𝐵 )(𝑝 − 𝑠) [ −
𝐺 ( 𝑁 𝜎 𝑁 )] − (𝑐 − 𝑠)𝑄 ∗
𝑋
𝑁 √𝑁 𝑢
√𝑁
𝐸 [Π𝐵 ] = (1 − 𝜌𝐵 )(𝑝 − 𝑠) [𝑥̅ − √𝑁𝜎𝑋 𝐺𝑢 (
𝑄∗ − 𝑥̅
√𝑁𝜎𝑋
)] − (𝑐 − 𝑠)𝑄∗
(A2)

(32)
NONE (𝜎𝜔 /𝜎𝜈 = 1)
LOW (𝐶𝑂𝑉𝜈 = 0.1)
LOW (𝑐𝜈 = 0.5𝑝)
HIGH (𝑐𝜈 = 0.9𝑝)
Proportion of
sales returned
Variation in
demand
LOW (𝜌𝐵 = 0.1)
LOW (𝜎𝑌 /𝑦̅ = 0.01)
HIGH (𝜌𝐵 = 0.3)
Deterioration in
forecast accuracy
Demand uncertainty at purchase
Total landed cost
as % of sale price
(33)
HIGH (𝐶𝑂𝑉𝜈 = 1)
LOW (𝑐𝜈 = 0.5𝑝)
HIGH (𝑐𝜈 = 0.9𝑝)
HIGH (𝜎𝜔 /𝜎𝜈 = 3)
LOW (𝐶𝑂𝑉𝜈 = 0.1)
LOW (𝑐𝜈 = 0.5𝑝)
HIGH (𝑐𝜈 = 0.9𝑝)
Proportion of
sales returned
Variation in
demand
LOW (𝜌𝐵 = 0.1)
LOW (𝜎𝑌 /𝑦̅ = 0.01)
HIGH (𝜌𝐵 = 0.3)
Deterioration in
forecast accuracy
Demand uncertainty at purchase
Total landed cost
as % of sale price
(34)
HIGH (𝐶𝑂𝑉𝜈 = 1)
LOW (𝑐𝜈 = 0.5𝑝)
HIGH (𝑐𝜈 = 0.9𝑝)
NONE (𝜎𝜔 /𝜎𝜈 = 1)
LOW (𝐶𝑂𝑉𝜈 = 0.1)
LOW (𝑐𝜈 = 0.5𝑝)
HIGH (𝑐𝜈 = 0.9𝑝)
Proportion of
sales returned
Variation in
demand
LOW (𝜌𝐵 = 0.1)
HIGH (𝜎𝑌 /𝑦̅ = 0.1)
HIGH (𝜌𝐵 = 0.3)
Deterioration in
forecast accuracy
Demand uncertainty at purchase
Total landed cost
as % of sale price
(35)
HIGH (𝐶𝑂𝑉𝜈 = 1)
LOW (𝑐𝜈 = 0.5𝑝)
HIGH (𝑐𝜈 = 0.9𝑝)
HIGH (𝜎𝜔 /𝜎𝜈 = 3)
LOW (𝐶𝑂𝑉𝜈 = 0.1)
LOW (𝑐𝜈 = 0.5𝑝)
HIGH (𝑐𝜈 = 0.9𝑝)
Proportion
of sales
returned
Variation in
demand
LOW (𝜌𝐵 = 0.1)
HIGH (𝜎𝑌 /𝑦̅ = 0.1)
HIGH (𝜌𝐵 = 0.3)
Deterioration in
forecast accuracy
Demand uncertainty at purchase
Total landed cost
as % of sale price
(36)
HIGH (𝐶𝑂𝑉𝜈 = 1)
LOW (𝑐𝜈 = 0.5𝑝)
HIGH (𝑐𝜈 = 0.9𝑝)
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