european journal of operational research · decision support environmental implications for online...

European Journal of Operational Research 239 (2014) 744–755

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European Journal of Operational Research

journal homepage: www.elsevier .com/locate /e jor

Decision Support

Environmental implications for online retailing

http://dx.doi.org/10.1016/j.ejor.2014.05.0380377-2217/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +1 (352) 392 5858; fax: +1 (352) 392 5438.E-mail addresses: [email protected] (J.E. Carrillo), [email protected] (A.J. Vakharia),

[email protected] (R. Wang).

Janice E. Carrillo a,⇑, Asoo J. Vakharia a, Ruoxuan Wang b

a Department of Information Systems and Operations Management, Warrington College of Business Administration, University of Florida, Gainesville, FL 32611-7169, United Statesb Management Information Systems, College of Business Administration, San Diego State University, San Diego, CA 92182-8234, United States

a r t i c l e i n f o

Article history:Received 22 May 2013Accepted 26 May 2014Available online 12 June 2014

Keywords:RetailingPricingEnvironmente-CommerceDual channel

a b s t r a c t

Recent press has highlighted the environmental benefits associated with online shopping, such asemissions savings from individual drivers, economies of scale in package delivery, and decreasedinventories. We formulate a dual channel model for a retailer who has access to both online andtraditional market outlets to analyze the impact of customer environmental sensitivity on its supply.In particular, we analyze stocking decisions for each channel incorporating price dependent demand,customer preference/utility for online channels, and channel related costs. We compare and contrastresults from both deterministic and stochastic models, and utilize numerical examples to illustrate theimplications of industry specific factors on these decisions. Finally, we compare and contrast the findingsfor disparate industries, such as electronics, books and groceries.

� 2014 Elsevier B.V. All rights reserved.

1. Motivation

The environmental benefits associated with online shopping,such as emissions savings from individual drivers, economies ofscale in package delivery, and decreased inventories, are welldocumented. Weber et al. (2008) performed a case study for buy.-com comparing the environmental impact of e-commerce vs. a tra-ditional retailer for the purchase and delivery of a flash drive. A keyfinding of this study is that the total energy usage for a traditionalretailer is higher than that typically associated with e-commercedelivery. The main factors driving this result are the distance thatthe customer has to drive to buy the item via a traditional retailer(on average they drive 14 miles for a round trip), and the consumerfuel economy (assumed to be 22 miles/gallon from the US EPA).The authors also note the limitations of these results. For instance,if express air shipping is chosen as the delivery method by the cus-tomer, then the carbon emissions for both modes (i.e. e-commerceand traditional retailer) are roughly comparable.

Moreover, consumer awareness concerning the environmentalimpact associated with particular product choices is growing. A2010 article appearing in the Wall Street Journal summarizes theresults of a poll which finds that 17% of U.S. consumers and 23%of European consumers are willing to pay more for environmen-tally friendly products (O’Connell, 2010). These numbers haveincreased significantly over the past year. Consequently, major

retailers such as Wal Mart are undertaking initiatives to includeenvironmental information on labels along with pricinginformation. To start the process of gathering more environmentalinformation from suppliers, Wal Mart will require its suppliers toanswer questions concerning energy costs and emissions, materialefficiency, natural resources, and ethical workforce concerns(Bustillo, 2009). According to O’Connell (2010), the percentage ofadvertisements in major magazines making ‘‘green claims’’ hasalso grown. However, many vendors have overstated the environ-mental properties of their goods (a practice commonly referred toas ‘‘greenwashing’’) such that the Federal Trade Commission hastaken actions against these claims.

Internet companies are undertaking initiatives to highlight theenvironmental choices to consumers when they purchase goodsvia the internet. For example, Amazon.com has received a patenton ‘‘environmentally conscious electronic transactions,’’(Engleman, 2010). Their goal is to distinguish the environmentalimpact between different shipping methods, and to specificallymarket this service to consumers who are willing to pay morefor delivery methods which have a lower environmental impact.Engleman (2010) also notes that, ‘‘These shipping options couldcost more, and entail a longer wait for a package, but presumablyAmazon sees a potential market for this.’’ Examples of such envi-ronmental shipping practices include the use of hybrid vehicles,minimization of packaging materials, and efficient truck utilizationtechniques.

Many retail firms are grappling with the issue of how to bestmanage dual distribution channels for their goods as demand viainternet channel grows. To illustrate, the U.K. retailer Tesco

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established a home delivery service in 2000 and advertised theirnew internet channel with the slogan, ‘‘You shop. We drop.’’(Anonymous, 2006). While other retailers may fear that there is aconflict between these two important channels, Tesco embracedthe complementarities between the new and old channels whileconcurrently continuing to expand its traditional bricks-and-mor-tar stores. In contrast, Webvan tried to establish a single onlinechannel to deliver groceries by investing in large warehouses andinventory management systems (Spurgeon, 2001). Unfortunately,they went bankrupt due to a lack of customers willing to pay ahigher premium for their service. Therefore, primary concerns ofdual channel distribution include supply chain costs, customer ser-vice, and pricing.

In this paper, we introduce a stylized single firm model focusingon marketing choices for a dual channel strategy. We explicitlyaddress the environmental implications of each channel todetermine appropriate pricing and stocking decisions. Throughour analysis, we address the following key research questions:

1. If a retailer has both traditional and online sales channels, howshould he/she manage the split between these?

2. Are there circumstances under which a retailer should focusonly on online and/or traditional channels?

3. How will consumer behavior evolve in response to theseenvironmental channel concerns?

4. Which factors associated with e-commerce have the mostsignificant impact on the environment?

5. How will policy issues such as a carbon tax impact on theretailer’s decision?

The paper is organized as follows. In Section 2, we furtherdiscuss the existing body of literature as it relates to our keyresearch questions. In Section 3.1, we introduce and analyze adeterministic model based on price dependent demand functionsto determine when a dual strategy is appropriate. We extend thismodel in Section 3.2 to incorporate demand uncertainty via anewsvendor framework. A numerical analysis that analyzes theimpact of various environmental factors on the optimal solutionsand profits is included in Section 4. Conclusions and directionsfor future research are discussed in Section 5.

2. Literature review

2.1. e-Commerce and the environment: empirical literature

Several notable case-based and empirical studies have beenpublished which analyze the environmental effects of e-commercefor specific industries, including electronics, groceries and books.For a more complete description of this literature, see Carrillo,Vakharia, and Wang (2010). As previously mentioned, Weberet al. (2008) utilize monte-carlo simulation techniques to analyzekey factors involved in the delivery of a flash drive for buy.com.Fernie, Pfab, and Marchant (2000) survey senior executives cur-rently working in grocery supply chain companies and concludethat some of the top issues that these executives are concernedabout for the future included both e-commerce and environmentalfactors. Siikavirta, Punakivi, Krkkinen, and Linnanen (2002) employsimulation methodologies to analyze green house gas emissionsassociated with home delivery grocery services. They identify sce-narios under which the home delivery service can cut green housegases by up to 87%. Matthews, Hendrickson, and Soh (2001) per-form a study of the online book industry to directly analyze theenvironmental impact of online vs. traditional book retailers. Theyfind that, when there are no returns, both modes have a compara-ble environmental impact. However, when the remainder rates aresignificant (they are typically 35% for best-selling books that are

not sold at the end of the selling season from the retailer), the envi-ronmental impact of the traditional retailer is much worse, as theymust stock higher inventories. Our model utilizes the evidencefrom this body of empirical studies to motivate certainrelationships which link environmental factors to consumerdecisions concerning channel choice.

2.2. Literature on e-commerce

Agatz, Fleischmann, and van Nunen (2008) offer a detailed over-view of both the empirical and analytic literature which addressese-fulfillment in a multi-channel environment. These authors notethat, ‘‘One recurrent pattern is the combination of ‘bricks-and-clicks’, the integration of online sales into a portfolio of multiplealternative distribution channels.’’ They offer numerous examplesof retail firms where (a) traditional retailers are adding an onlinechannel and (b) internet retailers are opening physical stores.One of the conclusions that these authors reach is that, ‘‘Pricingmodels for a multi-channel setting appear to be scarce as of yet.’’Our model directly addresses this shortcoming in the literature.Specifically, we develop optimal pricing and stocking strategiesfor a multi-channel retailer based on factors such as (a) theconsumer’s propensity to buy from the online channel, (b) theenvironmental costs associated with both channels, (c) price sensi-tivity to demand in both channels, and (c) cross price substitutioneffects between the channels.

2.2.1. Empirical literature on e-commerceIn his seminal paper, Bakos (2001) offers an overview of the

impact of e-commerce on the retailing landscape and summarizesseveral key issues associated with e-commerce. Factors relevant inour context include increased price competition and differentiationvia pricing for goods ordered online. Brynjolfsson and Smith (2000)explore the impact of internet commerce on price by analyzingdata from book and CD industries for both traditional and e-com-merce channels. These authors find that prices on the internetare significantly lower than those in a traditional retailer evenwhen accounting for taxes, shipping, shopping and transportationcosts. Brynjolfsson, Hu, and Rhaman (2009) further characterizethe nature of competition between traditional bricks-and-mortarstores and an internet retailer. Their empirical study shows thatthe competition between these two channels is strongest whenthe goods are mainstream products that are typically associatedwith lower search costs. We utilize this literature in motivatingour model by incorporating a cross price sensitivity parameterbetween the channels which reflects the competition betweenthe two channels. Consequently, we can analyze the circumstancesunder which prices may be lower in a particular channel.

2.2.2. Analytic dual channel modelsA body of literature within the operations management area

addresses supply chain issues typically associated with dual chan-nel models of distribution. For an overview of these models, seeAgatz et al. (2008) and also Cattani, Gilland, Heese, andSwaminathan (2006). In particular, many of these analytic modelsaddress the manufacturer’s decision concerning the addition of adirect retail channel (i.e. online sales) and sales via a traditionalestablished independent retailer (i.e. bricks-and-mortar). The keydecision variables in these models classically include both thewholesale/transfer price between the manufacturer and the retai-ler and the price offered to customers in both of the channels(Cattani et al., 2006; Chiang, Chhajed, & Hess, 2003; Chiang &Monahan, 2005; Dumrongsiri, Fan, Jain, & Moinzadeh, 2008; Tsay& Agrawal, 2004; Yue & Liu, 2006). These game theoretic modelsdirectly address the problem of double marginalization and char-acterize the circumstances under which the traditional retailer

Table 1Notation used in the paper.

Symbol Description

i Index for channel structuresi ¼ 1 for RC; i ¼ 2 for OC; and i ¼ 3 for DC

ci Unit cost for channel i (i ¼ 1;2)e Environmental unit cost savings/premium for OC channelb Unit Cost savings/premium for OC channelxi Demand for channel i (i ¼ 1;2)pi Unit price for channel i (i ¼ 1;2)p3i Unit price for channels i (i ¼ 1;2) for channel structure DCqi Quantity offered through channel i (i ¼ 1;2)p3i Quantity offered through channels i (i ¼ 1;2) for channel structure

DCai Maximum market size for channel i (i ¼ 1;2)a Total market sizek Propensity of customers for OC (0 6 k 6 1)bi Price elasticity of demand for channel i (i ¼ 1;2)s Symmetric price substitution parameter�i Random variable associated with uncertain demandfið�Þ Probability density function for �i

Fið�Þ Cumulative density function for �i

½�di; di� Minimum and maximum values for �i

h Salvage value for an unsold unitPi Firm profit associated with channel structure i (i ¼ 1;2;3)

746 J.E. Carrillo et al. / European Journal of Operational Research 239 (2014) 744–755

may actually benefit from the second online channel. In addition,Tsay and Agrawal (2004) explicitly consider investments in salesactivities, while Chen, Kaya, and Ozer (2008a) considerinvestments in activities which improve product availability (forthe traditional retailer) or leadtime (for the online channel).Cattani et al. (2006) and Chen et al. (2008a) take into account therelative ‘‘inconvenience’’ of shopping in a traditional retailer vs.an online retailer via channel cost differentials. Boyaci (2005)addresses stocking decisions for both channels and explicitly mod-els substitution effects for the situation where there is a stockout inone of the channels. Finally, Tsay and Agrawal (2000) considercompetition between two retailers via price and service mecha-nisms when selling a single product procured from a singlemanufacturer.

Our model is focused on a single stage channel for a singleproduct. In contrast, other authors including Cattani et al. (2006),Chiang et al. (2003), Chiang and Monahan (2005), Dumrongsiriet al. (2008), Tsay and Agrawal (2004), and Yue and Liu (2006)all explicitly address a dual stage situation where the retailer nego-tiates with the manufacturer in addition to setting prices for thetraditional retail channel. Compared with these dual channel mod-els, our model is unique as it addresses the situation where bothchannels (online and traditional) are owned by a single retailer.Consequently, we do not explicitly include the manufacturer inthis problem. The Tsay and Agrawal (2000) model is closest to oursas it utilizes similar demand functions to ours and it considers twocompeting retailers. In addition, we also incorporate environmen-tal factors into the retailer’s decision.

2.3. Operations/demand related literature

Several papers utilize price dependent demand models to ana-lyze various stocking and pricing decisions for a duopoly wherethere are two substitute products in the marketplace. Singh andVives (1984) derive linear demand functions with substitutionfrom quadratic utility functions. Specifically, they characterizedemand for each product as (a) a decreasing function of the prod-uct’s own price and (b) an increasing function of the substituteproduct’s price. Lus and Muriel (2009) also consider two differentforms of price linear demand functions and conclude that this formof the function may lead to ‘‘unrealistically high prices and profitsas products become more substitutable.’’ Tsay and Agrawal (2000)utilize a price-quantity linear demand structure when developingoptimal wholesaler and retailer pricing policies for two competingretailers selling the same product. Under a different context, Chen,Vakharia, and Alptekinoglu (2008b) also use price-quantity lineardemand functions to analyze the situation under which a firmshould introduce a ‘‘fusion’’ product which combines products cur-rently selling in different markets into a single product.

Stochastic demand and pricing models typically utilize a news-vendor approach to determine optimal stocking policies. For acomplete review of these papers, see Qin, Wang, Vakharia, Chen,and Seref (2011). One such paper is particularly relevant to ourmodel. Petruzzi and Dada (1999) analyze pricing decisions for dif-ferent variations of the newsvendor model for a single product.One case that they consider utilizes a price linear additive functionof demand which is similar in nature to those shown in the deter-ministic demand literature. These authors derive mathematicalconditions under which an optimal solution for both price andquantity can be determined for the situation when there is demanduncertainty. Specifically, they show that when the probability dis-tribution function which characterizes demand uncertainty hascertain properties, then the optimal solution within a pre-specifiedrange is unique. We utilize several elements from this body ofoperations/demand related literature to motivate our choice forspecific functional forms in the model.

2.4. Contribution to the literature

While several authors have addressed the environmentalimpact of e-commerce via case-based and empirical methodolo-gies, we contribute to this literature by developing an analyticalmodel which offers managerial guidance concerning this impor-tant area of inquiry. Our model links the empirical literature onenvironmental issues in e-commerce with classic marketing andoperations models. Specifically, we formulate a dual channelmodel of a single retailer which has access to both online and tra-ditional market outlets to analyze the impact of environmental fac-tors on its demand. We also analyze optimal pricing and stockingdecisions for each channel incorporating price linear demand, cus-tomer preference for online shopping, and channel related costs.We develop analytic solutions for both deterministic and stochas-tic versions of the dual channel models, and utilize numericalexamples to illustrate the implications of industry specific factorson these decisions. The insights that we derive are particularlyrelevant for a single retail firm deciding whether or not to comple-ment its traditional sales with an online sales channel, in indus-tries, such as electronics, books and groceries.

3. Modeling framework

3.1. Preliminaries

In this section, we outline the key parameters and variables uti-lized in our model. A summary of the model notation is included inTable 1. Our stylized modeling scenario focuses on examining asingle retailer’s channel choice decision for a single product. Thethree choices for the retailer we investigate are to offer its productthrough: (a) the traditional retail (‘‘bricks and mortar’’) channel orRC indexed as j ¼ 1; or (b) the online channel or OC indexed asj ¼ 2; and (c) both the RC and OC or a DC (Dual Channel) andindexed as j ¼ 3. The RC represents the established configurationwhere the firm stocks its product and customers are required totravel to the location to purchase the product. These types ofstructures are well established in practice and the cost per unitto process a product through this channel is assumed to be c1.

An ‘‘online’’ channel (OC) could be introduced as a replacementfor the current channel or as an additional channel for serving themarket demand and in this setting the retailer incurs a per unit

Table 2Prices, quantities, and firm profits for each strategy.

Strategy Prices Quantity Profits

RC p�1 ¼a1þc1b1

2b1q�1 ¼

a1�c1b12 P�1 ¼

½a1�c1 b1 �24b1

OC p�2 ¼a2þðc1þeþbÞb2

2b2q�2 ¼

a2�ðc1þeþbÞb22 P�2 ¼

½a2�ðc1þeþbÞb2 �24b2

DC p�31 ¼b2ða1þc1 b1Þþsða2�sc1Þ

2ðb1b2�s2Þ q�31 ¼a1�c1b1þsðc1þeþbÞ

2P�3 ¼ x�1f½b2ða1 � c1b1Þ þ sða2 þ c1sÞ�ða1 � c1b1 þ sðc1 þ eþ bÞÞg

p�32 ¼b1ða2þb2ðc1þeþbÞÞþsða1�sðc1þeþbÞÞ

2ðb1 b2�s2Þ q�32 ¼a2�b2ðc1þeþbÞþsc1

2þx�1f½b1ða2 � b2ðc1 þ eþ bÞÞ þ sða1 þ sðc1 þ eþ bÞÞ�ða2 � b2ðc1 þ eþ bÞ þ sc1Þg

In this table, a1 ¼ ð1� kÞa; a2 ¼ ka; and x ¼ 4ðb1b2 � s2Þ.

1 In case of strategy DC, the profit function is strictly and jointly concave in thedecision variables provided b1 > s and b2 > s.


cost c2 for processing the product through this channel. In order toinvestigate the impact of environmental aspects, we assume thatthe cost differential between the RC and the OC is c2 � c1 ¼ eþ bwhere the parameter e represents the environmental cost/savingsof the OC as compared to the RC, and b represents cost differencesbetween channels due to other factors. We allow e to be eitherpositive or negative, and note that the differential in these costsis partially driven by environmental issues associated with channelcosts. To illustrate, e < 0 implies that the OC provides environmen-tal economies as compared to the RC while the reverse is truewhen e > 0. For example, when considering the OC for non-perish-able products (e.g., books), it is highly likely that there would be areduction of total inventories due to pooling effects. This would bereflected in environmental savings associated with using less papersince fewer books would need to be printed for the OC (i.e. e < 0).On the other hand, for perishable (or short shelf life) grocery items,an OC would require the use of delivery vehicles with freezers.Such vehicles may increase the ‘‘carbon footprint’’ associated withthe OC and hence, would result in a negative value of e.

On the demand side, we assume that for j ¼ 1;2, the marketdemand (xj) is linear in price (pj). We let a1 and a2 represent themaximum potential market for the RC and OC respectively. Simi-larly, bj represents the price elasticity of demand for channel jwhereby an increase by a dollar of the price in channel j will leadto a decrease of bj in the demand. For the case where the retailerhas the possibility of operating in both channels simultaneously,we also incorporate a symmetric cross-price based substitutioneffects parameter s. Consequently, if the price of the item sold inone channel increases by a unit, then some consumers may switchtheir channel choice. Specifically, the demand in the channel willincrease by an amount of s for a dollar increase in the price inthe alternate channel. This cross-price substitution effect alsocaptures the competitive intensity between the two channels forconsumer demand. Note that Tsay and Agrawal (2000) choose sim-ilar demand forms for a situation where two independent retailersare selling the same product procured from a single manufacturer.When analyzing the channel choice decision under demand uncer-tainty, we also use a random term �j for each channel’s demandfunction where �j is a continuous random variable with probabilitydensity function f ð�Þ and distribution function Fð�Þ defined in theinterval ½�dj; dj�.

We also define the following additional notation. Let qjðqUj Þ rep-

resent the quantity stocked by channel j under demand certainty(uncertainty) when the retailer chooses either single channel strat-egy RC (j ¼ 1) or OC (j ¼ 2); q3jðqU

3jÞ represent the quantity stockedby channel j (j ¼ 1;2) under demand certainty (uncertainty) whenhe retailer chooses the DC strategy and hence, offers the productthrough both channels simultaneously; pjðpU

j Þ represent the mar-ket price for channel j under demand certainty (uncertainty) whenthe retailer chooses either single channel strategy RC (j ¼ 1) or OC(j ¼ 2); p3jðpU

3jÞ represent the market price for channel j underdemand certainty (uncertainty) when the retailer chooses the DualChannel (SC) strategy; and PjðPU

j Þ represent the firm profits forchannel j under demand certainty (uncertainty) for j ¼ 1;2;3.

The primary focus of our analysis is on analyzing the channelselection decision for the retailer in the presence of the environ-mental related savings/costs on the supply side and consumerpreferences on the demand side. We start by focusing on the casewhere the firm demand is deterministic and follow this up withanalyzing the stochastic demand scenario.

3.2. Deterministic demand

Under this setting, the optimal stocking quantity for the retailerfor each channel setting is analogous to the market demand satis-fied. Hence, the demand functions for each strategy choice are:

� For channel strategy RC: q1ðp1Þ ¼ a1 � b1p1;� For channel strategy OC: q2ðp2Þ ¼ a2 � b2p2; and� For channel strategy DC: q31ðp31; p32Þ ¼ a1 � b1p31 þ sp32 and

q32ðp31; p32Þ ¼ a2 � b2p32 þ sp31.

Under each strategy choice, the retailer solves the followingprofit maximization problems:

� For strategy choice RC

Maximizep1P0P1 ¼ ½p1 � c1�q1ðp1Þ ð1Þ

� For strategy choice OC

Maximizep2P0P2 ¼ ½p2 � c1 � e� b�q2ðp2Þ ð2Þ

� For strategy choice DC

Maximizep31 ;p32P0P3 ¼ ½p31 � c1�q31ðp31;p32Þþ ½p32 � c1 � e� b�q32ðp31;p32Þ ð3Þ

For each setting, it is easy to show that the profit functions arestrictly concave in the decision variables.1 Based on this, theoptimal prices, quantities and firm profits under each strategy choiceare shown in Table 2 (with all proofs shown in Appendix A).

To further delineate the impact of demand on our optimalsolution, we utilize a change of variables. Specifically, we replacethe variables a1 and a2 which reflect the maximum market sizefor the RC and the OC with two alternate variables. We let a repre-sent the maximum total market size such that a ¼ a1 þ a2. We alsointegrate a propensity of customers for the OC by a parameterk ¼ a2

a which represents the proportion of the total number of cus-tomers who would prefer the online channel ð0 6 k 6 1Þ. For thevariable substitution, we let a2 ¼ ak represent the maximumdemand for channel OC and a1 ¼ að1� kÞ represent the maximumdemand for channel RC. Hence, a higher value of k is associatedwith a higher total potential market for the OC and vice versa.

In examining Table 2, it is quite obvious that the retailer’schoice of channel strategies is parameter dependent. However, as


stated in Theorem 1 below, these can be structurally characterizedbased on the k parameter. First, we define the following additionalnotation.

� for the lowest value breakpoint: k1 ¼ ðc1ðb2�sÞþðeþbÞb2Þa ;

� for the highest value breakpoint: k2 ¼ 1� ðc1ðb1�sÞ�sðeþbÞÞa ; and

� for the difference in the breakpoints: Dk ¼ 1�ðc1ðb1þb2�2sÞþðb2�sÞðeþbÞÞ

a .

Theorem 1. Assuming that all three strategies are feasible, theoptimal strategy choice for the retailer is as follows:

1. If 0 6 k < k1, the retailer should choose strategy RC (i.e., onlyoffer the product through the retail bricks and mortar channel);

2. If k1 6 k < k2, the retailer should choose strategy DC (i.e., offerthe product through dual channels); and

3. If k2 6 k 6 1, the retailer’s choice is the OC strategy (i.e., onlyoffer the product through the online channel).

Proof. See Appendix B.From Theorem 1, it is clear that k (which reflects the channel

choice propensity) is a key factors driving the retailer’s optimalchannel strategy choice. Recall that k can also be interpreted as aproxy for customer utility for goods sold through a particularchannel, and is influenced by factors such as convenience, distanceto the traditional store, the type of product (i.e. mainstream orniche), and customer service.

A second key result concerns the impact of the environmentalcosts/savings. As would be expected, as the value of the e increasesthe region of dominance of the RC strategy grows (i.e. k1 increases).Similarly, the region of dominance for the OC strategy shrinks (i.e.k2 increases), and the region of dominance for the differential forthe two channels shrinks (i.e. Dk decreases). In particular, if theunit cost for the traditional channel increases, or if the unit costfor the online channel decreases, then it’s less likely that thebricks-and-mortar channel strategy will be optimal. Suppose thecost of stocking online is lower due to risk pooling, then the retailershould use an online or dual channel strategy. To illustrate, con-sider online book stores such as Amazon which sell solely throughan online channel and reap the benefits of lower costs due toinventory centralization (see Matthews et al., 2001). In contrast,in the grocery industry, the environmental costs for the onlinechannel may come at a premium due to the investment in trucksrefrigerator capabilities.

It seems clear that market related parameters also help todetermine the firm’s optimal strategy. The impact of the cus-tomer’s price sensitivity on demand for the individual channels issignificant in driving a single channel strategy. When the priceelasticity of demand ðbiÞ for channel i decreases, then (1) a singlechannel solution for channel i is more likely to be optimal, (2)the optimal price decreases for the single channel, and (3) the opti-mal quantity increases for the single channel. Conversely, if there isan increase in the total market for the product as represented bythe variable (a) or if there is an increase in the demand substitutionparameter (s), then it’s more likely that a dual channel solution willbe optimal. Indeed, the grocery/retail firm Tesco has introduced anonline channel in addition to their traditional channel to reap thebenefits from this unique channel with their slogan ‘‘You shop.We drop’’ (Anonymous, 2006).

A comparison of optimal channel prices in the DC setting is alsoof interest. Given the optimal market prices shown in Table 2 forthe setting where the retailer operates both channels, we note thatthe optimal market prices between channels will not be equal pro-vided that:

a1w1 � a2w2 – ðbþ eÞ ð4Þ

where w1 ¼ b2�sb1b2�s2 and w2 ¼ b1�s

b1b2�s2. Note that the left hand side is the

difference between the ‘‘weighted’’ market sizes of the RC and OCchannels (which are an explicit function of the consumer propensityk) while the right hand side reflects the cost differential betweenchannels. The ‘‘weights’’ applied to the market sizes are determinedby the relative differential of channel demand elasticity parameters(i.e., b1; b2, and s). Based on this relationship, the following resultshold:

� The retail channel price will always be greater than the onlinechannel price (i.e., p�31 > p�32), if either: (a) k < w1

w1þw2and

bþ e 6 0 or (b) k P w1w1þw2

and a½w1 � kðw1 þw2Þ� > ðbþ eÞ hold;

� The retail channel price will always be lower than the onlinechannel price (i.e., p�31 < p�32), if k P w1

w1þw2and

a½w1 � kðw1 þw2Þ� < ðbþ eÞ.

This result essentially indicates that only under very restrictiveconditions will the online channel price be higher than that of theretail channel. This finding is in line with that of Brynjolfsson andSmith (2000) who find that online channel prices are significantlylower than that of the retail channel for books and CD’s. In thissetting, it is likely that the environmental savings result in lowercosts for the online channel as compared to the retail channeland this compensates for lower levels of consumer propensity forthe online channel. It is only when the consumer propensity forthe online channel is high and the cost differential between chan-nels is not significant, that the optimal price for the online channelis higher than that of the retail channel.

Note that the results shown here can also be generalized to amulti-product version of the deterministic model. To illustrate,consider the situation where the retail firm offers to each customera selection consisting of two independent product groups. Fromthe supply perspective, we allow each product group to have adistinct cost while from the demand perspective, we allow forproduct group specific aggregate demand functions (i.e., the totalmarket size, elasticity, and substitution effects are product groupspecific). The revised demand functions and associated retail firmprofit maximization problems for each strategy choice under themulti-product setting are shown in Appendix C. As can be seenfrom the equations, the profit functions for each strategy choicefor the firm are separable in the product groups being offered.Hence, the analytical results still hold for multiple product groupsunder certain conditions. We recognize that this generalizationdoes not take into account (a) finite capacity limitations or (b)demand dependence between the two product groups (i.e. substi-tutions or complementarities), and we view these as a possibledirection for future research.

3.3. Stochastic demand

Similar to the previous section on deterministic demand, we startthis section by characterizing the retailer’s optimal decision for asingle channel setting and follow with an analysis of the case wherethe retailer chooses to operate both channels simultaneously.

3.3.1. Single channel settingFor each single channel setting, the process of obtaining an

optimal solution to the retailer’s profit maximization problem issimilar. Thus, in this section, we present the general procedurewhich applies to each channel setting (recall that the index i ¼ 1is used for the ‘‘bricks and mortar’’ channel while the index i ¼ 2is for the online channel). Considering either channel individually,it is assumed that the market demand is characterized by the fol-lowing linear demand function:


xUi ¼ ai � bipU

i þ �i ð5Þ

where �i is a random variable with probability density function f ð�Þand distribution function Fð�Þ and defined in the interval ½�di; di�such that �di > �ai and li is the mean for �i. In this setting, weallow for the possibility that the retailer could have leftover inven-tory (if qU

i > xUi ) and we assume that this is sold at a markdown

price per unit h.2 Hence, the retailer makes the market pricing andstocking quantity decision using a newsvendor framework. Basedon this, to maximize expected end-of-season firm profits, the firmsolves the following problem:

Maximize E½PUi ðzi;pU

i Þ� ¼Z zi

�di

½pUi ðai � bipU

i þ �iÞ þ hðzi � �iÞ�f ð�iÞd�i

( )

þZ di

zi

½pUi ðai � bipU

i þ ziÞ�f ð�iÞd�i

( )

� ciðai � bipUi þ ziÞ ¼ ðpU

i � ciÞðai � bipUi Þ

� ðci � hÞzi � ðpUi � hÞ

Z di

zi

ð�i � ziÞf ð�iÞd�i � li

" #ð6Þ

where zi ¼ qUi � ai � bipU

i (similar transformations were proposedby Ernst (1970) and Thowson (1975)). The first-order conditionsfor this problem are:

@E½PUi ðzi;pU

i Þ�@zi

¼ �ci þ hþ ðpUi � hÞ½1� FðziÞ� ð7Þ

@E½PUi ðzi;pU

i Þ�@pU

i

¼ 2biai þ bici

2bi� pU

i

� ��Z di

zi

ð�i � ziÞf ð�iÞd�i þ li ð8Þ

and the second-order conditions are:

@2E½PUi ðzi; pU

i Þ�@z2

i

¼ �ðpUi � hÞf ðziÞ ð9Þ

@2E½PUi ðzi; pU

i Þ�@pU

i2 ¼ �2bi ð10Þ

@2E½PUi ðzi; pU

i Þ�@zi@pU

i

¼ 1� FðziÞ ð11Þ

For strict concavity of Eq. (6) to hold, it is necessary to assume

that jH2ij ¼ 2biðpiS � hÞf ðziÞ � ½1� FðziÞ�2 > 0. Other technical con-ditions for the uniqueness of the solution to the problem statedin Eq. (6) have been specified by Petruzzi and Dada (1999). Regard-less of whether either of these conditions are met, it is relativelystraight forward to note that for a given zi, Eq. (10) indicates thatEq. (6) is strictly concave in piS. Hence, for a given value of zi, theoptimal p�iS obtained from the first order condition in Eq. (8) is:

pU�i ðziÞ ¼

ai þ bici �R di

zið�i � ziÞf ð�iÞd�i þ li

2bið12Þ

Based on this, the following search algorithm can be used toidentify the optimal market price, the optimal stocking quantity,and the corresponding optimal profit for the retailer.

1. Set zi ¼ �di � 0:01; Profit ¼ 0; v ¼ 0; ptemp ¼ pU�i ¼ 0; and ztemp ¼ 0.

2. zi ¼ zi þ 0:01. If zi > di, goto 5.

3. Compute pU�i ðziÞ using Eq. (12). Set ptemp ¼ pU�

i ðziÞ.4. Compute E½PU

i ðzi; ptempÞ� using Eq. (6). If Profit > E½PUi ðzi; ptempÞ�,

goto 2, else set Profit ¼ E½PUi ðzi; ptempÞ�; ztemp ¼ zi; v ¼ ptemp and

goto 2.5. The optimal market price is v, the optimal stocking quantity is

qU�i ¼ ai � biv þ ztemp, and associated optimal profit is Profit.

2 Similar to Petruzzi and Dada, 1999, we do not consider a ‘‘lost-sales’’ cost in ouranalysis and also assume that the markdown price is not channel specific.

We now turn our attention to determining the optimal solutionto the retailer’s profit maximization problem in a multiple channelsetting.

3.3.2. Both channelsIn this setting, the market demand functions for each channel

are assumed to be characterized by the following linear demandfunctions:

xU31 ¼ a1 � b1pU

31 þ spU32 þ �1 ð13Þ

xU32 ¼ a2 � b2pU

32 þ spU31 þ �2 ð14Þ

where as defined earlier �1 and �2 are random variables defined inthe interval ½�d1;d1� and ½�d2;d2� with means l1 and l2 respec-tively. In order to maximize end-of-season profits, the retailersolves the following problem:

Maximize

E½PSBðz1 ;z2 ;pU31 ;p

U32Þ� ¼

Z z1

�d1

½pU31ða1�b1pU

31þ spU32þ�1Þþhðz1��1Þ�f ð�1Þd�1

� �

þZ d1

z1

½pU31ða1�b1pU

31þ spU32þ z1Þ�f ð�1Þd�1

( )

�c1ða1�b1pU31þ spU

32þz1Þ

þZ z2

�d2

½pU32ða2�b2pU

32þ spU31þ�2Þþhðz2��2Þ�f ð�2Þd�2

� �

þZ d2

z2

½pU32ða2�b2pU

32þ spU31þ z2Þ�f ð�2Þd�2

( )� c2ða2�b2pU

32þ spU31þz2Þ

¼X2

i¼1

ðpU3i�ciÞðai�bipU

3iÞ�ðci�hÞzi�ðpU3i�hÞ

Z di

zi

ð�i� ziÞf ð�iÞd�i�li

" #( )

þ spU31ðpU

32�c2Þþ spU32ðpU

31�c1Þ ð15Þ

where z1 ¼ qU31 � a1 þ b1pU

31 � spU32 and z2 ¼ qU

32 � a2 þ b2pU32 � spU

31.The first-order conditions for this problem are:

@E½PU3 �

@z1¼�c1þhþðpU

31�hÞ½1�Fðz1Þ� ð16Þ

@E½PU3 �

@z2¼�c2þhþðpU

32�hÞ½1�Fðz2Þ� ð17Þ

@E½PU3 �

@pU31

¼2b1a1þb1c1

2b1�pU

31

� ��Z d1

z1

ð�1� z1Þf ð�1Þd�1þ2spU32� sc2þl1 ð18Þ

@E½PU3 �

@pU32

¼2b2a2þb2c2

2b2�pU

32

� ��Z d2

z2

ð�2� z2Þf ð�1Þd�2þ2spU31� sc1þl2 ð19Þ


@2E½PU3 �

@z2i

¼ �ðpU3i � hÞf ðziÞ for i ¼ 1;2 ð20Þ

@2E½PU3 �

@pU3i

2 ¼ �2bi for i ¼ 1;2 ð21Þ

@2E½PU3 �

@z1@pU31

¼ 1� Fðz1Þ ð22Þ

@2E½PU3 �

@z1@pU32

¼ 0 ð23Þ

@2E½PU3 �

@z2@pU32

¼ 1� Fðz2Þ ð24Þ

@2E½PU3 �

@z2@pU31

¼ 0 ð25Þ

@2E½PU3 �

@pU31@pU

32

¼ 2s ð26Þ

As in the single channel setting, we can see that for specific val-ues of z1 and z2, Eq. (19) is strictly and jointly concave in pU

31 andpU

32.3 Thus, for given values of z1 and z2, the optimal prices can be

3 This is a result of the fact that Eqs. (21) and (26) indicate that jH1j < 0 andjH2j ¼ 4b1b2 � s2 > 0 since it was assumed that bi > s for i ¼ 1;2.


determined by solving the following simultaneous equations(obtained by setting the first order conditions in Eqs. (18) and (19)equal to 0):

2b1pU31 � 2spU

32 ¼Z d1

z1

ð�1 � z1Þf ð�1Þd�1 þ sc2 � ða1 þ b1c1Þ ð27Þ

� 2spU31 þ 2b2pU

32 ¼Z d2

z2

ð�2 � z2Þf ð�2Þd�2 þ sc1 � ða2 þ b2c2Þ ð28Þ

The solution to this set of equations is:

pU�31ðz1; z2Þ ¼

b2u1 þ su2

2ðb1b2 � s2Þ ð29Þ


b1u2 þ su1


where u1 ¼ �ða1 þ b1c1Þ þR d1

z1ð�1 � z1Þf ð�1Þd�1 þ sc2 þ l1 and

u2 ¼ �ða2 þ b2c2Þ þR d2

z2ð�2 � z2Þf ð�2Þd�2 �þsc1 þ l2. Based on this,

the following search algorithm can be used to identify the optimalmarket prices, the optimal stocking quantities, and the correspond-ing optimal profit for the retailer.

1. Set z1 ¼ �d1 � 0:01; z2 ¼ �d2 � 0:01; Profit ¼ 0; v1 ¼ v2 ¼ 0;p1t ¼ pU�

31 ¼ 0; p2t ¼ pU�32 ¼ 0 and z1t ¼ z2t ¼ 0.

2. z1 ¼ z1 þ 0:01. If z1 > d1, goto 6.3. z2 ¼ z2 þ 0:01. If z2 > d2 goto 2.4. Compute pU�

31ðz1; z2Þ using Eq. (29) and pU�32ðz1; z2Þ using Eq. (30).

Set p1t ¼ pU�31ðz1; z2Þ and p2t ¼ pU�

32ðz1; z2Þ.5. Compute E½PU

3 ðz1; z2; p1t ; p2t � using Eq. (15). IfProfit > E½PU

3 ðz1; z2; p1t ; p2tÞ�, goto 3, else setProfit ¼ E½PU

3 ðz1; z2; p1t ; p2tÞ�; z1t ¼ z1; z2t ¼ z2; v1 ¼ p1t; v2 ¼ p2t and goto 3.

6. The optimal market prices are: v1 and v2; the optimalstocking quantities are: qU�

31 ¼ a1 � b1v1 þ sv2 þ z1t , andqU�

32 ¼ a2 � b2v2 þ sv1 þ z2t and associated optimal profit isProfit.

3.3.3. Sensitivity analysis for the stochastic modelWhile we do not have explicit expressions for the optimal val-

ues for the stochastic models, the separable nature of the pricefunctions as shown Eqs. (29) and (30) facilitates sensitivity analysison key parameters.

Corollary 1. Assuming that a dual channel (DC) strategy is optimal,then the optimal price for RC (pU�

31) will increase in response to thefollowing:

1. An increase in the maximum market size a.2. A decrease in the propensity of customers for the OC channel k.3. A decrease in the price sensitivity to demand for the RC channel b1.4. A decrease in the price sensitivity to demand for the OC channel b2.5. An increase in the symmetric price based substitution effects

parameter s.6. An increase in the unit cost for the RC channel c1.

Proof. See Appendix C. h

Corollary 2. Assuming that a dual channel (DC) strategy is optimal,then the optimal price for OC (pU�


1. An increase in the maximum market size a.2. An increase in the propensity of customers for the OC channel k.3. A decrease in the price sensitivity to demand for the RC channel b1.

4. A decrease in the price sensitivity to demand for the OC channel b2.5. An increase in the symmetric price based substitution effects

parameter s.6. An increase in the environmental cost premium for the OC channel

e.7. An increase in the unit cost premium for the OC channel b.

Proof. See Appendix D.Results from Corollaries 1 and 2 show that the optimal prices

for the dual channel in the stochastic environment behave simi-larly to those derived for the deterministic environment withregards to changes in demand related parameters. One key resulthere is that when a dual strategy is optimal (DC), the cost premiumfor the online channel (e) does not influence the price for the tra-ditional channel and visa versa. Although, the cost differentialsare likely to impact the region of dual channel optimality for whichthese prices are valid, as shown in Theorem 1.

4. Numerical analysis

In this section, we outline the results of numerical examplesintended to complement the analysis for the stochastic demandcase shown in the previous section. Because we cannot deriveexplicit solutions for the optimal values of the quantity and pricevariables for the stochastic dual channel model, we turn tonumerical examples to illustrate the impact of key factors on thesevariables and the overall firm profit. The numerical examples werewritten in the JAVA programming language, and utilize the searchalgorithms outlined in the previous section.

The specific parameter values used in the numerical base caseexample are as follows: (a) the unit cost for the RC (c1) is set to$20. In order to focus on the impact of environmental costs/savingsfor the OC, we set the value of b ¼ 0. Hence, the unit cost for theonline channel is c2 ¼ 10þ e; and (b) the maximum market size(a) is set equal to 2500. Both channels are assumed to have anequal price elasticity (i.e., b1 ¼ b2) and this value is set equal to30. The symmetric price substitution parameter (s) which appliesonly to channel structure DC is set at 10. The minimum and max-imum values of �i are equal across both channel structures and �i isassumed to be uniformly distributed. Finally, we vary the value of kbetween [0,1] by increments of .01 and calculate the optimalprices, quantities and profits for both single channel and the dualchannel solutions and this is used to identify the range of valuesover which single and/or dual channel solutions are optimal.

Consider a base case example where h ¼ $10; di ¼ 10, and e ¼ 0.For values of k 6 :23, the retailer optimally sells only via the tradi-tional channel and makes a fairly low profit. For values of kbetween .24 and .75, the retailer optimally sells via both channelsand reaps the benefits of higher profit. For values of k P :76, theretailer optimally sells via the online channel only and earns afairly low profit. A graph of the profit for this case as a functionof k is shown in Fig. 1 – Panel A. Note that the profit values aresymmetric around the value k ¼ :5, because the base case demandand cost parameters are similar for both channels. When k is extre-mely high or low and a single channel solution is optimal, then thedual channel solution is infeasible and the total profit in these tailsis fairly low. When a dual channel solution is feasible and optimal(i.e. in the center of the graph), the profit is much higher due to thesynergy between the two channels in terms of the demand substi-tution parameter. Therefore, the retailer should plan for singlechannel distribution if environmental and/or consumer related fac-tors drive the demand to be extremely high for one of the singlechannels.

Table 3Numerical results for sensitivity to salvage value and demand uncertainty.

d ¼ 10 d ¼ 375 d ¼ 675 d ¼ 1250 Strategy

h = 10 0 6 k 6 :24 0 6 k 6 :31 0 6 k 6 :41 0 6 k 6 :18 RC:25 6 k 6 :75 :32 6 k 6 :68 :42 6 k 6 :58 None DC:76 6 k 6 1 :69 6 k 6 1 :59 6 k 6 1 :82 6 k 6 1 OC

h = 20 0 6 k 6 :23 0 6 k 6 :26 0 6 k 6 :33 0 6 k 6 :24 RC:24 6 k 6 :76 :27 6 k 6 :73 :34 6 k 6 :66 None DC:77 6 k 6 1 :74 6 k 6 1 :67 6 k 6 1 :76 6 k 6 1 OC


In addition to the base case scenario, we also investigated theimpact of the salvage value (h) and demand variability ðd1; d2Þ onthe optimal channel choice. Table 3 summarizes the results ofthese examples for salvage values (h) of 10 and 20, and also fordemand variability (i.e. d1 and d2) values of 10, 375, 675 and1250. These levels of demand variability correspond to .4%, 15%,25% and 50% of the total demand (a = 2500) for the product amongboth channels. We also set the demand variability for both chan-nels to be equivalent for each example (i.e. d ¼ d1 ¼ d2). Finally,note that the previously discussed base case scenario is shown inthe upper left hand corner of Table 3 with values of h ¼ 10 andd ¼ 10.

The results shown in Table 3 illustrate that increasing levels ofdemand uncertainty for both channels decreases the range underwhich a dual channel solution is optimal. For example, focusingon the top row of the results where h ¼ 10 and comparing the val-ues where d ¼ 10 and d ¼ 375, we see that the range of customerpreference (k) where the dual channel strategy is optimal shrinksfrom between [.24, .75] to between [.32, .68]. For these situations,increasing demand uncertainty increases the risk of stocking bothchannels.

Fig. 1. Comparison of firm profits as a function of consumer propensity for variousvalues of environmental costs.

However, when the demand uncertainty is extremely high, adual channel solution is no longer optimal. Focusing on the rightmost column of Table 3, we find that for values of d ¼ 1250, theregion where a dual channel solution is optimal (and feasible)disappears. Instead, it is optimal for the retailer to operate with asingle channel only if demand for that channel is extremely high.When the customer preference is somewhat indifferent betweenthe two channels (i.e. k is between .19 and .81), then it is actuallyoptimal for the retailer to stay out of the market in this situation.We denote this situation as ‘‘No Channel’’ or NC. Apparently, thedemand uncertainty is too high such that stocking for these inter-mediate scenarios is excessively costly. Additional numericalexperiments show that when d is greater than approximately685, then the dual channel optimal solution disappears.

Next, we focus on the impact of the salvage value h on the opti-mal channel strategy. When a dual channel strategy is optimal,increasing the salvage value also increases the range of optimalityfor a dual channel strategy. To illustrate, focusing on the left mostcolumn of Table 3, we see that the range of customer preference ðkÞwhere the dual channel strategy is optimal grows from between[.24, .75] for a salvage value of h ¼ 10 to [.23, .77] for a salvagevalue of h ¼ 20. Recall that a higher salvage value corresponds toan increased value for the leftover inventory. Therefore, the retailercan absorb more risk in stocking two individual channels when thesalvage value is higher. To illustrate, consider the book industry.While stocking is risky at the traditional retailer, the salvage valuefor books is relatively high due to well developed secondarywholesale markets for remainder books. In contrast, in the groceryindustry, salvage values are very low due to the perishability of thefresh products. Consequently, the range for which a dual channelsolution exists may be smaller.

However, when the dual channel strategy is not optimal, anincrease in the salvage value increases the range for which thesingle channel strategy is optimal. This result concurs with thosetypically reported for a traditional single channel newsvendorproblem, where the quantity stocked increases in response to anincreased salvage value.

We also investigate the impact of the environmental costdifferential effects on the optimal strategy for the retailer. For theseexamples, we set the salvage value h ¼ 10 and the demanduncertainty d ¼ 375. The results for these examples (summarizedin Table 4) show that when the online channel is less costly and/or the environmental impact is lower, then the optimal range forthe dual channel strategy (DC) and the online channel strategy(OC) are more viable. Similarly, Panels B and C in Fig. 1 alsoillustrate the impact of environmental costs/savings on channelchoice. For example, in Panel B of Fig. 1, we see that whene ¼ �10 (i.e, the OC provides environmental savings as comparedto the RC), the break point k1 decreases and the difference Dkincreases. In Panel C of Fig. 1, we see that when e ¼ 10 (i.e., theOC is more costly than the RC due to environmental effects), thebreak point k2 increases and the difference Dk decreases. To sum-marize, if one channel has higher costs, then the optimal rangefor that channel shrinks.

Table 4Numerical results for sensitivity to environmental cost differential effects.

e ¼ �10 e ¼ 0 e ¼ 10 Strategy

0 6 k 6 :12 0 6 k 6 :31 0 6 k 6 :47 RC:13 6 k 6 :66 :32 6 k 6 :68 :48 6 k 6 :70 DC:67 6 k 6 1 :69 6 k 6 1 :71 6 k 6 1 OC


5. Policy issues

In the previous sections, we have investigated a retailer’schannel strategy decision as driven by factors including customerpreferences, demand uncertainty, and cost differentials. In this sec-tion, we investigate the impact of several policy issues on thisimportant decision. First, firms should consider the rising costsassociated with carbon emissions in the delivery of their goods.To illustrate, many countries have levied energy related taxesbased on the carbon content of the goods. In July 2011, Australiaimplemented a carbon tax whereby firms are charged 23 Austra-lian dollars per ton, and this tax will eventually be replaced witha carbon trading scheme (Curran (2011)). While many countriescurrently have not undertaken such taxation measures, many com-panies are voluntarily purchasing carbon credits to justify theemissions of carbon dioxide in their company. One such companyis Dell, who purchases renewable energy certificates which reflectinvestments in wind power energy projects to offset the carbonemissions from its facilities (Ball, 2008).

In terms of our model, the net effect of these schemes is toamplify the cost differential associated with environmental factorsas captured in the variable e. Recent studies have shown that thetotal energy usage for a traditional retailer is higher than thattypically associated with e-commerce delivery in the delivery ofcertain electronic goods (Weber et al., 2008). For such industries,e < 0 and the impact of a carbon tax or voluntary carbon creditprogram is to amplify the magnitude of the value of e, such thatthe differential between the costs for the two channel choices iseven greater. From Table 2, a retailer using an OC only strategyshould price the goods lower and to increase the total quantity soldvia the more environmentally efficient online sales channel. For aDC company in an industry where e < 0, the retailer should lowerthe price for the online channel, raise the quantity of goods sold viathe online channel, and lower the quantity of goods sold via thetraditional channel. Note also that the region of optimality forthe DC and OC grow, whereas the region of optimality for the RCshrinks in this situation. Conversely, for an industry where e > 0(such as groceries), the following occurs when the environmentaldifferential increases: (1) the RC and DC regions grow, (2) the OCregion shrinks, (3) the price of the online channel for a DCincreases, (4) the quantity of goods sold via the online channelfor a DC decreases, and (5) the quantity of goods sold via thetraditional channel for a DC increases. A key issue associated withcarbon tax schemes is how to apply it to different industry sectors.From our analysis, the outcome of such a tax can yield quite differ-ent results depending on the industry under consideration.

With regards to the carbon tax, another complicating factor con-cerns the logistics/delivery arrangements for the retailer. Consideragain the book industry where e < 0 and customers typically payan additional charge for the delivery of their goods. Suppose theretailer is currently utilizing a dual strategy arrangement. Thenthe retailer will pay proportionately more for the traditional retailcenter where more carbon taxes are incurred for delivering thegoods to the store. Consequently, the prices will increase for thebook via the traditional channel. Suppose also that the delivery ofthe goods for the retailer’s online sales channel is outsourced to athird party logistics provider, and that the customer pays anadditional charge for the delivery. In this scenario, the third party

logistics provider will incur a large portion of the carbon tax, pre-sumably which will be passed on to the customer. The retailer willlikely favor the internet channel in this situation, as it is penalizedproportionately more for its traditional channel. Consider also thecompany Amazon, which is an OC retailer that sales books via anonline channel only. Amazon has invested heavily in logistics assetssuch as warehouses and utilizes a practice of postal injection todeliver products to the mail carrier associated with thecustomer’s city of origin (Hammond, 2005). Amazon charges thecustomer an additional fee for the transportation portion ofthe item. Presumably, these fees will increase if a carbon tax isimplemented. As previously mentioned, Amazon has recentlyreceived a patent on ‘‘environmentally conscious electronic trans-actions’’, which will allow them to distinguish different deliveryoptions based on the carbon usage. If such a carbon tax occurs, thencustomers will be able to choose whether they want a high carbondelivery option with additional taxes (such as air delivery) or a lowcarbon option without additional taxes. However, further researchis necessary to verify the specific impact of the carbon tax on thedifferent parties (i.e. retailer, 3PL, and consumer) in this situation.

6. Conclusions

In this paper, we analyze a dual channel model for a retailerwho has access to both online and traditional market outlets toanswer several key research questions regarding the environmen-tal impact of the dual channel strategy for retail. The first questionwe address is, ‘‘If a retailer has both traditional and online saleschannels, how should he/she manage the split between these?’’In particular, we analyze three potential strategies for the retailer:the traditional retail channel only (RC), the online channel only(OC), and the dual channel which combines both (DC). Utilizingthe results from Theorem 1 concerning the optimal channel choicefor the case with deterministic demand, we find that all three ofthese strategies can be optimal depending on the customer’spropensity (k) to buy from the online channel. This propensity isdriven partially by customer awareness concerning the environ-mental impact of their product choice. When the customer’s pro-pensity is extremely low, then the retailer should focus on theirtraditional retail channel (RC). When the customer’s propensity isextremely high, then the retailer should focus on their online retailchannel (OC). When the customer’s propensity is of mediumstrength, then the retailer should focus on the dual channel strat-egy (DC) and can reap the benefits of higher profits due to synergybetween the two channels. Furthermore, the break points whichdetermine the optimal strategy choice are driven by the followingfactors: the unit costs for each channel, the environmental costsavings/premium for the online channel, the price elasticity ofdemand for each channel, the maximum market size, and the pricesubstitution effects.

The second question we address is, ‘‘Are there circumstancesunder which a retailer should focus only on online and/or tradi-tional channels?’’ As mentioned in the previous paragraph, analysisin Theorem 1 from the deterministic model shows that the cus-tomer’s propensity to buy from the online channel (k) is a crucialfactor in this decision. In particular, if this parameter is extremelyhigh or extremely low, then a single channel strategy is optimal.The numerical examples shown in Section 4 also highlight theimpact of stochastic elements on this important decision. In partic-ular, we find that a single channel strategy is more likely to be opti-mal when the salvage value (h) of the item sold is relatively low. Inthis situation, there is an increased risk associated with leftoveritems and consequently the region of optimality associated withthe single channel strategy is slightly greater. Interestingly, we alsoshow via the numerical results that when demand uncertainty isextremely high, then the region where a dual channel solution is

4 This is based on observing that jH1j < 0 and jH2j ¼ 4ðb1b2 � s2Þ > 0 since it isassumed that b1 > s and b2 > s.


optimal actually disappears. Under extreme demand uncertainty,the retailer should focus on a single channel strategy or stay outof the market altogether.

The third question we address is, ‘‘How will consumer behaviorevolve in response to these environmental channel concerns?’’ Inour model, we capture consumer behavior chiefly through the var-iable k, which represents the customer’s propensity to buy fromthe online channel. As listed in Sections 1 and 2 of our paper, evi-dence exists which links the consumer’s channel choice with envi-ronmental concerns. As firms start to promote the environmentalimpact of this alternative and as consumers become increasinglyaware of the implications of this choice, then it’s likely that theconsumer propensity will increase over time. Consequently, someretailers which had previously focused only on a traditional retailoutlet (RC) will need to plan for a dual channel (DC) strategy. Thereare some notable exceptions, however, based on factors such as thepopulation of the particular region where the traditional retailer islocated and also the service levels associated with the potentialonline retailer (OC) channel. For example, Matthews, Williams,Tagami, and Hendrickson (2002) show that in Japan, a traditionalbook retailer can be more energy efficient due to the highly con-centrated population.

The next question posed earlier was, ‘‘Which factors associatedwith e-commerce have the most significant impact on the environ-ment?’’ From the deterministic analysis, two main factors relevantto our model influence the environmental impact of e-commerce,including the customer propensity to buy online (k) and the costdifferential associated with each channel (e). From the numericalsection, the analysis of the cost differential (e) shows that environ-mental cost differences can significantly shift the ranges of opti-mality such that the dual channel (DC) option is more prevalent.In addition, if the online channel has a smaller environmentalimpact such that (e < 0), then the retailer should prepare for a dualchannel (DC) or strictly online sales (OC) in the future. From theNumerical analysis in Section 4, we also show that the salvagevalue and demand uncertainty are significant determinants ofthe firm’s strategy.

Industry specific characteristics are also important whenanswering the question concerning which factors have the mostsignificant impact on the environment. Three e-commerce indus-tries which have been studied in the past include groceries, elec-tronics, and books. For the grocery industry, the environmentalcost differential between the two channels could actually be posi-tive (e > 0) due to the refrigeration capabilities necessary for deliv-ery. Also, the high perishability of these items is such that thesalvage value (h) is fairly low. For the electronics industry, considerthe study by Weber et al. (2008) which shows that the environ-mental impact of e-commerce is lower such that e < 0. Obsoles-cence rates are also high in this industry due to the decrease inthe price of these items and the shorter product life cycles (i.e.low h). For the book industry, the existence of secondary marketsis such that the salvage value is fairly high (h). In addition, the costsof dealing with returns or remainders may actually drive the envi-ronmental differential costs (e) to favor the online channel. How-ever, further empirical analysis is needed in each of theseindustries to verify the relative magnitude of these environmentalfactors on the channel choice.

The last question posed in the introduction is, ‘‘How will policyissues such as a carbon tax impact on the retailer’s decision?’’ Fromthe previous section, carbon taxes and voluntary carbon creditschemes will have the effect of amplifying the environmental dif-ferences between the two different retail channels. The industryspecific characteristic relevant in this context is the environmentalcost differential. as reflected via the variable e. Therefore, policymakers need consider the disparate impact on different industriesfor carbon tax schemes.

Future topics of inquiry on e-commerce and the associatedenvironmental impact are numerous. Our model focuses on a spe-cific firm level decision, in particular trading off the environmentalimpact of online vs. traditional retail sales. While the focus of thismodel is on single firm decision making, there is an opportunity toconsider social policy issues in the future. For example, a holisticobjective which incorporates both consumer utility and firm profitcould yield insights concerning the implications of these firm deci-sions on broader societal goals. To illustrate, both Fichter (2002)and Sui and Rejeski (2002) discuss the possibility that sales viathe internet may lead to excessive consumer consumption, therebynegating some of the environmental improvements offered by thischannel. Second, the model here takes into account customers whowill potentially buy a single product either via a specific retailer’straditional channel or that same retailer’s online channel. Whileour results still hold when the customer is buying multiple prod-ucts from distinct groups, it would be interesting to analyze theimpact of a budget constraint or product complimentarities on thisdecision. Also, the topic of showrooming has the potential to showadditional synergies between the two channels. Finally, a modelwhich explicitly addresses the impact of competition on this deci-sion also has the potential to make an important contribution tothis field. For example, how does the relative size and bargainingpower of the competitive retailers influence channel distributiondecisions?

Appendix A. Optimal pricing for the dual channel (DC) strategy

Claim 1. For the following profit maximization problem:

Maximizep31 ; p32P0P3 ¼ ðp31 � c1Þq31 þ ðp32 � c2Þq32 ð31Þ

where q31 ¼ ð1� kÞa� b1p31 þ sp32 and q32 ¼ ka� b2p32 þ sp31. theoptimal prices are:

p�31 ¼b2ða1 þ c1b1Þ þ sða2 � sc1Þ




where a1 ¼ ð1� kÞa; a2 ¼ ka; and c2 ¼ c1 þ eþ b.

Proof. The first-order conditions (FOCs) for the problem stated inEq. (31) are:

@P3

@p31¼ a1 � b1p31 þ sp32 � b1ðp31 � c1Þ þ sðp32 � c2Þ ð34Þ

@P3

@p32¼ a2 � b2p32 þ sp31 � b1ðp32 � c2Þ þ sðp31 � c1Þ ð35Þ


@P23

@2p31

¼ �2b1 ð36Þ

@P23

@2p32

¼ �2b2 ð37Þ

@P23

@p31@p32¼ 2s ð38Þ

These second-order conditions indicate that P3 is strictly andjointly concave in p31 and p32

4. Hence, we can set the FOC’s inEqs. (34) and (35) equal to 0 and determine the optimal prices bysolving the following two simultaneous equations:


ð2b1Þp31 þ ð�2sÞp32 ¼ a1 þ b1c1 � sc2 ð39Þð�2sÞp31 þ ð2b2Þp32 ¼ a2 þ b2c2 � sc1 ð40Þ

and the result is:


2ðb1b2 � s2Þ


2ðb1b2 � s2Þ

This proves our claim. h

Appendix B. Proof of Theorem 1

Theorem 1. Assuming that all three strategies are feasible, theoptimal strategy choice for the firm is as follows:

1. If 0 6 k < ðc1ðb2�sÞþðeþbÞb2Þa , the firm should choose Strategy RC (i.e.,

only offer the product through the retail bricks and mortarchannel);

2. If ðc1ðb2�sÞþðeþbÞb2Þa 6 k < 1� ðc1ðb1�sÞ�sðeþbÞÞ

a , the firm should choosestrategy DC (i.e., offer the product through dual channels); and

3. If 1� ðc1ðb1�sÞ�sðeþbÞÞa 6 k 6 1, the firm’s choice is the OC strategy

(i.e., only offer the product through the online channel).

Proof. Our proof is based on the assumption that the firm willalways choose to adopt at least one of the three strategies: RC,DC, or OC. To start with, we make the following observations:

� Observation 1: If both p�31 and p�1 as defined in Table 2 are

positive then p�31 � p�1 ¼a1s2þb1sa2

2b1ðb1b2�s2Þ > 0.

� Observation 2: If both p�32 and p�2 as defined in Table 2 are

positive then p�32 � p�2 ¼a2s1þb2sa1

2b2ðb1b2�s2Þ > 0.

� Observation 3: If both q�31 and q�1 as defined in Table 2 arepositive then q�31 � q�1 ¼

sðc1þeþbÞ2 > 0.

� Observation 4: If both q�32 and q�2 as defined in Table 2 arepositive then q�32 � q�2 ¼

sc12 > 0.

� Observation 5: Strategy RC is feasible if 0 6 k 6 1� c1b1a since

this implies that q�1 is non-negative.� Observation 6: Strategy DC is feasible if ðc1ðb2�sÞþðeþbÞb2

a

6 k 6 1� c1ðb1�sÞ�ðeþbÞsa since this implies that both q�31 and q�32

are non-negative.� Observation 7: Strategy OC is feasible if ðc1þeþbÞb2

a 6 k 6 1 sincethis implies that q�2 is non-negative.

Case 1: 0 6 k < ðc1ðb2�sÞþðeþbÞb2Þa .

We start by assuming that this is a feasible range (i.e.,c1ðb2�sÞþðeþbÞb2

a P 0). Then, we observe that in this range: (a) strategyDC is infeasible (Observation 6) and (b) strategy OC is infeasible(Observation 7). For the RC strategy to be feasible in this range, we

need to show that ðc1ðb2�sÞþb2ðeþbÞÞa 6 1� c1b1

a . This is true provideda P ðb1 þ b2 � sÞc1 þ b2ðeþ bÞ which obviously holds sincea P ðb1 þ b2Þc1 þ b2ðeþ bÞ. Hence, in this range the RC is theoptimal strategy.Case 2: ðc1ðb2�sÞþðeþbÞb2Þ

a 6 k 6 1� ðc1ðb1�sÞ�sðeþbÞÞa .

In the range, we consider three sub-cases:

� ðc1ðb2�sÞþb2ðeþbÞÞa 6 k 6 1� c1b1

a . In this range, strategies DC and RCare both feasible (strategy OC is infeasible). However, basedon Observations 1 and 3, it is obvious that P�3 P P�1 and hence,DC is the optimal strategy.� 1� c1b1

a 6 k < ðc1þeþbÞb2a . In this range, both strategies RC and OC

are infeasible and the only feasible strategy is DC (Observation5). Hence, DC is the optimal strategy in this range.

� ðc1þeþbÞb2a 6 k 6 1� c1ðb1�sÞ�sðeþbÞ

a . In this range, strategies DC andOC are both feasible (strategy RC is infeasible). However, basedon Observations 2 and 4, it is obvious that P�3 P P�2 and hence,DC is the optimal strategy.

Case 3: 1� ðc1ðb1�sÞ�sðeþbÞÞa < k 6 1.

We start by assuming that this is a feasible range (i.e.,1� c1ðb1�sÞ�sðeþbÞ

a 6 1). Then, we observe that in this range: (a)strategy DC is infeasible (Observation 6); and (b) strategy RC isinfeasible (Observation 5). For the OC strategy to be feasible in thisrange, we need to show that ððc1þeþbÞb2Þ

a 6 1� c1ðb1�sÞ�sðeþbÞa . This is

true provided a P ðb1 þ b2 � sÞc1 þ ðb2 � sÞðeþ bÞ which obviouslyholds since a P ðb1 þ b2Þc1 þ b2ðeþ bÞ. Hence, in this range the OCis the optimal strategy.

This concludes our proof of Theorem 1. h

Appendix C. Multi-product group model

Under this setting, the optimal stocking quantity for the firm foreach channel setting is analogous to the market demand satisfied.Hence, the demand functions for each strategy choice (where thesubscript k is product group specific) are:

� For channel strategy RC: qk1ðpk

1Þ ¼ ak1 � bk

1pk1;

� For channel strategy OC: qk2ðpk

2Þ ¼ ak2 � bk

2pk2; and

� For channel strategy DC: qk31ðpk

31; pk32Þ ¼ ak

1 � bk1pk

31 þ skpk32 and

qk32ðpk

31; pk32Þ ¼ ak

2 � bk2pk

32 þ skpk31.

Under each strategy choice, the firm solves the following profitmaximization problems:

� For strategy choice RC

Maximizepk1P0P1 ¼

X2

k¼1

½pk1 � ck

1�qk1ðpk

1Þ ð41Þ

� For strategy choice OC

Maximizepk2P0P2 ¼

X2

k¼1

½pk2 � ck

1 � ek � bk�qk2ðpk

2Þ ð42Þ

� For strategy choice DC

Maximizepk31

; pk32

P0P3 ¼X2

k¼1

½pk31 � c1�qk

31ðpk31;p

k32Þ

þ ½pk32 � ck

1 � ek

� bk�qk32ðpk

31;pk32Þ ð43Þ

Appendix D. Proof for Corollary 1 and 2

Claim 2. Assuming that a dual channel (DC) strategy is optimal, thenthe optimal price for RC (pU�

2 ) will increase in response to thefollowing:

1. An increase in the maximum market size a.2. A decrease in the environmental propensity of customers k.3. A decrease in the price sensitivity to demand for the RC channel b1.4. A decrease in the price sensitivity to demand for the OC channel b2.5. An increase in the symmetric price based substitution effects

parameter s.6. An increase in the unit cost for the RC channel c1.

and


Claim 3. Assuming that a dual channel (DC) strategy is optimal, thenthe optimal price for OC (pU�


1. An increase in the maximum market size a.2. An increase in the environmental propensity of customers k.3. A decrease in the price sensitivity to demand for the RC channel b1.4. A decrease in the price sensitivity to demand for the OC channel b2.5. An increase in the symmetric price based substitution effects

parameter s.6. An increase in the cost premium for the OC channel e.

Proof. The optimal prices for the dual channel stochastic modelare as follows:


b2u1 þ su2



b1u2 þ su1


where u1 ¼ ða1 þ b1c1Þ � gðz1; d1Þ � sc2 þ l1, u2 ¼ ða2 þ b2c2Þ �gðz2;d2Þ � sc1 þ l2; gðz1;d1Þ ¼

R d1z1ð�1 � z1Þf ð�1Þd�1 and gðz2;d2Þ ¼R d2

z2ð�2 � z2Þf ð�2Þd�2.

Analyzing gðz1; d1Þ further, we find that gðz1; d1Þ ¼R d1

z1

ð�1 � z1Þf ð�1Þd�1 ¼R d1

z1ð�1Þf ð�1Þd�1 � z1

R d1z1

f ð�1Þd�1. In this expres-

sion, we find thatR d1

z1ð�1Þf ð�1Þd�1 6 l1;0 6

R d1z1

f ð�1Þd�1 6 1, and

�d1 6 z1 6 d1. Since d1 6 a1, then gðz1; d1Þ 6 l1 þ a1.

Taking the derivative of pU�31 with respect to various parameters,

we find that

@pU31

@a¼ b2ð1� kÞ þ ksÞ

2ðb1b2 � s2Þ P 0 ð46Þ

@pU31

@k¼ �aðb2 � sÞ

2ðb1b2 � s2Þ 6 0 ð47Þ

@pU31

@b1¼�b2½b2ða1þl1�gðz1;d1ÞÞþsða2þmu2�gðz2;d2ÞÞ�

2ðb1b2�s2Þ260 ð48Þ

@pU31

@b2¼�s½sða1þl1�gðz1;d1ÞÞþb1ða2þmu2�gðz2;d2ÞÞ�

2ðb1b2�s2Þ260 ð49Þ

@pU31

@s¼2b2sða1þl1�gðz1;d1ÞÞþðb1b2þs2Þða2þmu2�gðz2;d2ÞÞ

2ðb1b2�s2Þ2P0 ð50Þ

@pU31

@c1¼ 1

2P 0 ð51Þ

@pU31

@c2¼ 0 ð52Þ

The results for pU�32 are similar to those for pU�

31 and areomitted. h

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