n0080

Procurement and pricing strategyB2B spot marketMarket liquidityRisk

xamconin wcien

variability, and correlation coefcient affect a rms strategies and performance. We nd that demand

at B2Buld ha002).

or reopened on the Internet. Many commodity products, such ascommodity metal, chemical products, semiconductors, plastics,and agricultural products, are traded over B2B spot markets. In Chi-na alone, over 100 B2B spot markets have been established since2000, many of which have achieved reasonable success. BOCE(www.boce.cn, Tianjin), a leading B2B spot market for crude oil,

Another critical concern for resellers is the lack of liquidity inthe B2B spot market. As many B2B spot markets are still in theirearly development stage, most of them cannot provide buyers orsellers with perfect matches. In such business environment, resell-ers cannot effectively ofoad their excessive inventories or procurethe shortfall in the spot market. In addition, the speculation behav-ior may also be affected by the imperfectness of the spot marketaccess. Therefore, resellers should develop different pricing andprocurement strategies for different market liquidities, but it

Corresponding author.

European Journal of Operational Research 221 (2012) 8798

Contents lists available at

O

w.eE-mail address: xingweimail@gmail.com (W. Xing).ment of B2B spot markets has not been smooth. Expected by manyto be the next major innovation in business, many B2B spot mar-kets sprang up virtually overnight between 1999 and 2000, and atremendous amount of capital was poured in (Kaplan andSawhney, 2000). However, the frenzied development came to ahalt by the end of 2000 (Grey et al., 2005). During these gloomyyears, many B2B spot markets failed or were merged (Brunnet al., 2002). The boom and burst of the dot com during that periodcreated skepticism about the future of B2B spot markets. However,many did not lose hope, and the development continues until to-day. In recent years, hundreds of B2B spot markets have opened

inventories and eliminate stockout costs through B2B spot mar-kets. They can earn additional revenue by speculating (purchasingmore through contracts and then selling) in B2B spot markets. Onthe other hand, trading in B2B spot markets also exposes resellersto price volatility. Therefore, to participate in a B2B spot market, areseller needs to tailor his/her pricing and procurement strategiesto the new business environment. However, for many resellers,there is a lack of understanding of this evolving business environ-ment, which may limit the participation of resellers in the B2B spotmarket. Clearly, how a B2B spot market serves or is perceived toserve the reseller needs is crucial to its success.1. Introduction

Many organizations predicted thspot markets or e-marketplaces) woGartner Group, 2004; e-Marketer, 20377-2217/$ - see front matter 2012 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.ejor.2012.03.017variability signicantly affects both pricing and ordering strategies, whereas the spot price volatilityhas less inuence on pricing decisions. Our results also show that for a risk-averse reseller to charge alower retail price when the spot market liquidity increases is desirable. We further show that a B2B spotmarket cannot always improve a resellers utility. These ndings shed light on how resellers can adjusttheir procurement and pricing strategies to align with the new business environment created by theemergence of B2B spot markets, as well as have obvious implications for the development of a B2B spotmarket.

2012 Elsevier B.V. All rights reserved.

spot markets (onlineve a grand future (e.g.,However, the develop-

coke, and rebar, has achieved an average daily trading volume ofmore than 100,000 metric tons on rebar.

Resellers are major participants of B2B spot markets for com-modity products. B2B spot markets can be a double-edged swordto resellers. On the one hand, resellers can ofoad their excessiveKeywords:Supply chain management

and are unique. We then analytically examine the case in which a risk-averse reseller participates in afully liquid spot market. We also study numerically how varying liquidity, spot price volatility, demandProduction, Manufacturing and Logistics

Optimal ordering and pricing strategies i

Wei Xing a,, Shouyang Wang b, Liming Liu ca School of Management, Qufu Normal University, Shandong 276826, ChinabAcademy of Mathematics and Systems Science, Chinese Academy of Science, Beijing 10c Faculty of Business, Lingnan University, Hong Kong, China

a r t i c l e i n f o

Article history:Received 24 September 2010Accepted 8 March 2012Available online 20 March 2012

a b s t r a c t

In the current paper, we eformance of a reseller whoket. We analyze the casefunction and identify suf

European Journal of

journal homepage: wwll rights reserved.the presence of a B2B spot market

, China

ine the effect of a B2B spot market on the strategic behavior and the per-tinues to use the traditional channel while participating in a B2B spot mar-hich a risk-neutral reseller faces an additive or multiplicative demand

t conditions under which the optimal order quantity and retail price exist

SciVerse ScienceDirect

perational Research

lsevier .com/locate /e jor

ume of the manufacturer may increase or decrease, thesecondary market can always improve the supply chain perfor-

the spot market. In spot trading, the commodity can be bothbought and sold through the spot market. The optimal procure-ment strategies are analyzed based on different market situations.Their result shows that a signicant prot can be achieved throughthe readjustment of the order quantity. Martnez-de-Albniz andSimchi-Levi (2006) study a risk-averse manufacturers portfolio

et al. (2008), among others, have studied the joint decision prob-lem in a price-dependent stochastic setting. Studies also address

perational Research 221 (2012) 8798mance. Peleg et al. (2002) compare three procurement strategiesusing the long-term relationship-based contract, the short-termspot market, and the combination of both. They nd that the opti-mal strategy depends on the market characteristics. Etzion andPinker (2008) study the asymmetric competition between twotypes of suppliers in a B2B spot market environment; one usesthe combination of forward contracts and spot market, whereasthe other utilizes only the spot market. They nd that the supplierwith forward contracts can benet from the spot market more thanthe supplier without using forward contracts. Wu et al. (2002)examine the capacity reservation contract strategy for a capital-intensive product. The buyer purchases a certain amount of optioncontracts from the seller. On exercising day, both the buyer and theseller can sell excess capacities or buy additional quantities in aspot market. Buyerss optimal reservation quantity depends onboth the reservation cost and execution cost, whereas the sellersoptimal strategy is to set the execution cost as low as possible.Spinler and Huchzermeier (2006) extend Wu et al.s (2002) resultsto the case in which the buyers demand function is state depen-dent. They show that the combination of the option contract andthe spot market is a Pareto improvement compared with othercannot be done properly without a clear understanding of the ef-fect of the spot market liquidity. Motivated by the concerns elabo-rated above, we consider a single-period inventory model in whicha reseller participating in a B2B spot market faces an uncertainprice-sensitive demand. The reseller makes a procurement-quantity decision and a selling-price (retail price) decision simulta-neously before spot trading with the objective of maximizing his/her expected utility. We consider two types of resellers, that is,the risk-neutral reseller and the risk-averse reseller, and investi-gate how the B2B spot market affects the resellers strategies byfocusing on such characteristics as price sensitivity, demand uncer-tainty, and price volatility.

The rest of this paper is organized as follows. Section 2 reviewsthe relevant literature. Section 3 describes the basic model. Section4 presents the strategies for a risk-neutral reseller. In Section 5, weexamine the strategies for a risk-averse reseller. We rst analyti-cally investigate optimal strategies with a fully liquid B2B spotmarket and an additive demand function, and then numericallyinvestigate the effects of the B2B spot market on the resellersstrategies. Finally in Section 6, we give the concluding remarksand present some issues for future research.

2. Literature review

The popularity and development of B2B spot markets havestimulated extensive research in the last 10 years. Detailed reviewsof research on B2B spot markets from a supply chain perspectivecan be found in Swaminathan and Tayur (2003), Grieger (2003),Eng (2004), Grey et al. (2005), and Haksz and Seshadri (2007).Here, we only review the works closely related to this paper.

The emergence of B2B spot markets has provided manufactur-ers and resellers with a new business avenue while forcing themto adjust their strategies to align with the new business environ-ment. Thus, a key question is how the procurement and pricingstrategies of a reseller will be affected by the presence of a B2B spotmarket. Motivated by HPs Internet-based exchange Trading-Hub.com, Lee and Whang (2002) use a two-period newsvendormodel to explore the effect of a secondary market, which can read-just resellers inventories. They show that although the sales vol-

88 W. Xing et al. / European Journal of Omarket structures. Seifert et al. (2004) analyze the benets of anonline spot market from the supply chain operational perspective.In their model, the buyer can procure through forward contract orthe combined pricing and ordering strategy of a risk-averse news-vendor. For example, Agrawal and Seshadri (2000) model risk aver-sion with the general utility function, Chen et al. (2007) extendAgrawal and Seshadris (2000) model to a multi-period setting,and Chen et al. (2009) use CVaR as risk criteria. Our focus is differ-ent. We examine the effect of B2B spot markets with a volatileprice on the strategies and performance of a reseller.

3. Basic model description

We consider a one-period model in which the decisions andevents form a three-stage process, as shown in Fig. 1. Before theselling season, i.e., at T0, knowing the procurement price w and fac-ing a random price-sensitive demand D, the reseller decides thequantity q to order through forward contract and the retail pricepr for the resell channel simultaneously. During the selling seasonT1, knowing the realized demand and spot price, the reseller cansell his/her excessive inventory or buy some extra productsthrough the B2B spot market. After the selling season, i.e., at T2,the spot market is closed, and the unsold surplus is salvaged atprice s. To avoid trivial outcomes, we assume that s < w. A news-vendor type model is formulated to study the procurement andpricing decision of a reseller who faces uncertain future demandand a spot market with an uncertain exogenous spot price. We as-sume that the reseller cannot reorder from the manufacturer dur-ing the selling season. The reseller, such as catalog resellers orresellers with planned promotional campaigns, cannot changethe price during the whole selling season. These kinds of decisions

Time

Decide pr* and q*

Demand and spot uncertaintiesrealized; spot trading begins;reseller sells to customer

Salavaged if possibleprocurement strategy option contract and having access to a spotmarket. The analysis of Serel et al. (2001) and Inderfurth and Kelle(2011) of the capacity reservation in the presence of a spot marketis also an interesting source of information. The model presented inthe current paper differs from the above mentioned studies in thatit incorporates optimal pricing and ordering decisions in the pres-ence of price-dependent stochastic demands in the resell channeland an exogenous random price in the spot market. The resellersrisk attitude is also considered. These factors enable us to studyfrom different angles the effects of a B2B spot market on the per-formance and strategic behaviors of a reseller.

Our work relates to the literature on joint ordering and pricingdecisions. A recent work on this area is by Petruzzi and Dada(1999), who study a newsvendor problem in which the resellerhas to make the stocking and pricing decision simultaneously.They analyze the effect of the nature of the stochastic demandfunction on the pricing and stocking decisions. Elmaghraby andKeskinocak (2003) and Yano and Gilbert (2003) examine the vari-ous related issues and provide comprehensive reviews. Recently,Bernstein and Federgruen (2005), Ray et al. (2005), and SongT0 T1 T2

Fig. 1. Sequence of events on a timeline.

under uncertainty and risk are common in reality, and they havebeen studied extensively.

Owing to the large number of participants in the spot market,individual participants cannot manipulate the market. Therefore,the spot price pe of the product in the spot market is assumed an

exposexpecextens

0 6 Ation

p yp ewyp z1msmp ze; e6 z;

W. Xing et al. / European Journal of Operexogenous stochastic variable, with mean le and variance r2e ,and all the participants in the spot market are price-takers. As mostB2B spot markets are still at their development stage, not manyspot markets have achieved full liquidity, and as such a resellersorder may not be completely executed. In the current paper, we as-sume that when an order is placed in the spot market, it will beexecuted with a probability of m, which measures the liquidity ofthe spot market (Kleindorfer and Wu, 2003).

The resellers prot function can then be expressed as follows:

pr prD pemq D s1mq D pemD q

wq pr1mD q: 1The rst term on the right-hand side (RHS) represents the revenuefrom the resell channel if the demand is met in full. The second termis the revenue obtained by selling the surplus in the spot market.The third is the salvage value of the unsold surplus. We assume thats is lower than the realized spot price, so that the reseller will rsttry to salvage his/her inventory in the spot market, as reected bythe second and third terms on the RHS.1 The fourth is the cost forprocurement shortage from the spot market, the fth is the procure-ment cost through contract, and the last represents the value of theunmet demand in the resell channel. In summary, to maintain cus-tomer goodwill and prevent the erosion of the customer base inthe resell channel, a reseller usually goes the extra mile to meet cus-tomer demands, and he/she usually maintains a stable resellingprice. In other words, the reseller takes the risk of price volatilityin the spot market and an uncertain demand in the resell channelin return for a higher prot margin in the resell channel.

We consider two types of demand functions: the additive de-mand function and the multiplicative demand function. Demandis dened as D = y(pr) + e in the additive case and D = y(pr)e in themultiplicative case, where y(pr) is a deterministic and decreasingfunction of the selling price pr, and e is a random factor with meanld and standard deviation rd. Furthermore, we take the form ofy(pr) = h apr and ypr hpar , where h > 0 is the market baseand a > 0 measures the price sensitivity (Petruzzi and Dada,1999). Usually, a xed setup/initial participation cost is requiredto trade in a B2B spot market, and there are also some risk-associated costs; thus, most small-volume end-users do notparticipate in the B2B spot trading. In our example, although somelarge-volume end-users participate in the BOCE, over 95% of theusers of BOCE are steel distributors.2 Therefore, we assume thatthe spot price pe does not directly affect end-user demand D in theretail channel.

For each demand function, we consider the decisions of twotypes of resellers, the risk-neutral reseller and the risk-averse re-seller. In the risk-neutral case, the reseller makes decisions underthe expected value criterion. He/she intends to maximize his/herexpected prot E[pr] by setting the retail price and deciding thequantity to order from the manufacturer. In the risk-averse case,the reseller intends to maximize his/her meanvariance utility.Thus, in this case, the resellers decision problem is

1 A more general form for the second and third terms is I(pe s)[pem + s(1 m)](q D)+ + I(s pe)s(q D)+, and I() is the indicator function that takes the value of 1if its argument is positive or 0 otherwise.2 More detailed information can be found in the annual reports of the ChinaFederation of Logistics and Purchasing: China Logistics Development Report (20092010) and (20102011), China Logistics Publishing House, Beijing.prz;pr r r r epr yprzwyprzmpeprez; e>z:

Dene Kz R zAz xf xdx andHz R Bz x zf xdx. If e is inde-pendent of pe, the expected prot can be written as follows:

Eprz;pr Wpr Lz;pr; 3where W(pr) (pr w)[y(pr) + ld] andLz;pr w s1m mleKz pr mle pr wHz:Similar to Petruzzi and Dada (1999), we can verify that E[pr(z,pr)] isconcave in z for a given pr. We can then follow a sequential proce-dure to nd the optimal solution. We rst nd the optimal retailprice pr z given z, and then nd z to maximize E pr z;pr z

.

Theorem 1. For the additive demand, if e is independent of pe, thefollowing properties hold:

(1) For a xed z, the unique optimal retail price is given by

pr z h ld aw

2a 1mHz

2a: 4

(2) If F() is a distribution function whose hazard rate satises2r(z)2 + dr(z)/dz > 0 for A 6 z 6 B, and the market liquidity sat-ises m < (w s)/(le s), then z is the largest z in the region[A,B] that satises dE[pr(z,pr(z))]/dz = 0.

(3) If the conditions for (2) are met, and

2male 1maw 1mh 1m2Am1mld> 0;

then z is uniquely determined by dE[pr(z,pr(z))]/dz = 0.

For convenience, we relegate all the proofs in this paper to theappendix. The condition m < (w s)/(le s) can be rewritten asm(le w) < (1 m)(w s). Note that w s is the loss per unit be-cause of the inefciency of the spot market, and le w is the earn-ing per unit from speculation. If the expected gain from thespeculation is less than the expected loss due to the inefciencyof the spot market, the reseller will order a nite quantity by con-z q y(pr) in the additive demand case. The prot function canbe rewritten astract.quantwhich< B. Let r(x) = f(x)/[1 F(x)] be the hazard rate of the distribu-F(). Following Petruzzi and Dada (1999), we denote4. Strategies of a risk-neutral reseller

In this section, we consider the case in which the reseller is risk-neutral (k = 0). Let F() and f() represent CDF and PDF of e, respec-tively, and assume that this distribution has support on [A,B] withure. An alternative approach to model risk aversion is by theted utility framework. Van Mieghem (2003) provides anive discussion of utility theory and meanvariance analysis.maxpr ;q>0

Ur Epr kVarpr ; 2

where k > 0 represents the resellers risk attitude. Meanvarianceutility is rst proposed in the seminal work of Markowitz (1959),and it has been widely adopted by some operations managementstudies, such as Chen and Federgruen (2000), Ding et al. (2007),and Buzacott et al. (2011). To study the effect of online spot market,Seifert et al. (2004), Martnez-de-Albniz and Simchi-Levi (2006),and Dong and Liu (2007) also use meanvariance to measure risk

ational Research 221 (2012) 8798 89Otherwise, the reseller should either procure an inniteity through contract if w < E[pe] or order zero if w > E[pe],is similar to Milner and Kouveliss (2007) result.

ties. Whis/hemoreprotecthree

prot function can be rewritten as

perwhen the liquidity is relatively high and decreases in rd whenthe liquidity is relatively low.prz;prpryprewyprz1msmpeyprze; e6 z;pryprzwyprzmpepryprez; e> z:

Analogous to the additive case, if e is independent of pe the expectedprot can be written as follows:

Eprz;pr Wpr Lz; pr; 5where W(pr) (pr w)y(pr)ld andLz;pr yprw s1m mleKz pr mle pr

wHz:

Theorem 2. For multiplicative demand, if e is independent of pe, thefollowing properties hold:

(1) For a xed z, the unique optimal retail price is given by

pr z awa 1

aa 1

w 1msmleKz mle wHzld 1mHz

; 6

(2) If F() is a distribution function satisfying 2r(z)2 + dr(z)/dz > 0for A 6 z 6 B, and m < (w s)/(le s) and aP 2, then z isthe largest z in the region [A,B] that satises dE[pr(z,pr(z))]/dz = 0.

(3) If the conditions for (2) are met, and ma(le w)ld + [mld +(1 m)A](w mle) > 0, then z is uniquely determined bydE[pr(z,pr(z))]/dz = 0.

In the multiplicative demand case, we use the parameter valuesh = 2000, a = 3, w = 10, and s = 6, and assume e N(100,202),pe N(11,22), and q = 0.1. As shown in Fig. 2, the optimal retailprice slightly decreases in m, and the order quantity increases inm. We also observe that the reseller will set a higher retail pricefor higher rd. However, the order quantity tends to increase in rdIn the multiplicative demand case, we denote z q/y(pr). TheFromarkeindepith a higher liquidity spot market, the reseller can unloadr excessive inventory for a higher value, and so he will orderthrough contract. As rd increases, the reseller orders more tot the demand uncertainty and sets a lower retail price for allscenarios.Proposition 1. With additive demand, if the conditions in Theorem1(2) are met and w < le, both z and pr are increasing in m.

In the additive demand case, the effect of m on the optimal or-der quantity is a tradeoff between the two opposing effects: theoptimal order quantity increases in z and decreases in pr .

To understand further how the market liquidity and demanduncertainty affect the resellers strategies and performance, weuse the parameter values a = 1.5, w = 10, and s = 6, and assume(h + e) N(100,202), pe N(11,22) and q = 0.1 (the correlationcoefcient between e and pe). We focus on analyzing three scenar-ios with different liquidities: partially liquid with m = 0.4 andm = 0.7, and no liquidity with m = 0. Hence, the reseller does notparticipate in the spot market.

As shown in Fig. 2, the optimal retail price still increases in m,although the spot price and the demand are correlated. The opti-mal order quantity increases in m for different demand uncertain-

90 W. Xing et al. / European Journal of Om the proofs of Theorems 1 and 2, we also nd that the spott uncertainty re does not affect the resellers strategies if e isendent of pe. If e is correlated with pe, our numerical studyshows that the effects of re and q on the resellers strategies andperformance are insignicant.

5. Strategies of a risk-averse reseller

In this section, we rst analyze the scenario in which the spotmarket achieves full liquidity. We then present some numericalexamples to illustrate how the related parameters affect the opti-mal strategies of a risk-averse reseller facing both additive andmultiplicative demands.

5.1. Strategies under a fully liquid spot market

Suppose full liquidity is achieved in the spot market, i.e., m = 1.We can simplify (1) into

pr prD peq D wq peD q

prD peD q wq: 7

Usually, price movements in the spot market reect the overalldemand trend. Therefore, when the spot price pe is high, demand inthe resell channel is usually strong. For example, the price of hot-rolled sheets in a spot market in December 2008 was about 3000RMB per metric ton, down from the 5000 RMB per metric ton inJune of that year because of the sluggish demand in China causedby the on-going nancial crisis. Therefore, assuming a positive cor-relation between the demand in the resell channel and the spotprice is reasonable (Seifert et al., 2004). Accordingly, we assumefurther that e and pe together satisfy a bivariate normal distribu-tion with correlation coefcient 0 6 q < 1, i.e., e; pe BNld;le;r2d ;r2e

. This distribution helps the tractability of the mod-el, and it has been commonly used in the literature (Chod and Rudi,2005).

We rst consider the additive demand function in the resellchannel, i.e., D = h apr + e. The expected value and the varianceof the resellers prot can be expressed, respectively, as follows(see Appendix A for details):

Epr ap2r alehldprlewqqrdrehldle; 8Varpr 1q2r2d prle2r2e

h ia24able4b2l2e 2b2r2e ; 9

where a = (are + qrd)pr + qre (h + ld)re + qlerd and b = qrd.Clearly, the expected prot is a linear function of the order quantityq. A risk-neutral reseller would order an innite quantity throughcontract to speculate in the spot market if le > w or order zero ifle < w. Such strategy is unreasonable in practice. Similar to Seifertet al.s (2004) argument, we only consider the situation with k > 0,i.e., the case of risk-averse resellers.

To solve the optimization problem, we need the property givenin the following lemma:

Lemma 1. For the additive demand, if k > 0 and re > 0, the utilityfunction Ur(pr,q) is strictly joint concave in pr and q.

We have the following theorem to describe the optimalstrategy:

Theorem 3. For the additive demand, the optimal retail price and theoptimal order quantity for the risk-averse reseller are unique. They aregiven as follows:

pr le h ld ale

2rk kle w; 10 le w qrd

ational Research 221 (2012) 8798q h ld apr 2kr2ere

le pr ; 11

where rk a kr2d1 q2 and k (a + qrd/re)/[2r(k)].

Oper 38.5

39

39.5

40Additive Case

m=0.0 m=0.4 m=0.7

W. Xing et al. / European Journal ofThe optimal utility for the reseller is now given by

Ur reh ld 2ale aw qrdle w 2

4r2erk le w

2

4kr2e qrdre le wh ld ale kr2er2d1 q2: 12

From (10), we observe that the resellers pricing strategy is differentwhen the reseller participates in a fully liquid spot market. Insteadof using the wholesale price as a starting point, the expected spotprice is used. Starting from le, the reseller marks the price up by

36

36.5

37

37.5

38

2 4 6 8 10 12 14 16 18 20

p r*

d

40

45

50

55

60

65

70

75

80

2 4 6 8 10 12 14 16 18 20

q*

d

Additive Case

m=0.0 m=0.4 m=0.7

1000

1050

1100

1150

1200

1250

1300

2 4 6 8 10 12 14 16 18 20

r*

d

Additive Case

m=0.0 m=0.4 m=0.7

Fig. 2. Effects of demand uncertainty and m 15.6

15.8

16Multiplicative Case

m=0.0 m=0.4 m=0.7

ational Research 221 (2012) 8798 91a margin determined by the risk-adjusted expected potential de-mand in the resell channel. The parameter k is positive, and it rep-resents the retail price sensitivity with respect to the wholesaleprice. If le > w, the reseller benets from the price premium le w,which allows him/her to lower the retail price proportionally. Con-versely, when le < w, the reseller will set a higher retail price tocompensate for a higher procurement cost through contract.

Eq. (11) shows that the optimal order quantity is also stronglyinuenced by the spot market. The optimal order quantity is com-posed of three parts, reecting a rational procurement strategy.

15

15.2

15.4

2 4 6 8 10 12 14 16 18 20

p r*

d

50

55

60

65

70

2 4 6 8 10 12 14 16 18 20

q*

d

Multiplicative Case

m=0.0 m=0.4 m=0.7

250

260

270

280

290

300

2 4 6 8 10 12 14 16 18 20

r*

d

Multiplicative Case

m=0.0 m=0.4 m=0.7

arket liquidity in a risk-neutral case.

r , and the optimal order quantity increases in r ; if

perd d

h + ld 2ale + aw < 0, the optimal retail price increases inrd, and the optimal order quantity decreases in rd; the optimalutility always decreases in rd.

Let

T reh ld 2ale awqrd

: 13

Proposition 3. For the additive demand and q 0, there exists a pricepremium threshold T such that when le w < T, the optimal retail pricedecreases in k and becomes greater than the expected spot price, and theoptimal order quantity increases in k if le T, theoptimal retail price increases in k and becomes smaller than the expectedspot price, and the optimal order quantity decreases in k if le >w.

If the value of re is not very small, the condition le w < Twill be satised. In these cases, the spot market is not a goodchannel for buying or selling the product. Then, a more risk-averse reseller will decrease his/her retail price to stimulate de-mand in the resell channel. By extensive numerical experiments,we can show that le w < T is always true except under extremeparameter settings (e.g., a very small price volatility). In practice,price volatilities in most spot markets in China are moderate. Forexample, the maximum price change of steel or crude is less than25% in a month.

Proposition 4. For the additive demand, if q 0, the following hold:

(1) The optimal retail price increases in re if le >w and decreasesin re if le < w.

(2) There exists an expected market base threshold B1 that ifh + ld > B1, the optimal order quantity increases in re; other-wise, the optimal order quantity decreases in re.quantity decreases in re if le >w, and increases in re ifle 0, the optimal retail price decreases inThe rst part is the expected demand in the resell channel. The sec-ond part is the strategic quantity. If le > w, the reseller should or-der more to speculate in the spot market. However, when le < w,the reseller should order less and expect to meet a part of his/her demand from the spot procurement. Clearly, this term de-creases in k and re. For a more risk-averse reseller, there is lessincentive to get involved in speculation (procurement) in the spotmarket. As price volatility increases, speculating (procuring) in thespot market becomes less attractive to the reseller. The third partreects the adjustment function of the spot market. Whenpr < le, it is positive, indicating that the reseller can order morefrom the manufacturer to hedge against demand uncertainty, asselling this quantity in the spot market may still gain utility if itis not consumed by the demand in the resell channel. Whenpr > le, it is negative, indicating that the reseller will order lessfrom the manufacturer. The reseller can protect himself/herselffrom the demand uncertainty by buying from the spot market incase of a shortage in the resell channel.

When q = 0, (10)(12) become less complex, and we have thefollowing result.

Proposition 2. For the additive demand and q = 0, the followingproperties hold:

(1) The optimal retail price is unaffected by re; the optimal order

92 W. Xing et al. / European Journal of O(3) There exists an expected market base threshold B2 that ifh + ld > B2, the optimal utility increases in re; otherwise, theoptimal utility decreases in re.mand variability in the additive case but increases in the demandvariability in the multiplicative case. We also observe that theoptimal retail price decreases in the market liquidity in both theadditive case and multiplicative case. A reseller participating in afully liquid spot market will sell at the lowest price in the resellchannel.

When rd increases, a reseller participating in a fully liquid spotmarket will increase (decrease) his/her order quantity in the addi-tive (multiplicative) case. In the additive case, the reason is thesharply reduced retail price stimulating higher demand in the re-sell channel. However, in the multiplicative case, a higher orderquantity implies a higher risk than that in the additive case so thatthe reseller has to reduce his/her order quantity to control risk.With a lower liquidity, the optimal order quantity decreases inrd in both cases.

Fig. 3 also shows that the resellers utility decreases as the de-mand variability increases in both additive and multiplicativecases. We also nd that the utility is more sensitive to marketliquidity as demand variability increases.5.2. Comparative statics

In this subsection, we study the effect of the spot market on thestrategies and performance of a risk-averse reseller numerically.We also compare the differences as a result of additive and multi-plicative demands. Throughout this section, we use the generalprot function (1) and the same parameter values as in Section4, except with k = 0.01.

5.2.1. Effect of demand variabilityAs shown in Fig. 3, the optimal retail price decreases in the de-Our numerical experiment in Section 5.2 shows that the effectof price volatility in the spot market on the retail price is not verystrong. The effect of price volatility on the order quantity is strongwhen re is small and is insignicant when re is large.

Next, we investigate the multiplicative demand case, i.e.,D hpar e. Similar to the additive demand, the expected valueand the variance of the resellers prot can be expressed, respec-tively, as follows:

Epr pryprld yprldle qrdre le wq; 14Varpr ypr21 q2r2d pr le2 r2e

h i a2 4able

4b2l2e 2b2r2e ; 15where ypr hpar ;a req yprldre yprqrdpr le andb = qrdy(pr).

Lemma 2. For the multiplicative demand, if k > 0,re > 0, and giventhe retail price pr, the utility function Ur(pr,q) is strictly concave in q,and

q ldhpar le w2kr2e

qrdre

hpar le pr: 16

Comparing (16) with (11), in the multiplicative case, the opti-mal order quantity is also composed of three parts: the expecteddemand in the resell channel, the speculation (procurement) quan-tity, and the adjustment quantity. However, we cannot obtain theclosed-form solution for the optimal retail price. In the next sub-section, we provide some numerical examples to examine howthe demand uncertainty, spot price volatility, and correlation coef-cient affect the optimal retail price.

ational Research 221 (2012) 87985.2.2. Effect of price volatilityFig. 4 shows that price volatility has a weaker inuence on the

retail price in both the additive and multiplicative cases. The

Oper 30

35

40Additive Case

m=0.0 m=0.4 m=0.7 m=1.0

W. Xing et al. / European Journal ofreason is that the main purpose of setting a retail price is to opti-mize the utility of the resell channel, and the price volatility hasless effect on it.

In Fig. 4, price volatility has a signicant effect on the orderquantity in scenarios with a fully liquid spot market in both theadditive and multiplicative cases, whereas it has a smaller effecton the order quantity in other scenarios. The reason is that, as reincreases, the spot market becomes less attractive for the resellerto trade, and then he/she will reduce his/her speculative activityin a fully liquid spot market. When market liquidity is lower (in

10

15

20

25

2 4 6 8 10 12 14 16 18 20

p r*

d

30

40

50

60

70

80

2 4 6 8 10 12 14 16 18 20

q*

d

Additive Case

m=0.0 m=0.4 m=0.7 m=1.0

300

400

500

600

700

800

900

1000

1100

1200

2 4 6 8 10 12 14 16 18 20

Ur*

d

Additive Case

m=0.0 m=0.4 m=0.7 m=1.0

Fig. 3. Effect of demand variability in 16

16.5

17Multiplicative Case

m=0.0 m=0.4 m=0.7 m=1.0

ational Research 221 (2012) 8798 93our example, the liquidity threshold for speculating is about 0.8),the reseller is not involved in any speculative activity in the spotmarket; thus, price volatility has less effect on the order quantity.

We also nd that the reseller cannot always benet from spottrading in the additive case. When re is small, the reseller partici-pating in a fully liquid spot market can achieve a signicantly high-er utility than those participating in a lower liquid spot market inthe additive case. The reason is that higher liquidity facilitates thereseller to sell his/her surplus, which in turn stimulates the specu-lative activity and improves his/her utility. As re increases, the spot

14

14.5

15

15.5

2 4 6 8 10 12 14 16 18 20

p r*

d

40

45

50

55

60

65

70

75

80

2 4 6 8 10 12 14 16 18 20

q*

d

Multiplicative Case

m=0.0 m=0.4 m=0.7 m=1.0

200

220

240

260

280

300

320

340

2 4 6 8 10 12 14 16 18 20

Ur*

d

Multiplicative Case

m=0.0 m=0.4 m=0.7 m=1.0

a risk-averse case (re = 2, q = 0.1).

m=0.4 m=0.7

per 20p r* 25

30Additive Case

m=0.4 m=0.7 m=1.0

94 W. Xing et al. / European Journal of Omarket becomes less attractive because of the risk caused by spottrading.

5.2.3. Effect of correlation coefcientFig. 5 shows that the optimal retail price slightly increases as q

increases in both the additive and multiplicative cases. When mar-ket liquidity increases, the effect of correlation coefcient on theoptimal order quantity becomes more signicant. In scenarios withhigher values of liquidity, the optimal order quantity is reducedsharply as q increases. With an increase in q, the incentive forordering more excess inventory to sell through the spot markets

10

15

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2e

20

40

60

80

100

120

140

160

180

200

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

q*

e

Additive Case

m=0.4 m=0.7 m=1.0

300

400

500

600

700

800

900

1000

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ur*

e

Additive Case

m=0.4 m=0.7 m=1.0

Fig. 4. Effect of spot price volatility in a 15

15.5

p r*

m=1.0 16Multiplicative Case

ational Research 221 (2012) 8798decreases. That is, when excess inventory is high, there is less de-mand in the resell channel, and the spot price is more likely to below, and vice versa. Furthermore, in the additive case, the utility isconvex in q with a fully liquid spot market, and q increases whenmarket liquidity is lower. However, in the multiplicative case, theutility decreases in these three scenarios.

5.2.4. SummaryTable 1 summarizes the sensitivity analysis on both risk-neutral

and risk-averse cases. The retail price is less sensitive to spot pricevolatility and the correlation coefcient in all four cases. However,

14

14.5

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2e

20

40

60

80

100

120

140

160

180

200

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

q*

e

Multiplicative Case

m=0.4 m=0.7 m=1.0

200

300

400

500

600

700

800

900

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Ur*

e

Multiplicative Case

m=0.4 m=0.7 m=1.0

risk-averse case (rd = 20, q = 0.1).

Oper 26

28

30Additive Case

m=0.4 m=0.7 m=1.0

W. Xing et al. / European Journal ofthe risk-averse reseller will signicantly reduce the retail pricewhen demand uncertainty increases in the additive demand case.In sum, to set an appropriate retail price, a reseller should paymore attention to demand uncertainty and his/her own risk atti-tude. When demand uncertainty is large, the reseller should set alower retail price if he/her faces an additive demand, and set ahigher price if he/she faces a multiplicative demand. When theliquidity in the spot market is higher, a reseller should set a lowerretail price if he/her faces a multiplicative demand. However,

16

18

20

22

24

0 0.1 0.2 0.3 0.4 0.5 0.6

p r*

20

30

40

50

60

70

80

90

100

0 0.1 0.2 0.3 0.4 0.5 0.6

q*

Additive Case

m=0.4 m=0.7 m=1.0

350

400

450

500

550

0 0.1 0.2 0.3 0.4 0.5 0.6

Ur*

Additive Case

m=0.4 m=0.7 m=1.0

Fig. 5. Effect of correlation coef 15.8

16Multiplicative Case

m=0.4 m=0.7 m=1.0

ational Research 221 (2012) 8798 95facing an additive demand, a risk-averse reseller should set a lowerretail price, whereas a risk-neutral reseller should set a higherprice.

The optimal order quantity is more sensitive to demand uncer-tainty and the correlation coefcient. The optimal order quantitymay increase or decrease as demand uncertainty increasesdepending on different demand functions and risk attitudes. Thecorrelation coefcient has a signicant negative effect on the opti-mal order quantity if a risk-averse reseller participates in the spot

15

15.2

15.4

15.6

0 0.1 0.2 0.3 0.4 0.5 0.6

p r*

40

45

50

55

60

65

70

75

80

0 0.1 0.2 0.3 0.4 0.5 0.6

q*

Multiplicative Case

m=0.4 m=0.7 m=1.0

200

220

240

260

280

300

0 0.1 0.2 0.3 0.4 0.5 0.6

Ur*

Multiplicative Case

m=0.4 m=0.7 m=1.0

cient in a risk-averse case.

Werst analyze the cases inwhich the risk-neutral reseller faces

Ur

UU

gni

peran additive or multiplicative demand function and obtain the suf-cient conditions under which the optimal strategies exist and areunique. Then, we examine analytically the special case in which arisk-averse reseller participates in a fully liquid market with addi-tive demand and obtain closed-form solutions to the optimal pric-ing and stocking policy. Our study shows that instead of using thewholesale price as a starting point, the expected spot price is used.Starting from the expected spot price, the reseller marks the retailprice up by a margin determined by the risk-adjusted expected po-tential demand in the resell channel. To determine the optimalordering quantity, a reseller should consider the speculation func-tion and the adjustment function of the spot market.

Our numerical study shows that to set an appropriate retailprice, a reseller should pay close attention to demand uncertaintymarket with a higher liquidity. Moreover, price volatility signi-cantly affects the optimal order quantity when market liquidityis high enough for the reseller to speculate in the spot market, asa spot market with higher liquidity can better facilitate the resel-lers buying and selling in the spot market, motivating the resellerto become more involved in speculative activities. However, whenmarket liquidity is low, the effect of price volatility on the optimalorder quantity is insignicant.

Higher demand uncertainty always hurts the reseller in all fourcases. However, a higher liquid spot market does not always im-prove the resellers utility. In the additive case, only when pricevolatility is small can participating in a spot market with a higherliquid improve the resellers utility.

6. Conclusion

The advent of B2B spot markets has greatly changed the tradi-tional supply chain structure, and many resellers have started toconduct business in spot markets, thus adapting themselves toand taking advantage of this newly-emerging business environ-ment. In this paper, we analyze how the spot market affects the re-sellers decisions and performance. We study two types ofresellers: the risk-neutral reseller and the risk-averse reseller. Forboth types, we consider the additive demand function and themultiplicative demand function, respectively.

Table 1Summary of numerical illustration.

Additive

Risk neutral Risk averse

pr q Ur p

r q

m + + + Urd + Ure I I I I Uq I I I +

Note: +, , U, I represent increase, decrease, unclear (increase or decrease), and insi

96 W. Xing et al. / European Journal of Oand his/her own risk attitude. To decide on the optimal order quan-tity, the reseller should be careful of the demand uncertainty, spotprice volatility, market liquidity, and risk attitude. Our numericalstudy also shows that participating in spot markets will not alwaysbenet resellers. When price volatility is high, the spot market isless attractive to risk-averse resellers. Intuitively, a spot marketprovides a good channel for a reseller to deal with his/her excessiveinventory or shortage, and the reseller can also prot through spec-ulation. These advantages will benet the reseller. However, theincreased risk taken by the reseller in a spot market may also offsetpart or all of the advantages. This nding has an important man-agement implication for the development of B2B spot markets.For example, there are thousands of resellers (traders) in theChinese steel industry. However, only a very small fraction of themhas participated in spot markets. Avoiding exposure to risk in thespot market may have been a major factor preventing more resell-ers from participating in spot markets. As most of the steel resell-ers in China are small or medium sized, they have little experiencein dealing with such risk. One way to reduce risk is by hedging,which includes operational hedging and nancial hedging (VanMieghem, 2003; Van Mieghem, 2007). The former involves opera-tional strategies such as postponement decisions and inventorypolicies, and the latter involves forward and option contracts.

Note that some factors are not considered in our model andanalysis, such as asymmetric information and reseller competition.Including these factors in a model should be an interesting topic forfuture research. The model presented in this paper assumes oneordering opportunity by the reseller. Repeated ordering from man-ufacturers is a prominent characteristic in some industries. Allow-ing multiple ordering opportunities by the reseller may also beworth studying in the future.

Acknowledgements

We thank two anonymous referees and an Editor for theirinsightful comments and suggestions that have helped improveour paper greatly. This research was supported in part by The HongKong Polytechnic University under Grants G-U343 and G-U718,and the National Natural Science Foundation of China under Grants70731003 and 70971076.

Appendix A. Computing the mean and variance in the additivecase

Let d = ld + e. The prot for the reseller when he/she partici-pates in a fully liquid spot market with an additive demand canbe rewritten as

pr prD peq D wq peD q

apr qpe dpe pr wq ap2r :The expected prot can be computed as

Epr Eapr qpe dpe pr ap2r wq ap q h l l qr r h l p ap2 wq

Multiplicative

Risk neutral Risk averse

pr q Ur p

r q

Ur

+ + + ++ U + I I I + U I I I +

cant, respectively.

ational Research 221 (2012) 8798r d e d e d r r

ap2r ale h ldpr le wq qrdre h ldle:

The variance of prot can be computed as follows:

Varpr VarprdaprqpedpeEfVarprdaprqpedpejpegVarfEprdaprqpedpejpegEfprpe2VardjpegVarfaprqpeprpeEdjpegEprpe2Vardjpe

Var aprqpeprpe hldqrdre

pele

1q2r2d prle2r2e a24able4b2l2e 2b2r2e ;where a = (are + qrd)pr + qre (h + ld)re + qlerd and b = qrd.

d Rz dRz=dz df z

Dadas (1999), Thus, we omit the details. h

@q2 2kre ;

Ur(pr,q). For kr > 0 and re > 0, we have

results. h

Agrawal, V., Seshadri, S., 2000. Impact of uncertainty and risk aversion on price andorder quantity in the newsvendor problem. Manufacturing and Service

Oper1m 2aIf w < l , L(z) < 0. We also have oR(z)/@z < 0, as R(B) < 0, and z iswith forecast updates. IIE Transactions 43 (6), 415431.dz2 f z dz

1m2f z

2a1 Fz f z

rz 1 Fzdrz=dz

rz2" #

:

Then, we obtain

d2Rzdz2

dRz=dz0

1m2f z1 Fz2arz2

2rz2 drzdz

:

Under the condition 2r(z)2 + dr(z)/dz > 0,R(z) is either monotone orunimodal, which implies that R(z) dE[pr(z,pr(z))]/dz has at mosttwo roots. If m < (w s)/(le s), R(B) < 0. Therefore, if R(z) has onlyone root, it indicates a change in sign for R(z) from positive to nega-tive. Thus, it corresponds to a localmaximumof E[pr(z,pr(z))]. If it hastwo roots, the larger of the two values corresponds to a local maxi-mum, and the small corresponds to a localminimumof E[pr(z,pr(z))].In either case, E[pr(z,pr(z))] has only one local maximum, identiedeither as the unique value of z that satises R(z) = dE[pr(z,pr(z))]/dz = 0 or as the larger of two values of z that satises R(z) = 0. AsE[pr(z,pr(z))] is unimodal if R(z) has only one root, a sufcient condi-tion for unimodality of E[pr(z,pr(z))] is R(A) > 0 or, equivalently,2aR(A) > 0, where 2aR(A) = 2amle (1 +m)aw + (1 m)h + (1 m)2A +m(1 m)ld. We obtain the condition in part (3). This com-pletes the proof. h

Proof of Proposition 1. We still use the denition in the proof ofTheorem 1. By the implicit function rule, dz/dm = L(z)/(@R(z)/@ z),where L(z) =@R(z)/@m. Then, we have

Lz s le 1m1 FzHz2a

1

Fz h aw ld2a

s 1mHz

2a

:

As

1 Fz h aw ld2a

s 1mHz

2a

w 1msmle1m ;

so we have that

Lz le w 1mHz1 Fz

:

e

the largest z in the region [A,B] that satises dE[pr(z,pr(z))]/dz = 0,Appendix B. Proofs

Proof of Theorem 1. The proof of the rst part is similar to that inPetruzzi and Dada (1999), and we thus omit the details.

dEprz; przdz

mle 1msw 1

m h aw ld2a

1mHz2a

s

1 Fz:

Let R(z) dE[pr(z,pr(z))]/dz, thendRzdz

1m f z2a

2ah aw ld

2a s

1mHz 1m1 Fz

rz

;

and,

2

W. Xing et al. / European Journal ofthus, dz/dm > 0. We complete the rst part of the proof.Operations Management 2 (4), 410423.Bernstein, F., Federgruen, A., 2005. Decentralized supply chains with competing

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strategy. European Management Journal 20 (3), 286298.Buzacott, J., Yan, H., Zhang, H., 2011. Risk analysis of commitment-option contractsReferencesH11 @2Ur=@p2r < 0;detH 4akr2e 4k2r2dr2e 1 q2 > 0:Therefore, the Hessian matrix is negatively denite, and the utilityfunction Ur(pr,q) is strictly joint concave in pr and q. This completesthe proof. h

Proof of Theorem 3. By Lemma 1, a unique optimal retail price prand a unique optimal order quantity q exist. Applying the rstorder necessary and sufcient conditions, we obtain (10) and(11), respectively. h

Proof of Proposition 2. We rst dene two thresholds:

B1 3ale 2aw2a kr2dle w

kqrdre;

and

B2 2ale awa kr2dle w

kqrdre 2rkr

2e

le w

4krkr3erd1 q2

qle w:

Then, using the rst derivative of which, we can obtain the@2Ur@pr@q

2kreare qrd:

Let H denote the Hessian matrix of the resellers utility functionProof of Lemma 1. The rst-order derivatives of Ur(pr,q) are asfollows:

@Ur@pr

2apralehld2k 1q2r2dprleareqrda2ble

;

@Ur@q

lew2krea2ble:

The second-order derivatives of Ur(pr,q) are given by

@2Ur@p2r

2a 2k 1 q2r2d are qrd2h i

;

@2Ur 2Next, we have dpr

dm @pr

@m @pr

@zdzdm. We can verify that

@pr@m Hz

2a > 0,

and @pr

@z 1m1Fz

2a > 0. In conjunction with dz/dm > 0, we obtain

dpr=dm > 0. h

Proof of Theorem 2. A proof of this theorem can be carried out byfollowing a procedure similar to Theorem 1 and Petruzzi and

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98 W. Xing et al. / European Journal of Operational Research 221 (2012) 8798

Optimal ordering and pricing strategies in the presence of a B2B spot market1 Introduction2 Literature review3 Basic model description4 Strategies of a risk-neutral reseller5 Strategies of a risk-averse reseller5.1 Strategies under a fully liquid spot market5.2 Comparative statics5.2.1 Effect of demand variability5.2.2 Effect of price volatility5.2.3 Effect of correlation coefficient5.2.4 Summary

6 ConclusionAcknowledgementsAppendix A Computing the mean and variance in the additive caseAppendix B ProofsReferences