Who Benefits from Altruism in Supply Chain Management?

14 Pages·2013·2.49 MB·English

American Journal of Operations Research, 2012, 2, 59-72
http://dx.doi.org/10.4236/ajor.2012.21007 Published Online March 2012 (http://www.SciRP.org/journal/ajor)
Who Benefits from Altruism in Supply Chain
Management?
Zehui Ge1, Qiying Hu2
1Business School, University of Shanghai for Science and Technology, Shanghai, China
2School of Management, Fudan University, Shanghai, China
Email: [email protected], [email protected]

Received September 9, 2011; revised October 12, 2011; accepted October 22, 2011
ABSTRACT
The significant effect of social preference on strategic behavior has been convinced by recent research. Along this
stream of research, we study firms’ altruistic incentives in supply chains since the selfish rationality can’t deal with
economic behaviors. We show that the performance of the supply chain in consideration of altruism is between those of
scenarios under decentralization and under integration. We further shows that a manufacturer, as a leader, should find
an egoistic retailer, while a retailer, as a follower, should find a manufacturer with altruistic liability, to form a good
chain.

Keywords: Supply Chain Management; Coopetition; Altruistic Preference; Advertising/Sales Effort; Pricing
1. Introduction which combines pricing and inventory control. Reference
[5] investigates the effects of risk aversion on the price
A great deal of attention has been paid to supply chain
and order quantity. Furthermore, [6] studies a joint pric-
management (SCM) in the last decades, in which supply
ing/inventory game of multiple newsvendors under com-
chain coordination is mainly discussed due to double
petitive situations.
marginalization in decentralized chains. However, the
Besides pricing, firms often use advertising/sales effort
wholesale-price contract is commonly adopted by man-
to spur demand. This plays a key role in managing mar-
agers in practice, even though the literature has shown keting-operations interface. In considering the dimension
that it cannot coordinate the supply chain. Recently, of sales effort, [7] models a simultaneous choice of sales
some researchers try to explain this phenomenon (eg. [1]). effort and order quantities in a newsvendor environment.
Based on a generalized newsvendor model, this paper In considering the dimension of advertisement, there is
investigates the coexistence of competition and coopera- also a huge collection of literature regarding various
tion in a supply chain where pricing, ordering, and ad- kinds of advertising. For instance, [8] link advertising to
vertising/sales effort (henceforth ASE) are considered quantity decision in a newsvendor setting. While [9] dis-
simultaneously. Another, we introduce social preferences cusses optimal pricing and advertising in a durable good
into decision maker’s utility to study cooperation in the duopoly, and [10] considers brand name advertising into
supply chain. demand identification.
There are three streams of research related to our paper. The second stream related to our research is SCM with
In the following, we briefly review the most related re- stochastic demand. Along this direction, the classic
search and describe our contributions with respect to the newsvendor model is also extended to include the inter-
vast, growing literature (See Figure 1 for a sketch). face (contract) of a firm with its upstream suppliers. The
First, the newsvendor model is the most basic model in most prevalent contract in practice is the wholesale price-
SCM, where a retailer faces a random demand in a single only type, which involves the newsvendor paying a per-
period and must decide how many units of the product to unit wholesale price charged by the manufacturer. Ref-
stock before the demand is realized (see [2]). Reference erence [11] gives a complete analysis of this model under
[3] is the first to incorporate pricing into the newsvendor demand distributions with increasing generalized failure
model by assuming that demand rate depends linearly on rate (IGFR). The wholesale-price contract does not coor-
price. Following Whitin, the newsvendor problem has dinate the supply chain (see [12]), unless such social
been extended by many other researchers. Reference [4] preferences as fairness are taken into consideration (e.g.,
provides a significant review in the direction of research [1]).
Copyright © 2012 SciRes. AJOR
60 Z. H. GE ET AL.
demand under asymmetric information structure. He et al.
focus on how to coordinate a decentralized supply chain,
where the retailer’s sales effort, order quantity, and retail
price are involved in a random demand setting ([22]). In
light of the first and second streams of research, our first
objective is to apply further consideration to the manu-
facturer’s advertising efforts and focus on determining
solutions for the decentralized supply chain.
The third stream related to our research entails evalu-
ating firms’ utilities in SCM. Such evaluations are related
to decision-making patterns of SCM. Specifically, there
are two main patterns in the current literature. One is the
decentralized supply chain in which each member makes
decisions to optimize its own objective. The other pattern
is the centralized supply chain in which all decisions are
jointly made to maximize the total profit of all members.
Usually, the centralized chain is a benchmark for the

decentralized one. One can see these patterns in [23], or
Figure 1. The position of our research. A: the classical news-
[13].
vendor problem, e.g., [2]; B: a supply chain with wholesale-
However, firms in a chain form a relative loose verti-
price only payment, e.g., [11]; C: utility rationalizations or
decision making patterns, e.g., [23]; D: ordering + pricing cal relationship ([24]). The supply chain may encounter a
for a newsvendor, e.g., [4]; E: ordering + ASE for a news- significant loss in efficiency because of the loose rela-
vendor, e.g., [7,8]; F: ordering + pricing for a supply chain, tionship without contractual constraints. Therefore, mem-
e.g., [14]; G: ordering + ASE for a supply chain, e.g., [17]; bers in a supply chain need to coordinate their decisions
H: a decentralized supply chain (competition), e.g., [13]; I: a
to improve the chain’s efficiency. In fact, seldom do
centralized supply chain (cooperation), e.g., [23]; J: coopeti-
successful firms in SCM take selfish actions to maximize
tion, e.g., [28]; K: ordering + pricing + ASE for a supply
chain in the newsvendor setting, e.g., [22], this paper; L: their own profits while leaving their partners out to dry.
coopetition in consideration of altruism, this paper. There are plenty of studies on competitive scenarios that
highlight this phenomenon, e.g., [25,26].
As with the newsvendor model, other decisions are In practice, cooperative and competitive incentives
considered in SCM. By combining pricing, [13] analyzes generally coexist. This phenomenon is referred to as
the competition in a decentralized supply chain, and [2] “coopetition” ([27]). Coopetition is still an under-re-
presents a newsvendor pricing game in which there exist searched theme in SCM, even though it has been invest-
a single manufacturer and multiple retailers. Syntheti- tigated by several studies from the perspective of invent-
cally, [14] presents an extensive review of coordinated tory management. For instance, [28] develops a general
pricing and production decisions by classifying the ex- framework for analyzing decentralized distribution sys-
isting models along two dimensions: deterministic versus tems with sequential decisions of inventory and alloca-
stochastic, and static versus dynamic. Another review tion. In their model, ordering decisions of different re-
can be seen in [15], etc. tailers are assumed to be made independently/compete-
Nevertheless, the supply chain system can increase the tively, while allocation or transshipment decisions are
total business “pie” by ASE. For instance, [16] examines assumed to be made cooperatively. A common focus of
coordinating contracts of a decentralized supply chain in these studies is on firms’ decision-making, but not on
which the retailer can choose promotional effort. For a rationalization of firms’ utilities.
channel rebate contract, [17] employs a simple model in On the other hand, there is sufficient evidence that
which a retailer makes ordering and effort decisions and firms care about their partners’ profits as well as their
then observes demand. Furthermore, [18] investigates the own in order to improve the competitiveness of the total
impact of the retailer’s sales effort on the manufacturer’s supply chain. It is well known that the chain’s overall
sale-timing decision, in which the payment to the manu- strength benefits each member. A live case comes from a
facturer depends on the retailer’s order quantity. In re- global executives talk published in Harvard Business
lated research, Z. Huang and his cooperators, e.g., [19,20] Review (see [29]) where A. B. Cummings, the president
study cooperative advertising in a supply chain with and COO of the Coca-Cola’s Africa Group, recounts one
price independent/dependent demand. In the above re- of his successful altruistic decisions. In order to increase
search, the demand is deterministic. Reference [21] stud- their bottlers’ profits, Cummings increased the retail
ies cooperative advertising model with a price dependent price, which resulted in increased system profitability
Copyright © 2012 SciRes. AJOR
Z. H. GE ET AL. 61
after six months for both bottlers and the Coca-Cola p is a base price-demand function, s0 indicates
Company itself. From a biological viewpoint, [30] con- the effort effectiveness associated with the brand name
ducts experiments to show how the human brain limits advertising, and t 0 with local sales effort. Moreover,
the impact of selfish motives and implements fair behav- asat is assumed to be concave in both a and a ,
m r m r
ior. [31,32] also find that altruism is a gene-culture co- which implies that (the deterministic portion of) the de-
evolution and an internalization of norms. In the context mand increases with both types of effort, but at a dimin-
of SCM, [33-37] discuss the effect of altruism on strate- ishing rate.  in Equation (1) is a random variable in
gic behavior or partnership management. Differently A,B0, with the probability density function
with these papers, we consider altruism in a generalized f  and cumulative distribution function F.
supply chain with such decisions as ordering, pricing and Let qdp,a ,a  represent a stocking factor,
m r
ASE. Furthermore, our findings point out who should which describes the gap between the order quantity and
answers more for a good vertical partnership. the deterministic portion of the demand. After the ran-
Based on altruistic phenomena occurring independ- dom part of the demand is realized, if it exceeds , we
ently of contract machines, our second objective is to say there occurs stocking shortage, otherwise, stocking
study firms’ behavior in a cooperative supply chain. We residue. The expected sale quantity of the retailer is
study coopetition in a generalized newsvendor setting, Eminq,DqFd
which includes three kinds of simultaneous decisions: A
price (both wholesale price and retail price), order quan- pasat Fd.
tity, and ASE. To some extent, the wholesale pricing is m r A
for competition while ASE for cooperation. At the same Therefore, the retailer’s expected profit is
time, we interpret firms’ cooperative incentive as their π w,p,q,a ,a  pEminq,Dwc qa
r m r r r
altruism, and introduce altruistic preferences to charac- (2)
terize firms in the supply chain. We study firms’ deci- pwc q pFxdxa ,
r A r
sions in three supply chain scenarios: integration, decen-
and the profit of the manufacturer is
tralization, and coopetition. Also, we analyze the impact
of firms’ altruistic preferences on performance of the π w,a ,qwc qa . (3)
m m m m
supply chain through numerical analysis.
The total profit of the supply chain, defined as the sum
The rest of the paper is organized as follows. In Sec-
of those of the manufacturer and the retailer, is
tion 2 we present our model. Section 3 shows the exis-
tence of Nash equilibrium and compares three scenarios. π p,q,a ,a 
s m r
We further present the effects of altruistic preference on π w,a ,qπ w,a ,q,p,a  (4)
decision-making by numerical analysis in Section 4. Fi- m m r m r
nally, Section 5 concludes this paper. pc c q pFxdxa a .
m r A m r
2. Model For convenience, we abbreviate their profits as πr,
π , π , respectively.
m s
The supply chain considered here consists of one retailer Without loss of generality, we assume p ranges from
and one manufacturer. As usual in the literature, the c c to an upper bound p. Obviously, the retailer will
mr
manufacturer (denoted by M) acts as a leader, and the set pwc so as to get a positive profit. The fol-
r
retailer (denoted by R) follows. For a type of product lowing proposition presents the scope of the stocking
supplied, the manufacturer firstly offers a wholesale factor .
price w and a brand name advertising level a . As a Proposition 1 The stocking factor  always falls
m
response, the retailer orders q units and retails them at into the support set of , i.e., A,B.
price p per unit. At the same time, he decides his sales All the proofs see Appendix. Now, we make the fol-
effort level a . The stochastic demand faced by the re- lowing assumption for our model.
r
tailer depends on a , a , and p. Unmet demand is lost. Assumption 1 p is twice differentiable, and sat-
m r
The unit producing cost is c , and the retailing one is isfies: 1) p0andp0, and 2)
c . It is convenient to assume mthat the unit costs c and 2p2pp0.
r m
c are constants, since our purpose is to examine basic The twice differentiability above is merely for con-
r
properties of altruism in SCM. venience, for it simplifies our description. Item 1) above
The demand is as follows, indicates that the retailer faces a downward sloping and
nonnegative base demand curve. Item 2) above is en-
Ddp,a ,a pasat . (1)
m r m r sured by the concavity of p. Since it can be written
Here dp,a ,a  is the deterministic portion, where as p2p2 p when the demand is convex,
m r
Copyright © 2012 SciRes. AJOR
62 Z. H. GE ET AL.
it indicates that the degree of convexity is not too large since firms reasonably care about their own profits more
for any given p. Certainly, it holds when the demand is than that of others. The larger the altruistic preference,
concave. By examination, we find that Assumption 1 is the more altruistic the firm will be.
true for most demand functions (e.g., exponential de- The decision mechanism here is exactly as that in the
mand pep and linear demand pp scenario (DS). That is, first the manufacturer chooses w
for 0, power demand pp  with 1). and a , and then the retailer decides p, q, and a .
m r
Hence, the coopetition of the supply chain (denoted by
2.1. Integrated Supply Chain CS) can be formulated as
For the integrated supply chain (IS), both the manufac- Stage 1: maxU
m
turer and the retailer belong to the same enterprise with w,am (DS)
Stage 2: maxU
the total profit π . Thus, the problem is to maximize π r
s s p,q,ar
by choosing a ,q,p and a :
m r Clearly, (DS) is a special case of (CS).
max π pc c q pFxdxa a . (IS) We use superscripts D, C, and I to designate three
am,q,p,ar s m r A m r scenarios in this paper, (DS), (CS) and (IS), respectively.
For uniform symbol definition, π will be rewritten Remark 1
s
as U in the remainder. 1) Another interpretation of Equation (5) is that each
s
firm wants to maximize the weighted sum of his/her own
2.2. Decentralized Supply Chain profit and the chain’s profit. Then, the utility of the
manufacturer is π 1π π π 1π
In the decentralized supply chain (DS) the manufacturer, m m r m r
for any given parameter , which means  1.
as a leader, chooses her wholesale price w and brand m
The same with the retailer.
name advertising level a . Then the retailer chooses the
m 2) It should be noted that U U U when both
order quantity q, sales effort level a , and retailing price m s r
r  and  approach to 1, but (CS) here is not the in-
p as his response. They both want to maximize her/his m r
tegrated scenario, since (CS) is still a decentralized sys-
own expected profit by playing a Stackelberg game as
tem with the manufacturer and the retailer as its two de-
follows,
cision makers. However, this should be studied using a
Stage 1: maxπ , different method. Hence, we do not give much attention
m
w,am (DS) to it in this paper.
Stage 2: maxπ .
r
p,q,ar
3. Nash Equilibrium
This will be solved by the backward method in the
next section. In this section, we solve the three scenarios. Before doing
this, we first make some preparations.
2.3. Coopetitive Supply Chain
3.1. Some Preparations
In the literature of SCM, it is assumed that all members
in the supply chain exclusively pursue their own profits We will introduce two functions  p and M p
w w
and do not care about “social” goals per se. As we have in this subsection. For the first function  p, we con-
w
explained in the Introduction, firms may care about oth- sider a basic decentralized setting where
ers’ profits in order to enhance the system’s compete- 1) both effort levels a and a are exogenous, i.e.,
m r
tiveness. Certainly, they still pursue their own profits at constant; and
the same time. That is, they may be both egoistic and 2) the demand is deterministic, i.e., 0.
altruistic. When making decisions, each firm may trade So we can assume that the demand is
off its own profit together with their partner’s profit. For Ddpp. This basic setting will be used to
this, we introduce altruistic preferences  and  for compare our results with those in the literature.
m r
the manufacturer and the retailer, respectively. Since the supply chain is decentralized, we can get the
In this paper, we model altruistic preferences in firms’ following result when qp (it is essential to as-
utilities by adopting a weighted summing formulation. sume a a 1)
m r
This mean the utilities of the manufacturer and the re- π w,p,q,1,1 pEminq,pwc q
tailer are, respectively, r r
pwc pwc qp
U π π , r r  
Umπmmπ r. (5) pwc pπ w,p,p,1,1.
r r r m r r
It is assumed that both  and  belong to [0,1), Similarly, we still have the same result when
m r
Copyright © 2012 SciRes. AJOR
Z. H. GE ET AL. 63
qp. Therefore, it is optimal for the retailer to order lowing condition that an optimal price must satisfy:
qp for any given w and p. Then the retailer’s
profit (denoted by p) in the basic decentralized set- 0q ppamsartF()AFd
ting is  pπ w,p,p 1cm p1ttss pppcm cr
w pr wc p, (6) F1pcmcr pFdA
r A
pwcr. 1 p1ttss pF1pcmcr pFdA
cm cm A
The following proposition shows the existence and M p.
uniqueness of the optimal retail price in this basic setting. cm
Proposition 2 There exists a unique optimal retail (10)
price p* at which  p is maximized. Hence, the solution of Equation (8) can be found by
w w
The second function is defined by solving Equation (10), which includes only one variable
p. Actually, M p represents the marginal profit of
M p AF1pwcr pFd the integrated sucmpply chain on the retail price whenever
w A
the other decision variables change with p according to
 ts
12awm1stpw1(tps1twtpw,p  w wccmm, (7) p(9r)oT.f ihHt eeoorfre (eaIfmSte) .r1 ,T wUheins d cseahrlol owpMst itcmhmea lfpiotyll ofaownri na(IguS gt)mh, eteohnrete emodp .m ti maragli nrae-l
tail price satisfies M p0, and a , a , and q are
1 t cm m r
for any wc , where 1 sstt1ts and 2 t1t determined by Equation (9).
m From the theorem above we know decision-making in
are two constants determined by s and t, and (IS) can be realized by solving M p0. Thus, it is
F1F. The meaning of Mwp will be given important to judge the sign of M cmp for any given p.
in the following subsection. Here, we get one proposition cm
finrogTPm hr Moeth pwemo sciipontniiomt inniu num3 i t Tycoh mofe fr eMc Mmrw,wupsptp .e ,x .i is. te .a, pMricwe ppw**w** , mwinililm ibze- iaNnno dLRtwh eee mmwp bc*meem*am safui bcre 1tpdrh c*iemencrMg ed wnctimhtshrcaeautnlp isezsvpe esdc*mor 0 sm e iMetsft oipctnmrhrg oe,p a prLelce*lrm*e ttamieiplmse r0oa’f s. 1 co Mmepstctimamcbral,pilsp hpc*.mer is c ae,
used to judge whether the Nash equilibrium exists in the
comparison of p* with the minimizer of M p.
following subsections. cm cm
When the augmented marginal profit in (IS) is non-posi-
3.2. Optimal Solutions of (IS) tive, i.e., Mcm p0, the supply chain has no incentive
to further increase the retail price. In fact the chain will
In this subsection, we get optimal solutions for scenario drop the retail price in order to increase its profit. Then,
(IS). Its first-order condition is obviously as follows, the optimal retail price (denoted by pI ) in (IS) should
U pq ppasatFFd0, be larger than the basic decentralized pricing pc*m, as
 s m r A shown in the following theorem, where the existence of
U q pFc c 0, the optimal solution for (IS) is proved. In the theorem,
 s m r (8) we denote by Npp,qp,a p,a p the solu-
U a sppas1atF10, m r
s m m r tion induced by the retail price p for (IS) via Equation

Us ar tppamsart1F10. (9).
Theorem 2 For (IS), there must exist an optimal solu-
By using some mathematic technologies we can get tion pI,qI,aI,aI. Moreover,
am, ar, and q, as functions of p as follows. 1) if M pm**r0 then there is an interior solution
a1rts sst1scm p pI pc*m,cpmc*m*c msatisfying
am 1cm p11ts (9) McmpcIm0,Mcm pcIm0. (11)
 ts Furthermore, for any pI c c ,p satisfying Eq-
q1pcm p1ts F1pwcr p uation (11), NpI must be a mlocalr optimal solution of
(IS);
We write as ap , a p, and qp when nec-
m r 2) If M p**0, the optimal solution is Np;
essary. Substituting the above three equations into the cm cm
first equation in (8) and rearranging it, we get the fol- 3) If M p**0, the optimal solution is either
cm cm
Copyright © 2012 SciRes. AJOR
64 Z. H. GE ET AL.
Np** or Np. and a of the manufacturer.
cm The mfirst-order condition for the retailer is
We make no direct restriction on the distribution func-
otiuorn imFport,a ntht oreusguhl tist ims tahya ti nthfleu eonpctiem aMl rcemtaiplc *m*pri.c eO inne ( IoSf ) Us pq ppamsartFAFd0,

is larger than the one obtained in the basic decentralized U q pFwc wc 0, (12)
s r r m
setting; i.e., pI  p* . This result comes from our in- 
corporating with unccemrtainty demand and ASE, since the Us ar tppamsart1F10.
retailer sets a higher price so as to mitigate the effects of
uncertainty and promoting effort. Similar to (9), we get
The second result in Theorem 2 refers to such a non-
a1t tas p
normal market in which the augmented marginal profit is  r m w
always positive, no matter how high the retailing price is.  s t (13)
In this type of market, the retailer will set p to be the up- q2am1tpwp1t F1pwcr p
per bound p. When p is sufficiently large, it is obvi-
ous that Npp,B,0,0 in this time. That is, the where wwrwcm . Substituting (13) into the
first equation in (12), we obtain
retailer will order a quantity of B, and the deterministic
pstaorct koefd tohnel yd efmora nmda tacphpinroga tchhee ss ttooc hzaesrtoic, aplal rtB o uf ntihtes daree- 2a1st p1tt pF1pwcr pFdA
m w w A (14)
mand. Furthermore, both manufacturer and retailer need
M p0.
no advertising/sales efforts. Such a case is the contingent w
market, where almost all inventories meet emergencies,
There exist solutions of Equation set (12) as long as
and then retailers are inclined to bid up price. Therefore,
Equation (14) has roots. Thus, the existence of an opti-
this type of market would be better to be supervised by
mal response from the retailer can be obtained by solving
the government (e.g., a market of such products against M p0. Then, similar to Theorem 2, we have the
food crisis). w
following result about the retailer’s optimal response in
From the proof of Theorem 2 we know that if the scenario (CS). Here, we denote by NRpp,qp,
tMhec mfollpowin0g cthoeronl lapry . would not be optimal. This shows amp,arp the solution of the retailer induced from
p.
Corollary 1 If M p0 and Equation (11) has a
unique interior soluticomn pI cm cr,p, then NpI pThwe,oarem,q 3 wTh,aere ,maustw e,xaist an fooprt itmhea lr reetaspiloenr sien ( CS),
is the unique optimal solution of (IS). m m r m
provided with wc and a 0. Moreover,
Moreover, we present a sufficient condition to ensure 1) if M p**0m then thmere is an interior solution
the uniqueness of solutions for Equation (11). pCp* wc ,wp** satisfying
Proposition 4 If M p0 is downwards unimo- w r w
dal, Equation (11) has ac munique solution in c c ,p.
m r M pC0,M pC0. (15)
The proof of the proposition is obvious. w w
Remark 2 A given function is downwards (upwards)
Furthermore NRpC must be a local optimal re-
unimodal in an interval a,b, if and only if it has the
sponse of the retailer;
unique minimal (maximal) point x* and is monotone on
2) If M p**0 then the retailer’s optimal re-
either side of x* in the interval (see e.g., [38]). In the w w
sponse is either NRp or NRwc ;
following two special cases, the downwards unimodality 3) If M p**0 then the retailrer’s optimal re-
of M p is clear. w w
cm sponse is NRp**, NRwc , or NRp.
1) The stochastic portion  in the demand follows a w r
uniform distribution on A,B. Theorem 3 gives the retailer’s optimal response to the
2) The deterministic demand is linear in p, i.e., manufacturer. Thus p, q, and a are functions of w and
r
pQkp, where Q and k are constants and a , respectively. A sufficient condition to guarantee the
m
pc c ,Q k. In fact, one can examine that M p uniqueness of these response functions is that M p
is incremasinrg in pc c ,Q k when ts0.5. cTmhen, is unimodal. Substituting the functions into the manwufac-
m r
it is easy to conclude that M p is downwards uni- turer’s utility yields
cm
modal.
U w,a U w,a ,qw,a ,pw,a ,a w,a 
m m m m m m r m
3.3. Nash Equilibriums of (CS) π w,a  w,a ,
m m m r m
First we consider the retailer’s response provided with w The first-order condition for the manufacturer is
Copyright © 2012 SciRes. AJOR
Z. H. GE ET AL. 65
1mrwcmq w1mq0, (16) Table 1. Nash equilibria and profits when s = 0.15, t = 0.1.
1mrwcmq am1msar tam0. S m r w p q
Therefore, we can obtain the manufacturer’s best re-
(IS) - - - 9.202 10.756
sponse according to Equation (16).
(DS) 0 0 7.349 11.790 4.386
3.4. Comparison of Scenarios
(CS) 3/7 0 5.744 11.011 6.043
In this subsection, we compare retailer’s order quantities
(CS) 0 1/4 9.137 11.785 4.626
given the three scenarios. Denote the solutions in (DS),
(CS), (IS), as wD,aD,pD,qD,aD, wC,aC,pC,qC,aC, (CS) 2/3 1/4 5.822 10.583 7.172
m r m r
and wI,aI,pI,qI,aI, respectively. The following theo- S a a π π π
m r m r m r s
rem compares the order quantities.
(IS) 8.967 5.974 - - 47.648
Theorem 4 For the order quantities in the three sce-
narios, we have qI qC qD. (DS) 3.727 1.391 19.734 13.076 32.810
From the theorem above, cooperative incentives in-
(CS) 5.103 2.369 17.522 22.284 39.806
crease the retailer’s order quantity (vs. scenario (DS)).
On the other hand, the order quantity in (CS) may be (CS) 5.229 1.469 27.789 5.531 33.320
lower than that in (IS) because of the existence of the
(CS) 6.710 3.105 20.700 22.342 43.042
competitive incentives. Thus, the coexistence of compe-

tition and cooperation makes firms’ decisions inconsis-
observation above further illustrates not only this fact,
tent with those in (IS) or (DS), just between those of (IS)
but also all the other decisions and profits of the chain.
and (DS).
Figures 2-5 and Figures 6-9 show changes of deci-
sions and profits, respectively, with the altruistic prefer-
3.5. Effects of the Altruistic Preferences on
ences. From Figures 2, 3, and 6, 7, we find that for any
Decisions and Profits
given  , there is a switching level, denoted by * for
m r
This section gives some meaningful observations by the retailer, such that when  * is large enough, an
r r
analyzing numerical results. Especially, we focus on the altruistic retailer sets his optimal price as low as possible,
effects of the altruistic preferences on decisions and that is, pC wC c under the constraint pwC c .
r r
profits in (CS) (certainly, including (DS) as a special As a follower in the game, the retailer in this circum-
case). We assume the base price-demand function p stance benefits nothing from the selling, but has to suffer
to be linear, that is, pQkp for some positive from the effort and demand uncertainty, and thus has a
constants Q and k. Surely, the domain of the retail price negative profit, due to being too altruistic. Similarly,
is 0 pQ k . Furthermore, it is assumed that  from Figures 8 and 9, the manufacturer has negative
follows an exponential distribution with rate of , i.e. profit if she is very altruistic ( * for some * ,
m m m
f e when 0; otherwise f 0. Let which is near 1). We call this phenomenon “doing for
c 2, c 1, 1, Q15, k 1. others”. Moreover, the switching level for the manufac-
m r
Table 1 gives some numerical results under s0.15, turer is higher than that for the retailer, which implies
t0.1, in which the values of (DS) corresponds to a that the retailer is more likely to suffer from being too
classical scenario presented in the previous literature in altruistic than the manufacturer. This may be due to the
Figure 1. By comparing the Nash equilibria and profits manufacturer’s first-mover advantage.
for (IS), (DS), and (CS) given in the table, we find a rea- From the switching level in Figure 3, we know that as
sonable explanation why decisions diverge in reality, retailer’s altruistic preference 0,* increases, so
r  r
which is just our main contribution. Moreover, we get the does the wholesale price w and the retail price p, causing
following interesting observations different with those in demand to decrease along with the retailer’s order quan-
the current literature. tity q and effort a . But when the retailer is too altruistic
r
Observation 1 Among three scenarios, (IS) has the with  *, he is “doing for others”. So, both w and p
r r
highest chain’s profit, order quantity, advertising, sales decrease, and the demand increases along with q and a .
r
effort level, and the lowest retail price; Conversely, (DS) This switching becomes more serious as the manufac-
has the lowest chain’s profit, order quantity, advertising, turer’s altruistic preference  increases. In fact, when
m
sales effort level, and the highest retail price; And (CS) is  0, q and a increase a little in  * (Figure
m r r r
between (IS) and (DS). 2).
We have shown in Theorem 4 that the order quantity On the other hand, it can be seen from Figures 4 and 5
under (CS) is between those of (IS) and (DS). Now, the that the effect of the manufacturer’s  on decisions is
m
Copyright © 2012 SciRes. AJOR
66 Z. H. GE ET AL.

Figure 2. Decision shift with η. Figure 5. Decision shift with η .
r m

Figure 3. Decision shift with η. Figure 6. Profit shift with η.
r r

Figure 4. Decision shift with η . Figure 7. Profit shift with η.
m r
Copyright © 2012 SciRes. AJOR
Z. H. GE ET AL. 67
truistic preferences affect the profits of the manufacturer,
the retailer, and the system. In general, firms are willing
to benefit their partner only when they face positive prof-
its. Then, our analysis in the following focuses on the
normal circumstance in which both firms have positive
profits and so have incentives to participate (especially,
 * and  *). However, firms should not be
m m r r
too altruistic, i.e., their altruistic preferences should not
be too great. Hence, it is reasonable to limit our discus-
sion below in  * and  *.
m m r r
First, from Figures 6-7, one can find that the profits of
the retailer and the supply chain decrease with  but
r
that of the manufacturer increases in the region where
both firms have positive profits. However, Figures 8-9
show the inverse result.
The above observation is also to say that the profits of

both the manufacturer and the retailer decrease with their
Figure 8. Profit shift with η.
r own altruistic preference, but increase with the other’s

preference. That is,
π 0,π  0,i, jm,r,i j.
i i i i
Moreover, the profit of the supply chain decreases
with  and increases with  , i.e.,
r m
π  0,π  0.
s r s m
This implies that with change of the altruistic prefer-
ences, the retailer’s and the chain’s profits change in the
same direction, while the manufacturer’s profit changes
in the reverse direction.
By classifying the members as egoistic liability (when
his/her altruistic preference is low, henceforth, E) or al-
truistic liability (when his/her altruistic preference is high,
henceforth, A), we divide supply chains into the follow-
ing four types where M and R represents the manufac-
turer and the retailer, respectively.

Figure 9. Profit shift with η.
r
AA AE
(Altruistic M, Altruistic R) (Altruistic M, Egoistic R)
very regular and simple: with increase of  , both
m
prices w and p decrease while other decisions q, a , and EA EE
r
a increase. This surely benefits the supply chain (see (Egoistic M, Altruistic R) (Egoistic M, Egoistic R)
m
Figures 8 and 9).
Among all decisions, the retail price p is the weakest For example, type AA represents supply chains where
one affected by altruistic preferences, while the whole- both the manufacturer and the retailer have altruistic li-
sale price w is the most seriously affected. One possible abilities, and Type AE represents supply chains where
interpretation of this is that the retail price is mainly de- the manufacturer has altruistic liability but the retailer
termined by the market, other than by type of supply has egoistic liability. Then, we get the following obser-
chain, while w directly reflects the profit allocation be- vation for comparing the four types from the monotone
tween the retailer and the manufacturer. properties of the profits discussed above.
By comparing Figures 2 and 3 with Figures 4 and 5, Observation 2 The supply chain with Type AE is the
we find that an altruistic manufacturer will lead to high best for both the system and the retailer, while the supply
qC,aC,aC, and low wC, and also to high profits for chain with Type EA is the best for the manufacturer.
m r
the retailer and the supply chain. As for the type of re- It is intuitive that either the manufacturer or the retailer
tailer, its influence is not serious. may be damaged from being too altruistic, if his/her
In the following, we focus our attention on how the al- partner is too selfish. But it is interesting to discover that
Copyright © 2012 SciRes. AJOR
68 Z. H. GE ET AL.
the chain will be damaged from an altruistic retailer but With this, each firm considers not only his own profit but
benefited from an altruistic manufacturer. also the partner’s one when making decisions.
We further observe from Figures 6-9 that in compare- One of our important finds is that all the decisions and
son to  , the effect of  on π and π is more performance in the supply chain of the coopetitive sce-
m r m r
serious but the effect on π is less serious. In a word, nario are between those of the other two scenarios. An-
s
the profits of both firms change with  more sharply other important find is that a supply chain will benefit
r
than with  ; while π increases more sharply with when the manufacturer is altruistic, having concern for
m s
 . Especially, when the manufacturer is not too altruis- the total profit of the supply chain, and the retailer is
m
tic, e.g.,  0.2 when  0 or  0.2 when egoistic, only having concern for himself. This find may
m r m
 3 7, the increase of  would not reduce her own benefit firms in finding a suitable partner to form a good
r m
profit but increase both the retailer and the chain’ profits. supply chain (i.e., with larger profit).
But if the retailer increases his altruistic preference a However, we have not obtained enough analytical re-
little, he has to suffer a significant loss and so does the sults on the effect of altruistic preferences on the firms’
chain. Thus, we have the following observation. decisions and profits. This may be left for further re-
Observation 3 A manufacturer with altruistic liability search, though it may prove to be quite challenging. An-
will benefit both the supply chain and the retailer but other area for further research is to consider multiplica-
would not hurt herself, while a retailer with altruistic tive demand. Finally, it is interesting to consider the al-
liability will hurt both himself and the supply chain. truistic preferences in other models for supply chain
By summarizing the above discussions, we present the management.
following proposition.
5. Acknowledgements
Proposition 5 In order to form a good supply chain
with one manufacturer (as the leader) and one retailer
We would like to thank Yusen Xia, seminar participants
(as the follower), a manufacturer should find an egoistic
at the Fudan university for thoughtful comments. The
retailer, while a retailer should find a manufacturer who
project is supported in part by the National Natural Sci-
has altruistic liability.
ence Foundation of China through grant 71101092 and
One main insight of this paper is given in the proposi-
70832002, Shanghai Leading Academic Discipline Pro-
tion above. That is, the manufacturer, as the leader of the
ject (Number B210, S30501), Doctoral Fund of Ministry
game, should be in charge of the supply chain. This im-
of Education of China (20113120120012), and Shanghai
plies that she should consider not only her own profit but
Innovation Fund (11YS122).
also the retailer’s profit, i.e., the profit of the whole sup-
ply chain. So, the manufacturer behaves like a govern-
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