Journal of Service Science and Management, 2011, 4, 1-7
doi:10.4236/jssm.2011.41001 Published Online March 2011 (http://www.SciRP.org/journal/jssm)
1
Research on Supply Chain Coordination of TPL
Supplier Participation*
Yun Liang1, Xiaode Zuo2, Hong Lei2
1Business Administration Department, Gangdong University of Finance, Guangzhou, China; 2Management School of Jinan Univer-
sity, Guangzhou, China.
Received October 8th, 2010; revised November 9th, 2010; accepted November 14th, 2010.
ABSTRACT
This paper used the Game Theory to research how to coordinate a kind of supply chain, which is made up of a domi-
nant manufacturer, a TPL supplier and some retailers. It also discussed the node enterprises’ decision models in three
situations: no coordination, partly coordination and all coordination based on symmetric information and proved sys-
tem’s profit was optimal in the situation of all coordination. And then some ways of profit distribution were laid out.
Finally, verified the validity of the models and ways of profit distribution throug h examples.
Keywords: Supply Chain Coordination, Third Party Logistics, Profit Distribution
1. Introduction
Enterprises tend to enhance their core competence through
outsourcing logistics service under the fierce market
condition. The demand for third party logistics, TPL for
short, has growing gradually, so people pay more atten-
tion to the relationship between TPL providers and TPL
demanders. Aidan. Reference [1] established a logistics
service pricing model, which optimized the profits of
both parties in a simple supply chain based on the as-
sumption of linear demand. Reference [2] compared the
pricing and profit conditions of TPL provider and de-
mander before and after cooperation. Reference [3] ana-
lyzed some horizontal methods of the two parties used to
coordinate the conflicts and contradictions in the out-
sourcing process. Reference [4] used game theory to
study the coordination problem in a supply chain com-
posed of a manufacturer, a TPL provider and a retailer.
Reference [5] designed a TPL revenue sharing contract,
and proved that this contract can form a sound internal
incentive mechanism through a dynamic game approach.
It can be found that, current research mainly focus on
the coordination issue between TPL provider and a single
TPL demander. Little has done on the game relationship
and coordination mechanism among the TPL provider,
upstream and downstream enterprises. Also the condition
of more than one retailer and partial cooperation has sel-
dom been paid attention to.
2. Model Description
Gong Deyan [6] established a supply chain model with a
manufacturer, a retailer and a TPL provider. The differ-
ence between this paper to his is that, more than one re-
tailer was considered, and the situation of partial coop-
eration was discussed, which makes the analysis more
practical and can obtain more new conclusions. Node
enterprises operated themselves as follows: first, the
manufacturer selected a profit-optimizing wholesale
price, ; retailer selected a service price , which
can maximize his own profit based on the given whole-
sale price; finally, retailer i decided his optimal i
and order quantity i. l was shared by the manufac-
turer and TPL together, and the sharing ratios are 1
m
pl p
p
q p

,
2

respectively. The costs of manufacturer, TPL and
retailer are , , .
m l r
The following assumptions were made:
cc c
Assumption 1: Information was perfectly symmetrical
through the whole supply chain.
Assumption 2: All supply chain members were
risk-neutral, and they were to maximize their own prof-
its.
Assumption 3: The market demand is a linear function
of the retailer price, that is, , and a,
were constants, a > 0, b > 0.
pabQ b
*This paper is funded by the 211 Engineering Program of Jinan Uni-
versity, Pre-Funded-Research of Management School.

Research on Supply Chain Coordination of TPL Supplier Participation 2
Assumption 4: The unit cost and wholesale price for
each retailer are the same.
Assumption 5: The manufacturer’s capacity and TPL’s
ability were large enough to satisfy all demands..
3. Set up and Solve the Model
3.1. Decentralized Model
The manufacturer, TPL provider and retailers made their
own decisions separately, that is, no alignment has been
formed. So the Stackelberg model is:
 
1
max mmm ml ppcp   Q
 
..max lll l
s
tppc  Q

2
..max riiirml i
s
tppcpp   q
j

q 
Adopt the reverse inductive method, all the members’
price decision can be solved as followed:
Phase 1, retailer will optimize his profit on a given
, which is
i
l
p


2
2
max
riiirml i
rlml i
ppcp pq
abQc ppq




 
Suppose , we can get,
i
QqQ


2
max riii jrlmli pabqQcpp 

 ,
2
2
ri ij rlm
i
bqbQa cpp
q

l


 

Because , Qnq
j
ii
QQqnqq 
i
Therefore,

2
21
ri irlm
i
bnqa cpp
ql



 


Let it equals 0, it can be solved that,

2
1
rl ml
i
ac pp
qbn



 So,


2
1
rl ml
i
na cpp
Qnq bn



 
Phase 2, TPL provider will optimize his profit at a
given ,
m
p



max lll l ppc  Q
Substitute the value of Q, we can get,
2
2
2
lri m
l
accp
p




Phase 3, the manufacturer optimizes his profit,
 
1
max mmm ml ppcp   Q
Substitute the value of Q and , the optimal ,
is arrived.
l
pm p
*
m
p
2
*22
21
ml
m
ac cc
p




ri
Then we can get the optimal and :
*
l
p*
i
p



2 *
2
21
21
lrm
l
accc
p






,

*2
2
21 1
inR
pa n


 
The total order quantity of all retailers is:
 
*2
2
21
nR
Qbn


1
So the profit of each supplier is:

2
*2
2
41
mnR
bn


1

,
 
2
*2
2
2
41 1
lnR
bn


 ,
 
22
*2
22
2
41 1
ri R
bn



The profit of the whole supply chain is：

 
 
222
22
****
22
2
122
41 1
scm lr
nnnn R
bn

 
  
 
2
Here, 0
rml
Rac cc

 
3.2. Centralized Model
Ye Fei and Li Yina [7] discussed the cooperation problem
of a type of three-echelon supply chain with a manufac-
turer, a wholesaler and a retailer. Consider the partial
cooperation in their paper, the following forms of alli-
ances can be induced.
1) The manufacturer and TPL provider form a small
scale alliance, and the retailers are not included. So the
Stackelberg model should be:



 
2
max ,
mlmlmml l
ppp c cpQ   




2
..max riiirml i
s
tppcpp   q
Solve the model with reverse inductive method,

**
21
nR
Qbn 

,

**
21
inR
pan  


2
**
41
ml nR
bn
 

,

2
**
2
41
ri R
bn
 ,



2
** 2
2
2
41
sc
nn
R
bn



2) TPL and retailers form a small scale alliance, and
the manufacturer is not included. Now the Stackelberg
model is:




1
max mmm ml ppcp   Q

Research on Supply Chain Coordination of TPL Supplier Participation 3
 
1
..max ,
lrliirlm l
s
tpppccp   pQ
Solve the model, we can get: ***
4
R
Qb , ***
4
iR
pa

,
2
***
8
mR
b
 ,

2
***
16
lr R
b
 ,
2
*** 3
16
sc R
b
 
3) The manufacturer and retailers form a small scale
alliance, and TPL provider is not included. The Stackel-
berg model is:

max mr irml pcc pQ  

 
..max lll l
s
tppc  Q
Solve the model,
****
4
R
Qb , ****
4
R
pa ,
2
****
8
lR
b
 ,

2
****
16
mr R
b
 ,
2
**** 3
16
sc R
b
 
4) The manufacturer, TPL provider and retailers form a
large scale alliance and make decisions together, so the
profit function of the alliance is:



mlrii imlr
ppccc  Q
Solve the function, *****
2
R
Qb ,
*****
2
mlr
i
acc c
p ,
2
*****
4
sc R
b
 
3.3. Model Analysis
Conclusion 1: In the decentralized model, with the in-
crease of 2

, the retailer price decreases, the sales vol-
ume increases, and the profits of the manufacturer, re-
tailer, TPL provider and the whole supply chain increases.
Their profits reach the peak when 21

.
Prove: from
 
*2
2
2
21 11
211
inR nR
pa a
nn



 
 



,
it is found that is an decreasing function of
*
i
p2

.
From
 
*2
2
2
21 11
211
nR nR
Qbn bn




 



, we
know is an increasing function of
*
Q2

.
And

2
*
2
1
411
mnR
bn






,

2
*
2
2
1
41 1
lnR
bn







2
*
2
2
2
1
411
ri nR
bn






Because 21


, m

, l

, ri

are increasing func-
tions of 2

, and from
s
cmlr

  , so
s
c

is an
increasing function of 2

too. And when 21


, m

,
l

, ri

,
s
c

reach their peak value.
Conclusion 1 explains that, when outsourcing logistics
service to TPL, the manufacturer burdens a low fee rate
1

, that lowers his wholesale price, which in turn to re-
duce the retail price and increase the sales volume (de-
creasing rate of retail price is smaller than the increasing
rate of sales volume), and finally all parts’ profit are im-
proved. Therefore, the supply chain can get a Pareto im-
provement through rational sharing of logistics fee be-
tween the retailers and manufacturer.
Conclusion 2: In decentralized model, along with the
increase of , retailers’ retail price and order quantity
will increase, the profits of the manufacturer and TPL
provider will increase, but retailer’s profit will decrease.
n
Proof: from
 
*2
2
2
1 21 121 1
inR R
pa a
n
n


 
 



2
, it is easy
to find out that is a decreasing function of .
*
i
pn
From
 
*22
2
2
1
21 1
21 1
nR R
Qbn bn



 



, we
know is a increasing function of .
*
Qn
From

2
*2
2
1
41 1
mR
bn








,

2
*2
2
2
1
41 1
lR
bn







,
 
22
2
*2
2
2
41 1
ri R
bn

  , It
can be found that m

, l

are increasing functions of
but nri

is decreasing function of . n
Conclusion 2 tells that, the manufacturer will choose
more retailers to lower the retailer price, thus to increase
the sales volume and enhance his own profit; however,
the retailer expects fewer competitors, thus he can in-
crease his profit by raising retail price.


,
Conclusion 3: In the centralized model, when the three
form a big alliance, the whole supply chain’s profit
reaches the highest point and vise versa. In types of co-
operation relationship, supply chain’s profit is maximized
in the manufacturer- TPL case. That is,
**** **** *******
sc scscscsc
   
Proof:

Research on Supply Chain Coordination of TPL Supplier Participation 4

  
2
2
**** 222
22 22
2
232233 1
16 11
sc scR
nnnnn bn
 

  


a) when ,
1nSuppose that the revenue distributing coefficients of
manufacturer, TPL provider and retailer are respectively
m, l, r, and kkk1 mlr
kkk

. Only when each
party’s profit of a large scale alliance is bigger than that
of the small scale alliance and even no alliance, supply
chain members have the motive to participate in a large
scale alliance.

 
2
****
222
2
42 30
16 11
sc scR
bn
  
 , then
****
s
csc

 ;
b) when, 1n



2
222
22 2
2322331fnnnn n   

is
a concave parabolic curve with the vertex Y-coordinate 4.1. Revenue Distribution Based on Nash
Bargaining Model



2
2
2246
3143 1
nn
nnn



0
0
.
Take each party’s revenue (no alliance situation) as the
bargaining points, i.e., *
m

, *
l

, *
r

are bargaining
points, establish a bargaining model to solve each’s re-
venue after cooperation based on Nash bargaining model.
Since , , it
can be induced that ,
 
2
031fn

20f
 
0

1812fn 
01
2


0
And from , so
 
2
031fn 

18fn 120 

0f  , , 2 01






 
***** ****** ****** *
max mscmlsclrscr Zkk k

     
2
And , which means
****
0  
scsc 
..
s
t ******
msc m
k

 , ***** *
lscl
k

 , ***** *
rscr
k

 
**** ****
scsc
  (1)
 
**
*****
mlscm l
kk  

Since

2
****** 13
16
sc scR
nn
b
  0, so

***
*****
lrscl r
kk  
**** **
s
csc

  (2)
 
****
*****
mrscm r
kk  
That is, , so
** *****10
sc sc
 
1
mlr
kkk

 ** *****
sc sc
  (3)
4.2. Revenue Distribution Based on Minimum
Core Method
Combine Function (1), (2) and (3), it can be concluded
that,
According to minimum core method, a linear planning
model is set up as follows:
**** **** *******
sc scscscsc
   
Conclusion 3 shows that, in the large scale alliance
case, all parties enhance supply chain’s profit through
reducing retail price and increasing sales. Therefore, in
this case, not only all supply chain members maximize
their profits but also customers are well off. However,
partial cooperation can be a compromise if evitable ob-
stacles exist in the process of all-round cooperation.
Moreover, among the types of partial cooperation, supply
chain’s profit is maximized in the manufacturer-TPL case,
which tell us that the retailer’s competition can make
customers, TPL and the manufacturer well off.
min

,
..
s
t ******
msc m
k

 , ***** *
lscl
k

 , ***** *
rscr
k

 

**
*****
mlscm l
kk  

,
 
***
*****
lrscl r
kk  ,

****
*****
mrscmr
kk  
1
mlr
kkk


4.3. Revenue Distribution Based on Simplified
MCRS Method
4. Revenue Distribution under Joint Decision
Making According to simplified MCRS Method, the linear func-
tion group is set up as follows:
From the above analysis, it is clear that large scale alli-
ance can bring about greatest profit. However, revenue
conflict will lead to inefficient cooperation, the supply
chain can only be coordinated through reasonable fair
distribution of revenue.


minmax min
*****
1
, ,,
jjj j
n
jsc
j
jmlr  


 





Research on Supply Chain Coordination of TPL Supplier Participation 5
And, maxj

, minj

are defined as:



***
*****
max
****
*****
max
**
*****
max
**
minmin min
,
,
,
, ,
msclr
lscmr
rscml
mmllr

 
 
*
r

 









5. Numerical Analysis
Utilizing some data from reference 4 and 6, the parame-
ters’ value are set as follows: , , 30a0.2b5
m
c

,
, ,
2
l
c3
r
c20.8

.
1) 2

’s influence on order quantity, all parties’ pricing
decisions and profits.
When : 3n
From Figure 1, it’s clear that along with the increase
of 2

, the wholesale price, logistics service price and
retail price decrease while the order quantity increases,
and the increase rate of is bigger than the decrease
rate of .
Q
i
And from Figure 2, when 2
p

increases, all parties’
profits as well as the whole supply chain’s profit increase.
They reach the peak when 21


.
2) ’s influence on order quantity, all parties’ pricing
decisions and profits.
n
From Table 1, in the decentralized model and small
scale alliance situation, the order quantities increase with
the increase of , and when retailer is included into the
alliance, i.e., the large scale alliance situation, the value
of has no effect on order quantities.
n
n
From Table 2, in the decentralized model and small
scale alliance situation, the retail prices increase with the
increase of , and when retailer is included into the
alliance, i.e., the large scale alliance situation, the value
of has no effect on retail prices.
n
n
From Table 3, in the decentralized model and small
scale alliance situation, the total profits of the supply
chain increase with the increase of , and when retailer
is included into the alliance, i.e., the large scale alliance
situation, the value of has no effect on total supply
chain profits. And in the decentralized model, the profits
of manufacture and TPL provider increase with the in-
crease of , and the retailer’s profit is just opposite.
Therefore, the manufacturer can increase the whole sup-
ply chain’s profit and his own profit by increasing the
number of retailers, but he should consider some bad
effects such as retailers’ joint boycotts.
n
n
n
3) the comparison of order quantity, retail price and
sales volume and profit under three circumstances.
From the three above tables, it can be concluded that
in decentralized model, the order quantity was minimized,
Figure 1. 2

’s influence on order quantity, all parties’ pricing decisions.
Figure 2. 2

’s influence on all parties’ profits and total supply chain profit.

Research on Supply Chain Coordination of TPL Supplier Participation 6
Table 1. Order quantities in all situations.
Decentralized decision Small scale alliance Large scale alliance
Q
* Q ** Q *** Q **** Q *****
n = 1 11.111 25.000 25.000 25.000 50.000
n = 2 14.815 33.333 25.000 25.000 50.000
n = 3 16.667 37.500 25.000 25.000 50.000
n = 4 17.778 40.000 25.000 25.000 50.000
n = 5 18.519 41.667 25.000 25.000 50.000
Table 2. Retail prices of all situations.
Decentralized decision Small scale alliance Large scale alliance
p
i* p i** p i*** p i**** p i*****
n = 1 27.778 25.000 25.000 25.000 20.000
n = 2 27.037 23.333 25.000 25.000 20.000
n = 3 26.667 22.500 25.000 25.000 20.000
n = 4 26.444 22.000 25.000 25.000 20.000
n = 5 26.296 21.667 25.000 25.000 20.000
Table 3. Supply chain member’ profits and total profits of all situations.
Decentralized decision Small scale alliance Large scale
alliance
πm* πl* πr* πsc* πsc** πsc*** πsc**** πsc*****
n = 1 111.111 61.728 24.691 197.531 375.000 375.000 375.000 500.000
n = 2 148.148 82.305 21.948 252.401 444.444 375.000 375.000 500.000
n = 3 166.667 92.593 18.519 277.778 468.75 375.000 375.000 500.000
n = 4 177.778 98.765 15.802 292.346 480.000 375.000 375.000 500.000
n = 5 185.185 102.881 13.717 301.783 486.111 375.000 375.000 500.000
the retail price was the highest and the total profit was
the lowest, while in large scale alliance case they are
totally opposite. And in the small scale alliance case, the
total profit maximized when the manufacturer and TPL
provider form the alliance.
Use Excel and Lingo to calculate the profits of all par-
ties and their growth rates under different revenue distri-
bution method, the results are shown in Tables 4 and 5.
It is clear that in this numerical case, when adopting
the Minimum core method, the TPL provider gains all
the extra profit of the system, i.e., the manufacturer and
retailer’s profits are not improved. Therefore, this me-
thod cannot be used to distribute profits, but it can be a
basis for the three parties to negotiate. Each party’s profit
is improved greatly though the growth extent is not the
same when adopting Nash bargaining model and Simpli-
fied MCRS method. The manufacturer and TPL pro-
vider’s profits are maximized under the simplified MCRS
method while the retailer’s profit is maximized under
Nash bargaining model, which means when the three
begin to negotiate they prefer different revenue distribu-
tion methods. Since here is the supply chain situation led
by the manufacturer, which means he has the strongest
bargaining power, so the simplified MCRS method will
be used by the alliance. Besides that, the growth extent of
retailer’s profit under this method is greater than under
the other two methods, so in this case, the simplified
MCRS method is the ideal one. The distributing coeffi-

Research on Supply Chain Coordination of TPL Supplier Participation 7
Table 4. All parties’ profits under diffe re nt re venue distribution method.
Nash bargaining model Minimum core method Simplified MCRS Method
Manufacturer 240.741 166.667 244.186
TPL provider 166.667 314.814 197.674
retailer 92.592 18.519 58.140
Table 5. Growth rates under different distribution method.
Nash bargaining modelMinimum core methodSimplified MCRS method
manufacturer 44.44% 0.00% 46.51%
TPL provider 80.00% 240.00% 113.49%
Decentralized
model
retailer 399.98% 0.00% 213.95%
M + L 8.64% 28.39% 17.83%
L + R 107.41% 166.67% 104.65%
Small scale
alliance
M + R 166.67% 48.15% 141.86%
cients are separately 0.488, 0.396, 0.116.
6. Conclusions
Based on the above analysis of wholesale price contract,
the supply chain coordination problem with TPL partici-
pation was discussed associated with revenue sharing and
distribution theory. The following conclusions are ob-
tained:
1) In the decentralized model, Pareto improvement can
be realized through reasonable distribution of the logis-
tics fee between the retailer and manufacturer; as the
supply chain leader, the manufacturer has to choose a
certain number of retailers to balance their profits.
2) In the three types of small scale alliances, the total
supply chain profit is the greatest when the manufacturer
and the TPL provider form a alliance.
3) All node enterprise’s profits are maximized in the
large scale alliance, and minimized in the decentralized
model.
4) Supply chain firms can choose an appropriate reve-
nue distribution method, such as Nash bargaining model,
minimum core method and simplified MCRS method to
coordinate the supply chain.
REFERENCES
[1] A. Vining and S. Globerman, “A Conceptual Framework
for Understanding the Outsourcing Decision,” European
Management Journal, Vol. 17, No. 6, 1999, pp. 183-198.
[2] D. L. Yang and Y. Jiang, “Quantitative Research on the
Collaboration between Node Enterprise and Third Party
Logistics under SCM,” China Soft Science, Vol. 3, 2002,
pp. 1-5.
[3] Y. Y. Zheng, “Study on the Cooperation Relationship
between Third Party Logistics and Vendor under Supply
Chain,” Qing Dao University, 2005.
[4] S. Huang and B. Y. Li, “The Coordination of the Third
Party Logistics Based on Revenue Sharing,” Businuess
Economies, Vol. 11, 2008, pp. 5-8.
[5] B. Dan, Q. Wu, X. M. Zhang and J. Xiao, “Shared-Sav-
ings Contracts between a Third Party Logistics Service
Provider and a Client Enterprise,” System Engineer-
ing-Theory and Practice, Vol. 2, 2007, pp. 46-53.
[6] Y. D. Gong, B. Y. Li and T. Liu, “The Pricing and Coor-
dination Policies of Three-Echelon Supply Chain,” Price
Monthly, Vol. 9, 2008, pp. 12-14.
[7] F. Ye and Y. N. Li, “The Motivation Mechanism of
Three- echelon Supply Chain Cooperation,” Journal of
System Management, Vol. 16, No. 2, 2007, pp. 130-134.