Leadership selection in an unlimited three-echelon supply chain.
Jia, Peng ; Mahdiraji, Hannan Amoozad ; Govindan, Kannan 等
1. Introduction
A management construct cannot be effectively used by practitioners
and researchers if no uniform definition exists. Such is the case with
the term "supply chain management", which has numerous
definitions and little consensus on what it means (Mentzer et al. 2001).
Supply chain paradigms of today have predominated over the field of
business (Mentzer 2001). During the late 1950s, Forrester and his
colleagues at the Massachusetts Institute of Technology developed a
number of underlying ideas and theories (Blanchard 2010). The Council of
Supply Chain Management Professionals (CSCMP) defines supply chain
management (SCM) as the planning and management of all activities
involved in sourcing and procurement, conversion and all logistics
management activities (Stank et al. 2005). Many researchers believe that
in the last decades, competition between companies has turn into
competition between their supply chains (Jespersen, Larsen 2005).
Considering the role and importance of SCM, this concept is faced
with many challenges and problems. Although no comprehensive model of SC
issues exists, a literature review indicates that researchers are mostly
interested in relevant information systems, marketing, financial
management, logistical and organisational matters (Wang et al. 2007).
SCM is mostly focused on improving operations and increasing
profits; thus, conflicting goals and objectives of two or more SC levels
may result in problems for all levels and impact on the total profit.
Numerous conflicting objectives of different components and levels may
results in decreased strength and competitiveness of the entire supply
chain. This paper considers the main conflicts related to inventory,
pricing and marketing costs in an unlimited three-echelon SC. The game
theory considers goals of all levels and players, which makes it a
suitable and reliable tool for solving conflicting situations. On each
level, the best leadership option with the greatest payoff is sought for
between K retailer, M manufacturer and S supplier. According to
Stackelberg non-cooperative game theory, each SC level can become a
decision-making leader depending on the available negotiating power.
Consequently, three leadership types are modelled on each level and the
total SC profit is calculated and compared to ascertain the best option.
Different models of leadership based on non-cooperative Stackelberg game
theory are proposed to find the best option considering unlimited SC
with three levels and three decision variables, namely inventory,
marketing cost and pricing. The research considers shortages and
incremental behaviour of a manufacturer as well as undertakes
sensitivity analysis by design of experiment and validation of proposed
models by simulation, which are its key contributions.
The paper is structured as follows: first, literature review is
offered on SC coordination using game theory; next, assumption, steps
and methodology pertaining to developed models are presented; then,
variables and parameters are described. Three different leadership
methods and three mathematical model based on non-cooperative game
theory are then presented considering three types of negotiating power.
The best leadership option is found simulating numerical examples with
the help of design of experiment (DOE).
2. Literature review
As per definition, supply chain consists of all parties directly or
indirectly involved in fulfilling a customer need (Chopra, Meindel
2007). This process involves all activities required to turn raw
materials into a final product that is delivered to a customer (Gumus,
Guneri 2007). Such activities and functions include new product
development, marketing efforts, various other operations, distribution,
financial and also customer services. A typical supply chain involves a
variety of stages such as customers, retailers, wholesalers,
distributors, manufacturers and raw material suppliers (Chopra, Meindel
2007).
The main game theory concept was devised by mathematical
researchers from Argentina and Japan in 1940s. It was first used to
prove theories with the help of mathematics and calculus. Later, it was
applied in economics, industry and other practical sciences (Rasmusen,
Blackwell 2005). In 1950, John Nash presented equilibrium for
cooperative situations (Nash 1950a). He also developed a model for
bargaining problems (Nash 1950b); and a year later, he presented an
equilibrium point for non-cooperative situations (Nash 1951). This
research is primarily concerned with the use of game theory in general
and non-cooperative Stackelberg games in particular in supply chain
management. Review of similar researches suggests that:
1. Some scientists have focused on the use of Nash equilibrium
point in supply chain coordination by the use of profit sharing contract
(Feng et al. 2007; Jiazhen, Qin 2008; Feng 2008; Ying et al. 2007; Jaber
et al. 2006; Bai, Wang 2008; Xu, Zhong 2011; Liu, Zhang 2006; Wang et
al. 2009).
2. Others used Nash and Stackelberg games and compared their
results in supply chain coordination and cooperation problems (Leng,
Parlar 2010; Arda, Hennet 2005).
3. Many focused on the use of other kinds of coordinating contracts
such as buyback, rebate, cost sharing, profit sharing discount models,
option contracts and benefit sharing in multi-echelon SC problems
(Cachon, Lariviere 2005; Yali, Zhanguo 2010; Chen, Zhang 2008; Cao et
al. 2007; Cachon, Lariviere 1999; Zhang, Huang 2010; Cachon, Lariviere
2001; Leng, Parlar 2009; Xiao, Qi 2008; Chen, Xiao 2009; Xiao et al.
2007; Stein, Ginevicius 2010a; Stein 2010).
4. Some used Shapley value equilibrium and Eliasberg model for
coordination and cooperation problems in SC (Bahinipati et al. 2009;
Zhao et al. 2010; Leng, Zhu 2009).
5. Finally, some papers focus on other optimisation tools such as
queuing theory, Markov chain, backward induction, stochastic programming
and genetic algorithm for solving coordination and cooperation problems
in a supply chain, mostly in incomplete information games situations
(Cachon, Kok 2010; Hennet, Arda 2008; Stein, Ginevicius 2010b; Zhen et
al. 2006; Kaviani et al. 2011; Gupta, Weerawat 2006).
3. Research methodology and assumptions
Main steps used for the selection of leadership in an unlimited
three-echelon supply chain are presented in Figure 1.
[FIGURE 1 OMITTED]
3.1. Assumptions
1. Supply chain consists of K retailer, M manufacturer and S
supplier (Jaafarnejad et al. 2012)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] Customer.
2. The product demand function depends on a price and marketing
costs. This function is non-linear [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII], thus standard deterministic inventory models are
used. Alpha considers negative price behaviour in the model devised by
the article authors (Abad 1994; Lee 1993; Lee et al. 1996; Kim, Lee
1998; Jung, Cerry 2001; Jung, Cerry 2005; Esmaeili 2008; Jaafarnejad et
al. 2012).
3. In case of a manufacturer, shortages and stockout are allowed;
consequently, shortage costs are considered during the stockout period.
The total relative cost for the manufacturer when producing
incrementally, are calculated as provided below (Oganezov 2006; Wang,
Tang 2009; Chakrabortty et al. 2010; Chang 2008; Pentico et al. 2009;
Jaafarnejad et al. 2012):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)
In terms of this research, pricing, inventory and marketing costs
are the decision variables.
4. Production unit cost is a nonlinear function [MATHEMATICAL
EXPRESSION NOT REPRODUCIBLE IN ASCII] which is related to the demand and
decreases with growing demand (Bazaraa et al. 1993).
5. Each manufacturer sells a specific product to a specific
retailer. However, suppliers sell their raw materials to any
manufacturer as needed.
6. Irrespective of the level of the supply chain, to which it
belongs, each player has a reasonable behaviour and opts for higher
profit and lower cost.
7. As every player can act as a leader based on dominance and
negotiating power, three types of leadership are considered.
3.2. Notations
Table 1 provides variables and parameters used for models that are
designed in following section.
4. Modelling process
Based on the research methodology and using assumptions and
notations described in previous sections of the article, the primary
model for each player is identified. A retailer (r) confronts holding
and setup costs as well purchasing cost from manufacturer. In addition,
to participate in a supply chain, a retailer should have a positive
sales margin. Finally a retailer's income involves the revenue
achieved by selling goods to the final customer. Considering the above,
retailer's payoff function and its constraints are presented in (2)
(Jaafarnejad et al. 2012).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)
Manufacturer's (n) confront holding, setup, ordering and
stockout as well as purchasing and production costs. On the other hand,
a manufacturer receives revenues from selling the final product to a
retailer in large amounts. The production is incremental; in addition,
unit production costs are related to products sold to a retailer. In
2012, Jaafarnejad et al. proposed a manufacturer's model, which
does not include unit production costs while computing gross revenues in
an objective function; consequently, the model became unbounded in many
situations. Consequently, the authors of the article considered this
problem and revised the manufacturer's model. It was noticed that
manufacturer and retailer leadership model has to be revised due
accordingly. Considering the aforementioned, manufacturer's payoff
function and its constraints are shown in (3).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3)
Suppliers confront costs related to holding, setup, ordering as
well as purchasing or acquiring raw materials. In contrast, every
supplier gains revenues by selling raw materials to manufacturers
depending on their usage for production. Considering the aforementioned,
a supplier's payoff function and constraints are depicted in (4)
(Jaafarnejad et al. 2012).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)
[TABLE 2 OMITTED]
Each player of a three-level supply chain acts in its best interest
when playing a game. Considering reasonable behaviour of each player as
well as Nash best response principle, the best decision for each player
of a three-echelon SC is identified by derivation of the payoff function
to decision variables. The first order condition of each payoff function
is used for the best response and the second condition is used for
concavity analysis. By calculating the determinant of Hessian matrix for
each player depending on its decision variables, it can be concluded
that all models are concave to their decision variables; thus, optimal
solution for the proposed models are definable. Table 2 represents the
best response for each player if Nash principle is used, by calculating
the first order condition of each player's payoff function
according to their decision variables.
Once modelling is completed and the best response for each player
is found, it is time to finalise the research and produce the leadership
model for coordination of a three-level supply chain by Stackelberg
non-cooperative approach. As three levels are included in the SC game,
three types of leadership are possible. Each level--a supplier,
manufacturer and retailer--can act as a leader while the remaining two
would play the role of a follower. In this research, based on a make of
a system and type of a supply chain, three leadership followership
systems were considered. The main objective is to maximise the total
profit based on the best response of followers. Consequently, the sum of
leader payoffs will be the objective function and the best response of
followers will act as constraints. The aforementioned basic constraints
are considered in other models as well. Figure 2 presents leadership
types considered in this research.
[FIGURE 2 OMITTED]
4.1. Retailer leadership according to stackelberg model
The first model describes the situation with retailers as leaders
and manufacturers and suppliers as followers. The objective function
insist on maximising the retailer's profit, first four constraints
explain the rational behaviour of followers and the remaining constraint
describes the logic of the game, namely: demand should exist and the
selling price established by each player for the next level should be
greater than the purchasing price from previous level. Other relevant
information is presented in Table 3.
[TABLE 3 OMITTED]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
4.2. Manufacturer leadership according to stackelberg model
The first model describes the situation where manufacturers act as
leaders while retailers and suppliers are followers. The objective
function insists on maximising the manufacturer's profit, first
three constraints explain the rational behaviour of followers and the
remaining constraint describes the logic of the game, namely: demand
should exist and the selling price established by each player for the
next level should be greater than the purchasing price from previous
level. Other relevant information is presented in Table 4.
[TABLE 4 OMITTED]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)
4.3. Supplier leadership according to stackelberg model
The first model describes the situation where suppliers act as
leaders while manufacturers and retailers are followers. The objective
function insists on maximising the supplier's profit, first five
constraints explain the rational behaviour of followers and the
remaining constraint describe the logic of the game, namely: demand
should exist and the selling price established by each player for the
next level should be greater than the purchasing price from previous
level. Other relevant information is presented in Table 5.
[TABLE 5 OMITTED]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)
5. Numerical example
Considering the models mentioned above, for sensitivity analysis
and leadership selection, a three-echelon supply chain including 2
suppliers, 2 manufacturers and 2 retailers was designed. Table 6
indicates the numerical values of parameters in a proposed supply chain.
To select the best type of leadership and analyse the sensitivity
of the total profit, five constants were selected from demand and
production nonlinear functions including [alpha], [beta], [gamma], k, u.
The lower and upper bounds of these five elements are provided in Table
7.
Using design of experiment (DOE) and [2.sup.k-p] experiments as
well as including one central point in each block, 17 different
experiments were designed with the help of MINITAB 16.5 software. The
experiments are presented in Table 8.
The experiments listed in Table 7 were used in all three leadership
models. The models were coded, debugged and solved using LINGO 11. The
total profit in case of each different type of leadership was
calculated. The results are presented in Table 9.
Using the two paired test, results of all three types of leadership
in a supply chain were compared. The results from MINITAB 16.5 software
are provided below. The authors of the article concluded that retailer
leadership ranked first and manufacturer and supplier leaderships ranked
second and third, respectively. Consequently, it is proposed that if
negotiating power increases by moving from the end of chain to the
beginning, the total profit would decrease.
The main effects of each leadership game in terms of five critical
elements were calculated using MINITAB 16.5 software. The results are
provided in figures of Table 10. In all models, Gama and U have the
least effect and K, Alpha and Beta have the greatest, which indicates
that the sensitivity effect of a price and marketing changes on SC
profit is greater than unit production costs. K has a direct effect on
all three leadership models while Alpha has an inverse effect on the
retailer leadership, and Beta has an inverse effect on the manufacturer
and supplier models. Thus, it can be concluded that the increase in the
selling prices would bring down the total profit; in addition, while the
manufacturer and supplier act as leaders, increase in marketing cost
would decrease the total profit as they would be making the first
impact, which would require the retailer to invest more in marketing in
order to gain a greater market share, based on demand equation.
[TABLE 10 OMITTED]
[FIGURE 3 OMITTED]
Verification of different types of proposed leadership models based
on non-cooperative game theory was delivered considering assumptions of
models. For this purpose, a simulated supply chain was designed by Arena
software, based on data from the aforementioned numerical example. The
simulated model is demonstrated in Fig. 3. The simulated model is based
on random marketing costs and a random retailer price, each retailer has
a supply chain. By this randomisation, the demand of each product is
computable and other decision variables are reached using the best
response of each player calculated in the previous section, depending on
Nash equilibrium definition.
The simulated model performed 100 runs for each type of experiment
and the results are given in Table 11. As results suggest, the total
profit of the supply chain in case of the proposed leadership model is
similar to the total profit of SC based on Arena, where retailer is the
leader. The SC total profit is always between the upper and lower bounds
of the confidence interval.
6. Conclusion
The research considered coordination in multi-echelon supply
chains, in which non-cooperative game theory was used as a suitable tool
for coordination of pricing, inventory and marketing expenditure
policies in a three-level supply chain where the leadership changed
depending on negotiating power. The situation and assumptions used in
this paper will be valuable for future researches. In case of more
levels, researchers are guided towards a comprehensive model, which
would need to be coordinated in the future. In addition, as the
competency of information and also complete information sharing in
different levels seems to be impossible, using incomplete or imperfect
game theory approaches such as signalling game or Nash Bayesian game
would solve this problem and allow for more realistic options in the
future. As interaction between layers in SC occurs continuously,
repetitive games would adapt and fit real situations. This type of games
considers time and patience of players within a modelling process.
The coordination mechanism used in this paper is based on leader
follower Stackelberg game. It must be noted that other kinds and
coordination options such as a profit sharing contract, revenue sharing
contract, buyback contract and also option contract are all possible
solutions for establishing coordination, Thus, the total profit and each
stage profit would increase and bring more competitive advantages for
the entire chain. The aforementioned contracts are all based on
probabilistic demand function. Finally, Opt Quest application in Arena
software is a suitable tool for estimating the best amounts of nonlinear
model parameters. By identifying the optimal amount of the proposed
models, optimal solution for unlimited three-echelon supply chain would
be developed.
Caption: Fig. 1. Research methodology
Caption: Fig. 2. Leadership types
Caption: Fig. 3. Arena-based retailer leadership, a simulated model
doi: 10.3846/16111699.2012.761648
References
Abad, P. 1994. Supplier pricing and lot sizing when demand is price
sensitive, European Journal of Operation Research 78(3): 334-354.
http://dx.doi.org/10.1016/0377-2217(94)90044-2
Arda, Y.; Hennet, J. C. 2005. Supply chain coordination through
contract negotiation, in 44th IEEE Conference on Conference on Decision
and Control, 12-15 December, 2005, Seville, Spain. IEEE, 4658-4684.
http://dx.doi.org/10.1109/CDC.2005.1582897
Bahinipati, B. K.; Kanda, A.; Deshmukh, S. G. 2009. Revenue sharing
in semiconductor industry supply chain: cooperative game theoretic
approach, Sadhana 34(3): 501-527.
http://dx.doi.org/10.1007/s12046-009-0018-9
Bai, S.; Wang, D. 2008. Research on inventory game of supply chain
based on credit coordination mechanism, in IEEE International Conference
on Service Operations and Logistics, and Informatics, vol.2, 12-15
October, 2008, Beijing, China. IEEE, 3037-3042.
Bazaraa, M. S.; Sherali, H. D.; Shetty, C. M. 1993. Nonlinear
Programming: Theory and Algorithms. John Wiley & Sons.
Blanchard, D. 2010. Supply Chain Management Best Practices. John
Wiley & Sons.
Cachon, G. P.; Kok, G. A. 2010. Competing manufacturers in a retail
supply chain: on contractual form and coordination, Management Science
56(3): 571-589. http://dx.doi.org/10.1287/mnsc.1090.1122
Cachon, G. P.; Lariviere, M. A. 1999. Capacity allocation using
past sales: when to turn and earn, Management Science 45(5): 685-703.
http://dx.doi.org/10.1287/mnsc.45.5.685
Cachon, G. P.; Lariviere, M. A. 2001. Contracting to assure supply:
how to share demand forecasts in a supply chain, Management Science
47(5): 629-646. http://dx.doi.org/10.1287/mnsc.47.5.629.10486
Cachon, G. P.; Lariviere, M. A. 2005. Supply chain coordination
with revenue sharing contracts: strength and limitations, Management
Science 51(1): 30-44. http://dx.doi.org/10.1287/mnsc.1040.0215
Cao, X.; Lu, R.; Yao, Z. 2007. A study on coordination in three
stage perishable products supply chain based on false failure return, in
IEEE International Conference on Grey Systems and Intelligent Services,
18-20 November 2007, Nanjing, China. IEEE, 1222-1227.
http://dx.doi.org/10.1109/GSIS.2007.4443467
Chakrabortty, S.; Pal, M.; Nayak, P. K. 2010. Solution of
Interval-valued manufacturing inventory models with shortage,
International Journal of Engineering and Applied Sciences 4(2): 89-94.
Chang, H. C. 2008. A note on the EPQ model with shortages and
variable lead time, Information and Management Sciences 15(1): 61-67.
Chen, H.; Zhang, K. 2008. Stackelberg Game in a two echolon supply
chain under buy back coordination contract, in IEEE International
Conference on Service Operations and Logistics, and Informatics, vol. 2,
12-15 October, 2008, Beijing, China. IEEE, 201-208.
Chen, K.; Xiao, T. 2009. Demand disruption and coordination of the
supply chain with a dominant retailer, Elsevier: European Journal of
Operational Research 197(1): 225-234.
http://dx.doi.org/10.1016/j.ejor.2008.06.006
Chopra, S.; Meindel, P. 2007. Supply Chain Management, 3rd edition.
New York: Prenticehall.
Esmaeili, M.; Aryanejad, M.; Zeephongsekul, P. 2008. A game theory
approach in seller-buyer supply chain, European Journal of Operation
Research 195(2): 442-448. http://dx.doi.org/10.1016/j.ejor.2008.02.026
Feng, J. S.; Jia, L. M.; Jiao, H. L. 2007. The three stage supply
chain coordination by revenue sharing contracts, in IEEE International
Conference on Grey Systems and Intelligent Services, 18-20 November,
2007, Nanjing, China. IEEE, 1216-1221.
http://dx.doi.org/10.1109/GSIS.2007.4443466
Feng, S. X. 2008 Coordination of pricing decisions in multiple
product supply chains, in Wireless Communications, Networking and Mobile
Computing, 2008. WiCOM '08, 12-14 October, 2008, Dalian, China.
IEEE, 16-22.
Gumus, T. A.; Guneri, F. A. 2007. Multi-echelon inventory
management in supply chains with uncertain demand and lead times:
literature review from an operational research perspective, Journal of
Engineering Manufacture 221(10): 1553-1570.
http://dx.doi.org/10.1243/09544054JEM889
Gupta, D.; Weerawat, W. 2006. Supplier manufacturer coordination in
capacitated two stage supply chains, Elsevier: European Journal of
Operational Research 175(1): 67-89.
http://dx.doi.org/10.1016/j.ejor.2005.04.021
Hennet, J. C.; Arda, Y. 2008. Supply chain coordination; a game
theory approach, Engineering Applications of Artificial Intelligence
21(3): 399-405. http://dx.doi.org/10.1016/j.engappai.2007.10.003
Jaafarnejad, A.; Amoozad Mahdiraji, H.; Mohaghar, A.;
Modarresyazdi, M. 2012. retailers leadership mathematical modeling in
unlimited three echelon supply chain: non-cooperative game theory
approach, Archives Des Science 65(6): 81-90.
Jaber, M. Y.; Osman, I. H.; Guiffrida, A. L. 2006. Coordinating a
three level supply chain with price discounts, price dependent demand,
and profit sharing, International Journal of Integrated Supply Chain
2(1/2):28-49. http://dx.doi.org/10.1504/IJISM.2006.008337
Jespersen, B. D.; Larsen, S. T. 2005. Supply chain management: in
theory and practice. Copenhagen: Copenhagen Business School Press.
Jiazhen, H.; Qin, L. 2008. Revenue coordination contract based on
stackelberg game in upsteam supply chain, in Wireless Communications,
Networking and Mobile Computing, 2008. WiCOM '08, 12-14 October,
2008, Dalian, China. IEEE, 1-5. http://dx.doi.org/10.1109/WiCom.2008.1
Jung, H.; Cerry, M. K. 2005. Optimal inventory policies for an
economic order quantity model with decreasing cost functions. European
Journal of Operation Research 165(1): 108-126.
http://dx.doi.org/10.1016/j.ejor.2002.01.001
Jung, H.; Cerry, M. K. 2001. Optimal inventory policies under
decreasing cost functions via geomettric programming. European Journal
of Operation Research 132(3): 628-642.
http://dx.doi.org/10.1016/S0377-2217(00)00168-5
Kaviani, M. R.; Chaharsooghi, K.; Naimi Saidgh, A. 2011.
Stackelberg game theory approach for manufacturer-retailer supply chain
coordination using Imperialist Competitive Algorithm, in Logistics and
Supply Chain Conference, 22-23 November, 2011, Tehran, Iran. 130-145.
Kim, D.; Lee, J. W. 1998. Optimal joint pricing and lotsizing with
fixed and virable capacity, European Journal of Operation Research
109(1): 212-227. http://dx.doi.org/10.1016/S0377-2217(97)00100-8
Lee, J. W. 1993. Determining order quantity and selling price by
geomettric programming, Decesion Science 21(1): 76-87.
http://dx.doi.org/10.1111/j.1540-5915.1993.tb00463.x
Lee, J. W.; Kim, D.; Cabot, A. V. 1996. Optimal demand rate,
lotsizind and process reliability improvement decisions, IEEE
Trasactions: 941-952.
Leng, M. M.; Parlar, M. 2009. Allocation of cost savings in a three
level supply chain with demand information sharing: a cooperative game
approach, Operations Research 57(1) 200-213.
http://dx.doi.org/10.1287/opre.1080.0528
Leng, M. M.; Parlar, M. 2010. Game theoretic analysis of
decentralized assembly supply chains: non cooperative equilibria vs.
coordination with cost sharing contracts, Elsevier: European Journal of
Operational Research 204(1): 96-104.
http://dx.doi.org/10.1016/j.ejor.2009.10.011
Leng, M. M.; Zhu, A. 2009. Side payments contracts in two person
nonzero sum supply chain games: review, discussion and applications,
Elsevier: European Journal of Operational Research 196(2): 600-618.
http://dx.doi.org/10.1016/j.ejor.2008.03.029
Liu, Y.; Zhang, H. 2006. Supply chain coordination with contracts
for online game industry, in 3rd IEEE International Conference on
Management of Innovation and Technology, vol. 2, 21-23 June, 2006,
Singapore, IEEE 867-872. http://dx.doi.org/10.1109/ICMIT.2006.262345
Mentzer, J. T. 2001. Supply chain management, 2nd edition.
California: Sage Publication.
Mentzer, J. T.; Dewitt, W.; Keebler, J. S.; Min, S.; Nix, N. W.;
Smith, C. D., et al. 2001. Drfinmg supply chain management b, Journal of
Business Logistics 22(2): 1-25.
http://dx.doi.org/10.1002/j.2158-1592.2001.tb00001.x
Nash, J. 1950a. Equilibrium points in n-person games, Proceeding of
National Academy of Science 36(1): 48-49.
http://dx.doi.org/10.1073/pnas.36.L48
Nash, J. 1950b. Bargaining problem, Econometrica 18(2): 155-162.
http://dx.doi.org/10.2307/1907266
Nash, J. 1951. Non cooperative games, Annal of Mathematics 54(2):
286-295. http://dx.doi.org/10.2307/1969529
Oganezov, K. N. 2006. Inventory Models Fpr Production Systems with
Constant Linear Demand, Time Value of Money and Perishable or
Nonperiashable Items. Virginia: West Virginia University.
Pentico, D. W.; Drake, M. J.; Toews, C. 2009. The deterministic EPQ
with partial backordering: a new approach, Omega: The International
Journal of Management Science 37(3): 624-636.
http://dx.doi.org/doi:10.1016/j.omega.2008.03.002
Rasmusen, E.; Blackwell, B. 2005. Games and Information; an
Introduction to Game Theory, fourth ed. Indiana: Indiana University
Press.
Stank, T. P.; Davis, B. R.; Fugate, B. S. 2005. A strategic
framework for supply chain oriented logistics, Journal of Business
Logistics 26(2): 27-46.
http://dx.doi.org/10.1002/j.2158-1592.2005.tb00204.x
Stein, H. D. 2010. Allocation rules with outside option in
cooperation games with time inconsistency. Journal of Business Economics
and Management 11(1): 56-96. http://dx.doi.org/10.3846/jbem.2010.04
Stein, H. D.; Ginevicius, R. 2010a. Overview and comparison of
profit sharing in different business collabration forms. Journal of
Business Economics and Management 11(3): 428-443. http://
dx.doi.org/10.3846/jbem.2010.2121
Stein, H. D.; Ginevicius, R. 2010b. New coopettion approach for
supply chain applications and the implementation a new allocation rule,
in 6th International Scientific Conference, May 13-14, 2010, Vilnius,
Lithuania. Vilnius: Technika, 147-152.
Wang, L.; Sun, X.; Dang, F. 2009. Dynamic cooperation mechanism in
supply chain for perishable agricultural products under one to multi.
Springer, 1212-1221.
Wang, W. Y.; Michael, H. S.; Patrick, Y. 2007. Supply chain
management: issues in the new era of collaboration and competition.
Pensylvania: Idea Group Publishing.
Wang, X.; Tang, W. .2009. Fuzzy EPQ inventory models with
backorder, Journal of System and Science Complexity 22(2): 313-323.
http://dx.doi.org/10.1007/s11424-009-9166-6
Xiao, T.; Qi, X. 2008. Price competition, cost and demand
disruptions and coordination of a supply chain with one manufacturer and
two competing retailers, Omega: The International Journal of Management
Science 36(5): 741-753. http://dx.doi.org/10.1016/j.omega.2006.02.008
Xiao, T.; Qi, X.; Yu, G. 2007. Coordination of supply chain after
demand disruptions when retailers compete, Elsevier: International
Journal of Production Economics 109(1-2): 162-179.
http://dx.doi.org/10.1007/s11424-009-9166-6
Xu, Y.; Zhong, H. 2011. Benefit mechanism designing: for
coordinating three stages supply chain, in International Conference on
Management Science and Industrial Engineering (MSIE), 8-11 January,
2011, Harbin, China. IEEE, 966-971.
Yali, L.; Zhanguo, L. 2010. Coordination of price discount and
sales promotion in a two level supply chain system, in IEEE
International Conference on Emergency Management and Management Sciences
(ICEMMS), 8-10 August, 2010, Beijing, China. IEEE, 421-427.
Ying, H. L.; Qi, C. Y.; Sheng, J. Z. 2007. Research on the
coordination mechanism model of the three level supply chain, in
International Conference on Management Science and Engineering (ICMSE
2007), 20-22 August, 2007, Harbin, China. IEEE, 20-25.
Zhang, X.; Huang, G. Q. 2010. Game theoretic approach to
simultaneous configuration of platform products and supply chains with
one manufacturing firm and multiple cooperative suppliers, International
Journal of Production Economics 124(1): 121-136.
http://dx.doi.org/10.1016/j.ijpe.2009.10.016
Zhao, Y.; Wang, S.; Cheng, T. E.; Yang, X.; Huang, Z. 2010.
Coordination of supply chains by option contracts: a cooperative game
theory approach, European Journal of Operational Research 207(2):
668-675. http://dx.doi.org/10.1016/j.ejor.2010.05.017
Zhen, L.: Xiaoyuan, H.: Shizheng, G. 2006. The study on stackelberg
game of supply chain coordination with uncertain delivery, in
International Conference on Service Systems and Service Management,
25-27 Octtober, 2006, Troyes, France. IEEE, 1460-1465.
http://dx.doi.org/10.1109/ICSSSM.2006.320739
Peng Jia (1), Hannan Amoozad Mahdiraji (2), Kannan Govindan (3),
Ieva Meidute (4)
(1) Transportation Management College, Dalian Maritime University,
1 Linghai Road, Dalian, 116026, China
(2) Management Department, University of Tehran, Tehran, Iran
(3) Department of Business and Economics, University of Southern
Denmark, Odense, Denmark
(4) Business Management Faculty, Vilnius Gediminas Technical
University, Vilnius, Lithuania E-mails: 2 h.amoozad@ut.ac.ir
(corresponding author)
Received 09 October 2012; accepted 19 December 2012
Peng JIA has received the Doctor's Degree in Engineering at
Nagoya University, Japan. He is an Assistant Professor of Transportation
Management College and the Vice-Director of Institute of Corporation of
Social Responsibility and Sustainable Development (ICSD) at Dalian
Maritime University, where he teaches courses on Transport Geography and
Spatial Systems. His research is focused on supply chain management,
corporate social responsibility, transport network optimisation and
spatial simulation.
Hannan AMOOZAD MAHDIRAJI received his Ph.D. and masters degrees in
operation and manufacturing management from the University of Tehran and
bachelors in industrial engineering. He is an Assistant Professor of
Kashan branch, Islamic Azad University, and also Chief of Planning and
Systems Department of Iran Mercantile Exchange. He has published nearly
15 papers related to supply chains and MCDM models in international
journals and conferences.
Kannan GOVINDAN is currently an Associate Professor of operations
and supply chain management at the Department of Business and Economics,
University of Southern Denmark, Odense M, Denmark. His research
interests include logistics, supply chain management, green and
sustainable supply chain management, reverse logistics and maritime
logistics. He has published more than 65 papers in refereed
international journals and more than 70 papers in conferences. He was
awarded a gold medal for the Best Ph.D. Thesis.
Ieva MEIDUTE. Assoc. Prof., Dr of technological sciences (transport
engineering), Vilnius Gediminas Technical University, Faculty of
Business Management, Department of Business Technologies. Her research
interests are related with business process management, logistics and
supply chain management.
Paired T-Test and CI: ZSC(R); ZSC(N)
Paired T for ZSC(R)--ZSC(N)
N Mean StDev SE Mean
ZSC(R) 17 2233 599 145
ZSC(N) 17 1681 487 118
Difference 17 551.6 116.1 28.2
95% lower bound for mean difference: 502.5
T-Test of mean difference = 0 (vs > 0): T-Value = 19.59 P-Value =
0.000
Paired T-Test and CI: ZSC(R); ZSC(S)
Paired T for ZSC(R)--ZSC(S)
N Mean StDev SE Mean
ZSC(R) 17 2233 599 145
ZSC(S) 17 1639 485 118
Difference 17 593.1 118.2 28.7
95% lower bound for mean difference: 543.1
T-Test of mean difference = 0 (vs > 0): T-Value = 20.69 P-Value =
0.000
Paired T-Test and CI: ZSC(N); ZSC(S)
Paired T for ZSC(N)--ZSC(S)
N Mean StDev SE Mean
ZSC(N) 17 1681 487 118
ZSC(S) 17 1639 485 118
Difference 17 41.46 15.40 3.74
95% lower bound for mean difference: 34.94
T-Test of mean difference = 0 (vs > 0): T-Value = 11.10 P-Value =
0.000
Table 1. Variable and parameters
Description Note
Ordering cost from s to n [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE
IN ASCII]
Production function parameters u,[gamma]
Manufacturer holding cost [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE
IN ASCII]
Manufacturer stockout [B.sub.n]
Manufacturer's stockout cost [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE
IN ASCII]
Manufacturer's margin [G.sub.n]
Manufacturer's total revenue [TR.sub.n]
Manufacturer's total cost [TC.sub.n]
Manufacturer's production capacity [PC.sub.n]
Supplier's margin [G.sub.S]
Supplier's total revenue [TR.sub.S]
Supplier's total cost [G.sub.S]
Supplier's unit cost for each unit [G.sub.S]
of raw materials
Holding coefficient cost for [MATHEMATICAL EXPRESSION
a supplier NOT REPRODUCIBLE
IN ASCII]
Supplier's ordering cost [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE
IN ASCII]
Description Note
Retailer's margin [G.sub.r]
Selling price from r to a customer [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE
IN ASCII]
Selling price from n to r [P.sub.n]
Product demand [D.sub.n]
Marketing cost for product n [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE
IN ASCII]
Price and marketing and k, a, [beta]
demand coefficient
Retailer's setup cost [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE
IN ASCII]
Manufacturer's production quantity [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE
IN ASCII]
Holding Cost coefficient for a retailer [k'.sub.n]
Retailer's total revenue [TR.sub.r]
Retailer's total cost [TC.sub.r]
Retailer's total payoff [Z.sub.r]
Raw material coefficient in product n [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE
IN ASCII]
Raw material price from s to n [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE
IN ASCII]
Manufacturer's variable cost [MATHEMATICAL EXPRESSION
for each product NOT REPRODUCIBLE
IN ASCII]
Table 6. Initial data for the numerical example
Amount Par
2 M
4 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
0.15 [k'.sub.1]
1.1 [[phi]'.sub.1]
3 [k.sub.sn] (11)
3 [k.sub.sn] (21)
6 [Co.sub.sn] (11)
4 [Co.sub.sn] (21)
1 [C.sub.B](1) = [C.sub.B](2)
25 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
0.15 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
2 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
15 PC (1) = PC (2)
8 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
1.1 [[phi].sub.2]
Amount Par
2 R
2 S
5 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
0.2 [k'.sub.2]
1.15 [[phi]'.sub.2]
4 [k.sub.sn] (12)
3 [k.sub.sn] (22)
5 [Co.sub.sn] (12)
6 [Co.sub.sn] (22)
0.5 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1) =
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
24 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
0.2 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
1.5 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
7 [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
1.15 [[phi].sub.1]
Table 7. Key parameters for sensitivity analysis
Max Min
1.25 1.2 [alpha]
0.15 0.05 [beta]
0.1 0.01 [gamma]
4000 3000 k
4 2 u
Table 8. Types of experiments
Design [gamma] U K [alpha] [beta]
1 0.01 4 4000 1.2 0.15
2 0.1 2 3000 1.2 0.05
3 0.01 4 3000 1.2 0.05
4 0.1 4 3000 1.25 0.05
5 0.1 4 4000 1.25 0.15
6 0.1 4 3000 1.2 0.15
7 0.055 3 3500 1.225 0.1
8 0.01 4 3000 1.25 0.15
9 0.1 2 3000 1.25 0.15
10 0.01 2 3000 1.2 0.15
11 0.01 2 3000 1.25 0.05
12 0.1 4 4000 1.2 0.05
13 0.01 2 4000 1.2 0.05
14 0.1 2 4000 1.2 0.15
15 0.01 2 4000 1.25 0.15
16 0.01 4 4000 1.25 0.05
17 0.1 2 4000 1.25 0.05
Table 9. The total profit of the supply chain by type of leadership
The total profit of the supply chain
Supplier Manufacturer Retailer Design
leadership leadership leadership
2631 2686 3432 1
1328 1332 1838 2
1293 1331 1800 3
956 997 1370 4
1820 1866 2507 5
1866 1904 2554 6
1548 1577 2129 7
1314 1361 1852 8
1307 1362 1878 9
1888 1928 2568 10
994 1025 1395 11
1824 1854 2442 12
1853 1901 2470 13
2659 2686 3455 14
1851 1925 2529 15
1344 1399 1844 16
1395 1443 1890 17
Table 11. Model verification results in 17 experiments
Experiment Retailer leadership Ave total profit Half
model of simulation width
Design 1 3,432.21 3,302.76 153.22
Design 2 1,838.18 1,832.81 85.30
Design 3 1,800.10 1,810.25 83.98
Design 4 1,370.40 1,400.66 64.99
Design 5 2,506.56 2,457.33 114.00
Design 6 2,554.22 2,640.80 114.16
Design 7 2,129.12 2,100.36 97.44
Design 8 1,851.76 1,820.40 84.45
Design 9 1,878.19 1,827.09 84.76
Design 10 2,568.25 2,461.21 114.18
Design 11 1,394.95 1,400.12 64.95
Design 12 2,442.21 2,431.24 112.79
Design 13 2,469.80 2,429.41 112.71
Design 14 3,455.26 3,307.45 153.44
Design 15 2,528.73 2,459.10 114.10
Design 16 1,844.17 1,879.58 87.21
Design 17 1,890.24 1,882.27 50.00
Experiment 90% Confidence 90% Confidence
interval Min interval Max
Design 1 3,149.54 3,455.98
Design 2 1,747.51 1,918.11
Design 3 1,726.27 1,894.23
Design 4 1,335.67 1,465.65
Design 5 2,343.33 2,571.33
Design 6 2,526.64 2,754.96
Design 7 2,002.92 2,197.80
Design 8 1,735.95 1,904.85
Design 9 1,742.33 1,911.85
Design 10 2,347.03 2,575.39
Design 11 1,335.17 1,465.07
Design 12 2,318.45 2,544.03
Design 13 2,316.70 2,542.12
Design 14 3,154.01 3,460.89
Design 15 2,345.00 2,573.20
Design 16 1,792.37 1,966.79
Design 17 1,832.27 1,932.27
