Modeling and analyzing pricing and inventory problem in a closed-loop supply chain with return policy and multiple manufacturers and multiple sales channels using game theory

Document Type : Article

Authors

1 Department of Industrial Engineering, Science and Research branch, Islamic Azad University, Tehran, Iran

2 Department of Industrial Engineering, Alzahra University, Tehran, Iran

3 Department of Industrial Engineering, K.N.Toosi University of Technology, Tehran, Iran

Abstract

This paper focuses on determining ordering and pricing policies in a single-period closed loop supply chain. The assumed supply chain includes a number of manufacturers who provide their different but substitutable products for their customers via a common retailer; however the manufacturers can have their own internet-based sales channel in order to provide products for the customers. The customers can return products if they are not satisfied with. The return products are collected in a repair center, are repaired and sold as second-hand product through the retailer channel or through an internet-based sale channel. The customer demand is assumed to be stochastic. This study aims to determine the optimum prices for the internet-based and retailer sales channels for the initial and second hand products. It also tries to determine the optimal values of retailer order and production rates of manufacturers and repair centers. Three types of game strategies for the supply chain including Nash, Stackelberg game with retailer as the leader and Stackelberg game with manufacturers and repair center as the leaders are studied in decentralized condition. The analytical equilibrium solutions, equations and constraints are extracted for these strategies. Finally, the effect of variations in key parameter is investigated.

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Main Subjects

References

References
1. Gan, S.-S., et al. \Pricing decision for new and
remanufactured product in a closed-loop supply chain
with separate sales-channel", International Journal of
Production Economics, 190, pp. 120-132 (2017).
2. Chiang, W.K., Chhajed, D., and Hess, J. \Direct
marketing, indirect revenues: A strategic analysis
of dual-channel supply chain design", Management
Science, 49, pp. 1-20 (2003).
3. Kumar, N. and Ruan, R. \On manufacturers complementing
the traditional retail channel with a direct online
channel", Quantitative Marketing and Economics,
4, pp. 289-323 (2006).
4. Dai, Y., Chao, X., Fang, S., and Nuttle, H.L.W.
\Pricing in revenue management for multiple rms
competing for customers", International Journal of
Production Economics, 98, pp. 1-16 (2005).
5. Kurata, H., Yao, D.Q., and Liu, J.J. \Pricing policies
under direct vs. indirect channel competition and national
vs. store brand competition", European Journal
of Operational Research, 180, pp. 262-281 (2007).
L. Nazari et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2759{2774 2773
6. Hsieh, C.-C., Chang, Y.-L., and Wu, C.-H. \Competitive
pricing and ordering decisions in a multiplechannel
supply chain", International Journal of Production
Economics, 154, pp. 156-165 (2014).
7. Georgiadis, P. and Besiou, M. \Environmental and
economical sustainability of WEEE closed loop supply
chains with recycling: A system dynamics analysis
Technology", International Journal of Advanced Manufacturing,
47, pp. 475-493 (2010).
8. Huang, M., Song, M., Lee, L.H., and Ching, W.K.
\Analysis for strategy of closed-loop supply chain with
dual recycling channel", Int. J. Production Economics,
144, pp. 510-520 (2013).
9. Maiti, T. and Giri, B.C. \A closed loop supply chain
under retail price and product quality dependent
demand", Journal of Manufacturing Systems, 37, Part
3, pp. 624-637 (2015).
10. Ramezani, M., Kimiagari, A.M., and Karimi, B.
\Closed-loop supply chain network design: A nancial
approach", Applied Mathematical Modelling, 38, pp.
4099-4119 (2014).
11. Kaya, O. and Urek, B. \A mixed integer nonlinear
programming model and heuristic solutions
for location, inventory and pricing decisions
in a closed loop supply chain", Computers
& Operations Research, 65, pp. 93-103 (2016).
http://dx.doi.org/10.1016/j.cor.2015.07.005
12. Dan, B., Xu, G., and Liu, C. \Pricing policies in a
dual-channel supply chain with retail services", Int. J.
Production Economics, 139, pp. 312-320 (2012).
13. Chen, Y., Fang, S., and Wena, U. \Pricing policies
for substitutable products in a supply chain with
Internet and traditional channels", European Journal
of Operational Research, 224, pp. 542-551 (2013).
14. Zhao, J., Liu, W., and Wei, J. \Competition under
manufacturer service and price in fuzzy environments",
Knowledge-Based Systems, 50, pp. 121-133 (2013).
15. Xiao, T. and Xu, T. \Coordinating price and service
level decisions for a supply chain with deteriorating
item under vendor managed inventory", Int. J. Production
Economics, 145, pp. 743-752 (2013).
16. Zhao, J., Wei, J., and Li, Y. \Pricing decisions
for substitutable products in a two-echelon supply
chain with rms' di erent channel powers", Int. J.
Production Economics, 153, pp. 243-252 (2014).
17. Zhao, J. and Wang, L. \Pricing and retail service
decisions in fuzzy uncertainty environments", Applied
Mathematics and Computation, 250, pp. 580-592
(2015).
18. Maiti, B.C. and Giri, B.C. \Two-period pricing
and decision strategies in a two-echelon supply
chain underprice-dependent demand", Applied Mathematical
Modelling, 24, pp. 655-674 (2017). DOI:
10.1016/j.apm.2016.10.051
19. Zhou, L., Naim, M.M., and Disney, S.M. \The impact
of product returns and remanufacturing uncertainties
on the dynamic performance of a multi-echelon closedloop
supply chain", International Journal of Production
Economics, 183, Part B, pp. 487-502 (2017).
20. Seung, H.Y. and Byung, Ch.K. \Joint pricing of
new and refurbished items: A comparison of closedloop
supply chain models", International Journal of
Production EconomicsVolume, 182, December, pp.
132-143 (2016).
21. Chen, B. and Chen, J. \When to introduce an online
channel, and o er money back guarantees and personalized
pricing?", European Journal of Operational Research
Volume, 257(2), 1 March, pp. 614-624 (2017).
22. Topkis, D.M. \Equilibrium points in nonzero-sum nperson
submodular games", SIAM Journal on Control
and Optimization, 17, pp. 773-787 (1979).
23. Topkis, D.M., Supermodularity and Complementarity,
Princeton University Press, New Jersey (1998).
24. Milgrom, P. and Roberts, J. \Rationalizability, learning,
and equilibrium in games with strategic complementarities",
Econometrica, 58, pp. 1255-1277 (1990).
25. Matsumoto, T. and Shimemura, E. \The Kuhn-Tucker
conditions and multistage games", Journal of Mathematical
Analysis and Applications, 23, pp. 269-283
(1968).
26. Ley er, S. and Munson, T. \Solving multi-leaderfollower
games", Mathematics and Computer Science
Division Argonne National Laboratory, Argonne, IL
60439, USA, April (2005).
27. Stankova, K. \On Stackelberg and inverse Stackelberg
games & their applications in the optimal toll design
problem, the energy markets liberalization problem,
and in the theory of incentives", NGInfra PhD Thesis
Series on Infrastructures No. 22, ISBN 978-90-79787-
03-6 (2009).
28. Hsieh, C.C. and Wu, C.H. \Coordinated decisions for
substitutable products in a common retailer supply
chain", European Journal of Operational Research,
196, pp. 273-288 (2009).
29. Cachon, G.P. and Netessine, S. \Game theory in
supply chain analysis", In Handbook of Quantitative
Supply Chain, Boston: Kluwer Academic Publishers,
pp. 13-65 (2004).

Scientia Iranica
Volume 25, Issue 5 - Serial Number 5
Transactions on Industrial Engineering (E)
September and October 2018
Pages 2759-2774

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