References
1. Tao, J. and Zhao, S. The mode of di erent price in
dual-channel supply chain", International Journal of
u- and e- Service, Science and Technology, 7, pp. 133{
144 (2014).
2. Sana, S.S., Chedid J.A., and Navarro, S. A three
layer supply chain model with multiple suppliers,
manufacturers and retailers for multiple items", Appl.
Math. Comput., 229, pp. 139{150 (2014).
3. Modak, N.M., Panda, S., and Sana, S.S. Two-echelon
supply chain coordination among manufacturer and
duopolies retailers with recycling facility", Int. J. Adv.
Manuf. Technol., 87, pp. 1531{1546 (2016).
4. Modak, N.M., Panda, S., and Sana, S.S. Threeechelon
supply chain coordination considering
duopolistic retailers with perfect quality products",
Int. J. Prod. Econ., 182, pp. 564{578 (2016).
5. Sana, S.S., Herreva-Vidal, G., and Acevedo-Chedid,
J. Collaborative model on the agro-industrial supply
chain of cocoa", Cybernetics and Systems: An International
Journal, 48, pp. 325{347 (2017).
6. Modak, N.M., Modak, N., Panda, S., et al. Analyzing
structure of two-echelon closed-loop supply chain for
pricing, quality and recycling management", J. Clean.
Prod., 171, pp. 512{528 (2018).
7. Roy, A., Sana, S.S. and Chaudhuri, K. Optimal
pricing of competing retailers under uncertain demanda
two layer supply chain model", Ann. Oper. Res., 260,
pp. 481{500 (2018).
8. Tsay, A. and Agrawal, N. Channel con
ict and
coordination in the E-commerce age", Prod. Oper.
Manag., 13, pp. 93{110 (2004).
9. Mukhopadyay, S.K., Zhu, X., and Yue, X. Information
sharing of value-adding retailer in a mixed channel
hi-tech supply chain", J. BUS. RES., 61, pp. 950{958
(2006).
10. Yan, R. Pro t sharing and rm performance in
the manufacturer-retailer dual channel supply chain",
Electronic Commerce Research, 8, pp. 155{172 (2008).
11. Chen, T.H. E ects of the pricing and cooperative advertising
policies in a two-echelon dual-channel supply
chain", Comput. Ind. Eng., 87, pp. 250{259 (2015).
12. Panda, S., Modak, N.M., Sana, S.S., et al. Pricing and
replenishment policies in dual-channel supply chain
under continuous unit cost decrease", Appl. Math. and
Comp., 256, pp. 913{929 (2015).
13. Cai, G., Zhang, ZG., and Zhang, M. Game theoretical
perspectives on dual-channel supply chain competition
with price discounts and pricing schemes", Int. J. Prod.
Econ., 117, pp. 80{96 (2009).
3650 F. Zarouri et al./Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 3634{3652
14. Cai, G. Channel selection and coordination in dualchannel
supply chain", J. Retailing, 86, pp. 22{36
(2010).
15. Yan, R. and Pei, Z. Information asymmetry, pricing
strategy and rm's performance in the retailer-multichannel
manufacturer supply chain", Journal of Business
Research, 64, pp. 377{384 (2011).
16. Cao, E., Wan, C., and Lai, M. Coordination of
a supply chain with one manufacturer and multiple
competing retailers under simultaneous demand and
cost disruptions", Int. J. Prod. Econ., 141, pp. 425{
433 (2013).
17. Modak, N.M., Panda, S., Sana, S.S., et al. Corporate
social responsibility, coordination and pro t distribution
in a dual-channel supply chain", Paci c Science
Review, 16, pp. 235{249 (2014).
18. Matsui, K. When should a manufacturer set its
direct price and wholesale price in dual-channel supply
chain?", Eur. J. Oper. Res., 258, pp. 501{511 (2016).
19. Li, B., Zhu, M., Jiang, Y., et al. Pricing policies
of a competitive dual-channel green supply chain", J.
Clean. Prod., 112, pp. 2029{2042 (2016).
20. Li, B., Hou, P., Chen, P., et al. Pricing strategy and
coordination in a dual-channel supply chain with a
risk-averse retailer", Int. J. Prod. Econ., 178, pp. 154{
168 (2016).
21. Liu, M., Cao, E., and Salifou, C.K. Pricing strategies
of a dual-channel supply chain with risk aversion",
Transp. Res. E., 90, pp. 108{120 (2016).
22. Wang, L., Song, H., andWang, Y. Pricing and service
decisions of complementary products in a dual-channel
supply chain", Comput Ind Eng, 105, pp. 223{233
(2017).
23. Xu, J., Qi, Q., and Bai, Q. Coordinating a dualchannel
supply chain with price discount contracts
under carbon emission capacity regulation", Appl.
Math. Model., 56, pp. 449{468 (2018).
24. Modak, N.M. and Kelle, P. Managing a dual-channel
supply chain under price and delivery-time dependent
stochastic demand", Eur. J. Oper. Res., 272, pp. 147{
161 (2019).
25. Dan, B., Xu ,G., and Liu, C. Pricing policies in a
dual-channel supply chain with retail services", Int. J.
Prod. Econ., 139, pp. 312{320 (2011).
26. Zhao, J., Hou, X., Guo, Y., et al. Pricing policies
for complementary products in a dual-channel supply
chain", Appl. Math. Model., 49, pp. 437{451 (2017).
27. Qi, X., Bard, J.F., and Yu, G. Supply chain coordination
with demand disruptions", Omega, 32, pp.
301{312 (2004).
28. Xiao, TJ., Qi, X., and Yu, G. Coordination of supply
chain after demand disruptions when retailers compete",
Int. J. Prod. Econ., 109, pp. 162{179 (2007).
29. Changchao, H., Gang, Y., Song, W., et al. Disruption
management for supply chain coordination with exponential
demand function", Acta. Math. Sci., 26(B), pp.
655{669 (2006).
30. Chen, K. and Zhang, P. Disruption management for
a dominant retailer with constant demand-stimulating
service cost", Comput. Ind. Eng., 61, pp. 936{946
(2011).
31. Huang, Y. andWang, Z. Demand Disruptions, pricing
and production decisions in a closed loop supply chain
with technology licensing", J. Clean. Prod., 191, pp.
248{260 (2018).
32. Hou, J., Zeng, A.Z., and Zhao, L. Coordination
with a backup supplier through buy-back contract
under supply disruption", Transp. Res. E: Logistics
and Transportation Review, 46, pp. 881{895 (2010).
33. Zhu, A.X. Dynamic replenishment, production and
pricing decisions in the face of supply disruption and
random price-sensitive demand", Int. J. Prod. Econ.,
146, pp. 612{619 (2013).
34. Kumar, M., Basu, P., and Avittathur, B. Pricing and
sourcing strategies for competing retailers in supply
chains under disruption risk", Comput Ind Eng, 265,
pp. 533{543 (2018).
35. Xu, M., Qi, X., Yu, G., et al. Coordinating dyadic
supply chain when production costs are disrupted", IIE
Transactions, 38, pp. 765{775 (2006).
36. Xiao, J., Yu, G., Sheng, Z.H., et al. Coordination of a
supply chain with one-manufacturer and two-retailers
under demand promotion and disruption management
decisions", Ann. Oper. Res., 135, pp. 87{109 (2005).
37. Dongchuan, X., Hong, C., and Lai, W. How to
coordinate integrated supply chain when demand and
cost disruptions occur simultaneously", Management
Science and Engineering, 9, pp. 14{18 (2015).
38. Lei, D., Li, J., and Liu, Zh. Supply chain contracts
under demand and cost disruptions with asymmetric
information", Int. J. Prod. Econ., 139, pp. 116{126
(2012).
39. Xiao, T. and Qi, X. Price competition, cost and
demand disruptions and coordination of a supply chain
with one manufacturer and two competing retailers",
Omega, 36, pp. 741{753 (2008).
40. Huang, S., Yang, C., and Zhang, X. Pricing and
production decisions in a dual-channel supply chain
with demand disruption", Comput. Ind. Eng., 62, pp.
70{83 (2012).
41. Huang, S., Yang, C., and Liu, H. Pricing and
production decisions in a dual-channel supply chain
when production costs are disrupted, Econ. Model, 30,
pp. 521{538 (2013).
42. Xu, G., Dan, B., Zhang, X., et al. Coordination a
dual-channel supply chain with risk-averse under a
two-way revenue sharing contract", Int. J. Prod. Econ.,
147, pp. 171{179 (2014).
43. Zhang, J., Gou, Q., Liang, L., et al. Supply chain
coordination through cooperative advertising with reference
price e ect", Omega, 41, pp. 345{353 (2013).
44. Kopalle, P.K., Rao, A.G., and Assuncao, J.L. Asymmetric
reference price e ects and dynamic pricing
policies", Informs, 15, pp. 60{85 (1996).
F. Zarouri et al./Scientia Iranica, Transactions E: Industrial Engineering 28 (2021) 3634{3652 3651
45. Lattin, J.M. and Buckin, R.E. Reference e ects of
price and promotion on brand choice behavior", J.
Marketing. Res., 26, pp. 299{310 (1989).
46. Geng, Q., Wu, C., and Li, K. Pricing and promotion
frequency in the presence of reference price e ects
in supply chain", California Journal of Operations
Management, 8, pp. 74{82 (2010).
47. Zhang, J., Chiang, W.Y.K., and Liang, L. Strategic
pricing with reference e ects in a competitive supply
chain", Omega, 44, pp. 126{135 (2014).
48. Lin, Zh. Price competition with reference price e ects
in supply chain", Transp. Res. E., 85, pp. 52{68
(2016).
49. Taleizadeh, A.A., Moshtagh, M.S., and Moon, L.
Optimal decisions of price, quality, e ort level and
return policy in a three level closed-loop supply chain
based on di erent game theory approaches", Eur. J.
Ind. Eng., 11(4), pp. 486{525 ( 2017).
50. Hsieh, C.C., Chang, Y.L., and Wu, C.H. Competitive
pricing and ordering decisions in a multiple-channel
supply chain", Int. J. Prod. Econ., 154, pp. 156{165
(2014).
51. Zhang, R., Liu, B., and Wang, W. Pricing decisions
in a dual channels system with di erent power structures",
Econ. Model, 29, pp. 523{533 (2012).
52. Mahmoodi, A. and Eshghi, K. Price competition in
duopoly supply chains with stochastic demand", J.
Manuf. Syst., 33, pp. 604{612 (2014).
53. Li, J., Wang, S., and Cheng, TCE. Competition
and cooperation in a single-retailer two-supplier supply
chain with supply disruption", Int. J. Prod. Econ.,
124, pp. 137{150 (2010).
54. Husseinzadeh Kashan, A. League championship algorithm:
A new algorithm for numerical function optimization",
Soft Computing and Pattern Recognition,
pp. 43{48 (2009).
55. Husseinzade Kashan, A. League Championship Algorithm
(LCA): A new algorithm for global optimization
inspired by sport championships", Applied Soft Computing,
16, pp. 171{200 (2014).
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