Abstract
This paper addresses coordination of pricing and cooperative advertising policies in a two-echelon supply chain under fuzziness of demand function’s parameters and manufacturing costs. Three different decentralized scenarios are introduced with regard to the players’ market power: (1) manufacturer-Stackelberg game where the manufacturer has the dominant power in the channel, (2) retailer-Stackelberg game where the manufacturer follows the strategies taken by a dominant retailer, and (3) Nash game where the manufacture and the retailer with the same market power make the decisions simultaneously. The equilibrium wholesale and retail prices, national and local advertising expenditures, and participation rate are determined using the concepts of possibilistic game theory, and the results are compared with the centralized channel scenario. A numerical example is presented to illustrate the effectiveness of the proposed modeling approach, and sensitivity analyses are carried out to measure the impact of the demand function’s parameters as well as the levels of uncertainty.
Similar content being viewed by others
References
Alaei S, Behravesh M, Karegar N (2013) Evaluation of marketing-pricing decisions in a two-echelon supply chain. Eng Econ 24(2):135–143
Arshinder K, Kanda A, Deshmukh SG (2011) A review on supply chain coordination: coordination mechanisms, managing uncertainty and research directions. In supply chain coordination under uncertainty, pp 39–82. Springer, Heidelberg
Aust G, Buscher U (2012) Vertical cooperative advertising and pricing decisions in a manufacturer–retailer supply chain: A game-theoretic approach. Eur J Oper Res 223(2):473–482
Aust G, Buscher U (2014) Cooperative advertising models in supply chain management: A review. Eur J Oper Res 234(1):1–14
Aviv Y (2001) The effect of collaborative forecasting on supply chain performance. Manage Sci 47(10):1326–1343
Bayat M, Khanzadi M, Nasirzadeh F, Chavoshian A (2020) Financial conflict resolution model in BOT contracts using bargaining game theory. Constr Innov
Chaab J, Rasti-Barzoki M (2016) Cooperative advertising and pricing in a manufacturer-retailer supply chain with a general demand function: a game-theoretic approach. Comput Ind Eng 99:112–123
Chan CK, Man N, Fang F, Campbell JF (2020) Supply chain coordination with reverse logistics: a vendor/recycler-buyer synchronized cycles model. Omega 95:102090
Chen T-H (2014) On the impact of cooperative advertising and pricing for a manufacturer-retailer supply chain. J Ind Product Eng 31(7):417–424
Chen CC, Schonfeld P (2017) A hybrid heuristic technique for optimal coordination in intermodal logistics scheduling. Int J Shipp Transp Logist 9(4):475–499
De Giovanni P (2020) Smart supply chains with vendor managed inventory, coordination, and environmental performance. Eur J Operat Res
De SK, Nayak PK, Khan A, Bhattacharya K, Smarandache F (2020) Solution of an EPQ model for imperfect production process under game and neutrosophic fuzzy approach. Appl Soft Comput 106397
Eliashberg J, Steinberg R (1987) Marketing-production decisions in an industrial channel of distribution. Manage Sci 33(8):981–1000
Ghashghaei H, Mozafari M (2020) A game theoretic approach to coordination of pricing, ordering, and co-op advertising in supply chains with stochastic demand. Scientia Iranica 27(6):3289–3304
Guo F, Liu Q, Liu D, Guo Z (2017) On production and green transportation coordination in a sustainable global supply chain. Sustainability 9(11):2071
He X, Prasad A, Sethi S (2009) Cooperative advertising and pricing in a dynamic stochastic supply chain: feedback Stackelberg strategies. Prod Oper Manage 18(1):78–94
He Y, Wang H, Guo Q, Xu Q (2019) Coordination through cooperative advertising in a two-period consumer electronics supply chain. J Retail Consum Serv 50:179–188
Hong X, Xu L, Du P, Wang W (2015) Joint advertising, pricing and collection decisions in a closed-loop supply chain. Int J Prod Econ 167:12–22
Jorgensen S, Zaccour G (1999) Equilibrium pricing and advertising strategies in a marketing channel. J Optim Theory Appl 102(1):111–125
Jorgensen S, Zaccour G (2003) Channel coordination over time: incentive equilibria and credibility. J Econ Dyn Control 27(5):801–822
Kang JH, Kim YD (2010) Coordination of inventory and transportation managements in a two-level supply chain. Int J Prod Econ 123(1):137–145
Ke H, Jiang Y (2020) Equilibrium analysis of marketing strategies in supply chain with marketing efforts induced demand considering free riding. Soft Comput, pp 1–12
Ke H, Wu Y, Huang H, Chen Z (2017) Pricing decision in a two-echelon supply chain with competing retailers under uncertain environment. J Uncertain Anal Appl 5:5. https://doi.org/10.1186/s40467-017-0059-2
Larsen TS, Thernoe C, Anderson C (2003) Supply chain collaboration theoretical perspective and empirical evidence. Int J Phys Distrib Logist 33(6):531–549
Lee H, Padmanabhan V, Whang S (1997) Information distortion in a supply chain: the bullwhip effect. Manage Sci 43(4):546–558
Li DF (2014) Decision and game theory in management with intuitionistic fuzzy sets, vol 308, pp 1–441. Springer, Berlin
Li T, Sethi SP, He X (2015) Dynamic pricing, production, and channel coordination with stochastic learning. Prod Oper Manage 24(6):857–882
Liu B, Liu Y (2002) Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans Fuzzy Syst 10(4):445–450
Liu Y, Liu B (2003) Expected value operator of random fuzzy variable and random fuzzy expected value models. Int J Uncertain Fuzz Knowl Based Syst 11(2):195–215
Malekian Y, Rasti-Barzoki M (2019) A game theoretic approach to coordinate price promotion and advertising policies with reference price effects in a two-echelon supply chain. J Retail Consum Serv 51:114–128
Mardani A, Hooker RE, Ozkul S, Yifan S, Nilashi M, Sabzi HZ, Fei GC (2019) Application of decision making and fuzzy sets theory to evaluate the healthcare and medical problems: a review of three decades of research with recent developments. Expert Syst Appl 137:202–231
Martín-Herrán G, Sigué SP (2017) An integrative framework of cooperative advertising: Should manufacturers continuously support retailer advertising? J Bus Res 70:67–73
Mozafari M, Karimi B, Mahootchi M (2016) A differential Stackelberg game for pricing on a freight transportation network with one dominant shipper and multiple oligopolistic carriers. Scientia Iranica 23(5):2391–2406
Naimi Sadigh A, Karimi B, Farahani RZ (2011) A game theoretic approach for two echelon supply chains with continuous depletion. Int J Manage Sci Eng Manage 6(6):408–412
Naimi Sadigh A, Chaharsooghi SK, Sheikhmohammady M (2016) Game-theoretic analysis of coordinating pricing and marketing decisions in a multi-product multi-echelon supply chain. Scientia Iranica 23(3):1459–1473
Naimi-Sadigh A, Chaharsooghi SK, Mozafari M (2021) Optimal pricing and advertising decisions with suppliers' oligopoly competition: Stackelberg-Nash game structures. J Ind Manage Optim 17(3):1423–1450
Noh J, Kim JS, Sarkar B (2019) Two-echelon supply chain coordination with advertising-driven demand under Stackelberg game policy. Eur J Ind Eng 13(2):213–244
Noorul Haq A, Kannan G (2006) Design of an integrated supplier selection and multi-echelon distribution inventory model in a built-to-order supply chain environment. Int J Prod Res 44(10):1963–1985
Sarkar B, Omair M, Kim N (2020) A cooperative advertising collaboration policy in supply chain management under uncertain conditions. Appl Soft Comput 88:105948
Schlosser R (2017) Stochastic dynamic pricing and advertising in isoelastic oligopoly models. Eur J Oper Res 259(3):1144–1155
Seddighi AH, Naimi-Sadigh A (2018) A mathematical model for fuel pricing considering supply chain network design decisions. Energy Eng Manage 8(2):58–69
SeyedEsfahani MM, Biazaran M, Gharakhani M (2011) A game theoretic approach to coordinate pricing and vertical co-op advertising in manufacturer-retailer supply chains. Eur J Oper Res 211(2):263–273
Sharanlou H, Husseinzadeh Kashan A, Tavakkoli-Moghaddam R (2020) Determining the price and refund of products in a supply chain with quality and advertising costs in a fuzzy environment. Soft Comput. https://doi.org/10.1007/s00500-020-05307-7
Shi J, Wang G, Xiong J (2016) Leader–follower stochastic differential game with asymmetric information and applications. Automatica 63:60–73
Spengler JJ (1950) Vertical integration and anti-trust policy. J Polit Econ 58(4):347–352
Taleizadeh AA, Charmchi M (2015) Optimal advertising and pricing decisions for complementary products. J Ind Eng Int 11(1):111–117
Taleizadeh AA, Mamaghan MK, Torabi SA (2020) A possibilistic closed-loop supply chain: pricing, advertising and remanufacturing optimization. Neural Comput Appl 32(4):1195–1215
Wang C, Tang W, Zhao R (2007) On the continuity and convexity analysis of the expected value function of a fuzzy mapping. J Uncertain Syst 1(2):148–160
Wang X, Liu Z, Chen H (2019) A composite contract for coordinating a supply chain with sales effort-dependent fuzzy demand. Int J Mach Learn Cybern 10(5):949–965
Woźniak M, Zielonka A, Sikora A, Piran MJ, Alamri A (2020) 6G-enabled IoT home environment control using fuzzy rules. IEEE Int Things J. https://doi.org/10.1109/JIOT.2020.3044940
Xie J, Neyret A (2009) Co-op advertising and pricing models in manufacturer-retailer supply chains. Comput Ind Eng 56(4):1375–1385
Xie J, Wei J (2009) Coordinating advertising and pricing in a manufacturer–retailer channel. Eur J Oper Res 197(2):785–791
Yan R (2010) Cooperative advertising, pricing strategy and firm performance in the e-marketing age. J Acad Mark Sci 38(4):510–519
Yue J, Austin J, Wang M, Huang Z (2006) Coordination of cooperative advertising in a two-level supply chain when manufacturer offers discount. Eur J Oper Res 168(1):65–85
Zadeh LA (1965) Fuzzy sets. Inform Control 8(3):338–353
Zhang J, Lei L, Zhang S, Song L (2017) Dynamic vs. static pricing in a supply chain with advertising. Comput Ind Eng 109:266–279
Zhou Y-W, Li J, Zhong Y (2018) Cooperative advertising and ordering policies in a two-echelon supply chain with risk-averse agents. Omega 75:97–117
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix A: Preliminaries
Appendix A: Preliminaries
Lemma 1
(Wang et al. 2007). Let \(\xi_{i}\) be independent fuzzy variables defined on the possibility spaces (\(\Theta_{i} , P\left( {\Theta_{i} } \right), {\text{Pos}}_{i} )\) with continuous membership function, \(i = 1,2,\ldots,n\) and \(f:X \subset R^{n} \to R\) a measurable function. If \(f\left( {x_{1} ,x_{2} , \ldots ,x_{n} } \right)\) is monotonic with respect to \(x_{i}\), respectively, then
-
(a)
\(f_{\alpha }^{U} \left( \xi \right) = f\left( {\xi_{1\alpha }^{V} ,\xi_{2\alpha }^{V} , \ldots ,\xi_{n\alpha }^{V} } \right)\) where \(\xi_{i\alpha }^{V} = \xi_{i\alpha }^{U}\), if \(f\left( {x_{1} ,x_{2} , \ldots ,x_{n} } \right)\) is nondecreasing with respect to \(x_{i} ;\xi_{i\alpha }^{V} = \xi_{i\alpha }^{L}\), otherwise,
-
(b)
\(f_{\alpha }^{L} \left( \xi \right) = f\left( {\xi_{1\alpha }^{{\overline{V}}} ,\xi_{2\alpha }^{{\overline{V}}} , \ldots ,\xi_{n\alpha }^{{\overline{V}}} } \right)\) where \(\xi_{i\alpha }^{{\overline{V}}} = \xi_{i\alpha }^{L}\), if \(f\left( {x_{1} ,x_{2} , \ldots ,x_{n} } \right)\) is nondecreasing with respect to \(x_{i} ;\xi_{i\alpha }^{{\overline{V}}} = \xi_{i\alpha }^{U}\), otherwise, where \(f_{\alpha }^{U} \left( \xi \right)\) and \(f_{\alpha }^{L} \left( \xi \right)\) denote the \(\alpha\)-optimistic and \(\alpha\)-pessimistic value of the fuzzy variable \(f\left( \xi \right)\), respectively.
Definition 1
(Liu and Liu 2002). Let \(\xi\) be a fuzzy variable, the expected value of \(\xi\) is defined as.
provided that at least one of the two integrals is finite.
Definition 2
(Liu and Liu 2002). Let \(f\) be a function on \(R \to R\) and \(\xi\) be a fuzzy variable, then the expected value \(E\left[ {f\left( \xi \right)} \right]\) is defined as
provided that at least one of the two integrals is finite.
Lemma 2
(Liu and Liu 2003). Let \(\xi\) be a fuzzy variable with finite expected value, then
Rights and permissions
About this article
Cite this article
Mozafari, M., Naimi-Sadigh, A. & Seddighi, A.H. Possibilistic cooperative advertising and pricing games for a two-echelon supply chain. Soft Comput 25, 6957–6971 (2021). https://doi.org/10.1007/s00500-021-05595-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-021-05595-7