Abstract
This paper studies a two-tier duopoly competing supply chain system consisting of two manufacturers and two exclusive retailers. Both manufacturers produce differentiated products and both retailers provide extended warranties for the products they sell. Two types of channel-structure strategy options are considered: a decentralized structure with a wholesale price contract and a coordinated structure with a sophisticated contract. We first derive the equilibrium outcomes under three possible chain-to-chain competition scenarios. Subsequently, we reveal how manufacturers control their retail channels to gain more supply chain system profit under an interactive environment with supply chain competition and retailers’ extended warranties. We find that pure coordinated channel competition and pure decentralized channel competition may both reach equilibrium. Furthermore, the interaction forces of supply chain competition and extended warranty service significantly impact the characteristics of the equilibria. Finally, we analyze the competing supply chain’s coordination contract design by using the example of a two-part tariff contract, and determine the feasible contract parameter range that results in a win-win solution for supply chain members.
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References
Ai, X. Z., Chen, J., Zhao, H. X., & Tang, X. W. (2012a). Competition among supply chains: Implications of full return policy. International Journal of Production Economics, 139, 257–265.
Ai, X. Z., Chen, J., & Ma, J. H. (2012b). Contracting with demand uncertainty under supply chain competition. Annals of Operations Research, 201(1), 17–38.
Akerlof, G. A. (1970). The market for ’“Lemons”: Quality uncertainty and mechanism design. Quarterly Journal of Economics, 84(3), 488–500.
Anderson, E. J., & Bao, Y. (2010). Price competition with integrated and decentralized supply chains. European Journal of Operational Research, 200(1), 227–234.
Balachander, S. (2001). Warranty signaling and reputation. Management Science, 47(9), 1282–1289.
Barnes, D. (2006). Competing supply chains are the future. Financial Times, November 8.
Berner, R. (2004). The warranty windfall: Service contracts are cash cows—But retailers are mum about their importance. Business Week, December 20, pp. 84–86.
Cachon, G. P. (2003). Supply chain coordination with contracts. In A. G. de Kok & S. C. Graves (Eds.), Handbooks in operations research and management science: Supply chain management. North-Holland: Elsevier.
Cachon, G. P., & Gürhan, Kök A. (2010). Competing manufacturers in a retail supply chain: On contractual form and coordination. Management Science, 56(3), 571–589.
Cooper, R., & Ross, T. W. (1985). Product warranties and double moral hazard. RAND Journal of Economics, 16(1), 103–113.
Coughlan, A. T. (1985). Competition and cooperation in marketing channel choice: Theory and application. Marketing Science, 4(2), 110–129.
Demirag, O. C., Keskinocak, P., & Swann, J. (2011). Customer rebates and retailer incentives in the presence of competition and price discrimination. European Journal of Operational Research, 215(1), 268–280.
Desai, P., & Padmanabhan, P. (2004). Durable goods, extended warranty and channel coordination. Review of Marketing Science, 2(2), 1–23.
Dybvig, P. H., & Lutz, N. A. (1993). Warranties, durability, and maintenance: Two-sided moral hazard in a continuous-time model. Reviews of Economic Studies, 60(3), 575–597.
Emons, W. (1988). Warranties, moral hazard, and the lemons problem. Journal of Economic Theory, 46(1), 16–33.
Emons, W. (1989). The theory of warranty contracts. Journal of Economic Surveys, 3(1), 43–57.
Fang, Y., & Shou, B. (2015). Managing supply uncertainty under supply chain Cournot competition. European Journal of Operational Research, 243(1), 156–176.
Feng, Q., & Lu, L. X. (2012). The strategic perils of low cost outsourcing. Management Science, 58(6), 1196–1210.
Feng, Q., & Lu, L. X. (2013). Supply chain contracting under competition: Bilateral bargaining versus Stackelberg. Production and Operations Management, 22(3), 661–675.
Gallego, G., Wang, R., Hu, M., Ward, J., & Beltran, J. L. (2015). No claim? Your gain: Design of residual value extended warranties under risk aversion and strategic claim behavior. Manufacturing & Service Operations Management, 17(1), 87–100.
Grossman, S. (1981). The informational role of warranties and private disclosure about product quality. Journal of Law and Economics, 24(3), 461–483.
Gupta, S., & Loulou, R. (1998). Process innovation, production differentiation, and channel structure: Strategic incentives in a duopoly. Marketing Science, 17(4), 301–316.
Gupta, S., & Loulou, R. (2008). Channel structure with knowledge spillovers. Marketing Science, 27(2), 247–261.
Ha, A. Y., & Tong, S. L. (2008). Contracting and information sharing under supply chain competition. Management Science, 54(4), 701–715.
Ha, A. Y., Tong, S. L., & Zhang, H. (2011). Sharing demand information in competing supply chains with production diseconomies. Management Science, 57(3), 566–581.
Heal, G. (1977). Guarantees and risk sharing. The Review of Economic Studies, 44(3), 549–560.
Heese, H. S. (2012). Retail strategies for extended warranty sales and impact on manufacturer base warranties. Decision Sciences, 43(2), 341–367.
Hollis, A. (1999). Extended warranties, adverse selection and aftermarkets. Journal of Risk Insurance, 66(3), 321–343.
Huffman, M. (2015). Why retailers are betting you’ll buy the extended warranty. http://www.consumeraffairs.com/news/why-retailers-are-betting-youll-buy-the-extended-warranty-010715.html.
Jeuland, A. P., & Shugan, S. M. (1983). Managing channel profits. Marketing Science, 2(3), 239–272.
Jiang, B., & Zhang, X. B. (2011). How does a retailer’s service plan affect a manufacturer’s warranty? Management Science, 57(4), 727–740.
Li, K., Mallik, S., & Chhajed, D. (2012). Design of extended warranties in supply chains under additive demand. Production and Operations Management, 21(4), 730–746.
Liu, X., Li, J., Wu, J., & Zhang, G. (2017). Coordination of supply chain with a dominant retailer under government price regulation by revenue sharing contracts. Annals of Operations Research, 257(1–2), 587–612.
Lus, B., & Muriel, A. (2009). Measuring the impact of increased product substitution on pricing and capacity decisions under linear demand models. Production and Operations Management, 18(1), 95–113.
Ma, P., Wang, H., & Shang, J. (2013). Contract design for two-stage supply chain coordination: Integrating manufacturer-quality and retailer-marketing efforts. International Journal of Production Economics, 146(2), 745–755.
McGuire, W., & Staelin, R. (1983). An industry equilibrium analysis of downstream vertical integration. Marketing Science, 2(2), 161–191.
Moorthy, K. S. (1987). Managing channel profits: Comment. Marketing Science, 6(4), 375–379.
Moorthy, K. S. (1988). Strategic decentralization in channels. Marketing Science, 7(4), 335–355.
Mussa, M., & Rosen, S. (1978). Monopoly and product quality. Journal of Economic Theory, 18(2), 301–317.
O’Brien, D. P., & Shaffer, G. (2005). Bargaining, bundling, and clout: The portfolio effects of horizontal mergers. Rand Journal of Economics, 23(3), 573–595.
Padmanabhan, V. (1995). Usage heterogeneity and extended warranty strategy. Journal of Economics & Management, 4(1), 33–53.
Padmanabhan, V., & Rao, R. C. (1993). Warranty policy and extended service contract: Theory and application to automobiles. Marketing Science, 12(3), 230–247.
Partha Sarathi, G., Sarmah, S. P., & Jenamani, M. (2014). An integrated revenue sharing and quantity discounts contract for coordinating a supply chain dealing with short life-cycle products. Applied Mathematical Modelling, 38, 4120–4136.
Piccolo, S., & Reisinger, M. (2011). Exclusive territories and manufacturers’ collusion. Management Science, 57(7), 1250–1266.
Seifbarghy, M., Nouhi, K., & Mahmoudi, A. (2015). Contract design in a supply chain considering price and quality dependent demand with customer segmentation. International Journal of Production Economics, 167, 108–118.
Shugan, S. M. (1985). Implicit understandings in channels of distribution. Management Science, 31(4), 435–460.
Sinha, S., & Sarmah, S. P. (2011). Price and warranty competition in a duopoly supply chain. In T. M. Choi & T. C. Edwin Cheng (Eds.), Supply chain coordination under uncertainty (international handbooks on information systems) (pp. 281–314). Berlin: Springer.
Soberman, D. A. (2003). Simultaneous signaling and screening with warranties. Journal of Marketing Research, 40(2), 176–192.
Spengler, J. (1950). Vertical integration and antitrust policy. Journal of Political Economy, 58(4), 347–352.
Stiglitz, J. E. (1977). Monopoly, non-linear pricing and imperfect information: The insurance market. Review of Economic Studies, 44(3), 407–430.
Trivedi, M. (1988). Distribution channels: An extension of exclusive retailership. Management Science, 44(7), 896–909.
Wu, C. C., Chou, C. Y., & Huang, C. (2009a). Optimal price, warranty length and production rate for free replacement policy in the static demand market. Omega: International Journal of Management Science, 37(1), 29–39.
Wu, D. S., Baron, O., & Berman, O. (2009b). Bargaining in competing supply chains with uncertainty. European Journal of Operational Research, 197(2), 548–556.
Yang, R., & Ma, L. (2017). Two-part tariff contracting with competing unreliable suppliers in a supply chain under asymmetric information. Annals of Operations Research, 257(1–2), 559–585.
Zhang, J. X., Liu, G. W., Zhang, Q., & Bai, Z. Y. (2015). Coordinating a supply chain for deteriorating items with a revenue sharing and cooperative investment contract. Omega: International Journal of Management Science, 56, 37–49.
Acknowledgements
The authors gratefully acknowledge the editor and two anonymous referees for their helpful comments and suggestions which significantly improve the quality of the paper. This research is supported by the National Natural Science Foundation of China (Grant Nos. 71402101, 71372140, 71402102, 71472126, 71432003, 71572114, and 71531003).
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Appendix
Appendix
Proof of equilibrium outcomes under DD case
At the competition stage of the DD case, given manufacturer i’s wholesale price \(w_i\), retailer i makes decisions on the product retail price and the extended warranty price to maximize its own profit. Noting that the contracts are unobservable to the firms of the rival supply chain, retailer i’s best response in terms of retail price and extended warranty price \((p_i, x_i)\) depends on its own contract parameter \(w_i\) and on the influence of its competitor’s contract parameter \(w_j\), which is implicitly captured through \((p_j, x_j)\), where \(i=1,2\); \(j=3-i\). Equation (A.1) gives the expression of retailer i’s best response functions, \(i=1,2; j=3-i\).
Manufacturers take the retailers’ retail price decisions into account when setting their wholesale prices, which yield the manufacturers’ wholesale price decisions as the functions of \(p_i\) and \(p_j\),
Substituting the wholesale price decisions given above into the response functions of the retail prices and extended warranty prices given in (A.1), we obtain the equilibria of the retail prices \(p_i^{i(D)j(D)}\) and the extended warranty prices \(x_i^{i(D)j(D)}\) as given in Table 2. The equilibrium product quantity \(q_i^{i(D)j(D)}\) and extended warranty quantity \(Q_i^{i(D)j(D)}\) can be determined based on the equilibrium retail prices and equilibrium extended warranty prices. Again, substituting equilibrium retail prices into the wholesale prices response functions as given in (A.2) yields the equilibrium wholesale price \({w_i}^{i(D)j(D)}\) as given in Table 2. Using the equilibrium expressions \(p_i^{i(D)j(D)}\), \(x_i^{i(D)j(D)}\) and \(w_i^{i(D)j(D)}\), we find the supply chain players’ profits and total chain profit, which are shown in Table 2. \(\square \)
Proof of Proposition 2
Based on the calculations given in Sects. 3.1 and 3.3, it can be proved that
where \(i=1, 2\); \(j=3-i\). Based on the calculations given in Sects. 3.2 and 3.3, we can compute
where \(i=1, 2\); \(j=3-i\). \(\square \)
Proof of Theorem 1
Given that supply chain \(j (j=3-i)\) is decentralized, the difference in profit for the supply chain \(i(i=1,2)\) from choosing a coordinated channel or a decentralized channel is as follows:
where
It can be calculated that if \(0<t<0.9282d\) and \(0\le r<r_{cd,dd}\), or \(0.9282d<t\le t_0\), then \(G_2>0\), which indicates \(\pi _i^{i(C)j(D)}>\pi _i^{i(D)j(D)}\). Otherwise, \(\pi _i^{i(C)j(D)}\le \pi _i^{i(D)j(D)}\). Moreover, iff \(0<t<0.9282d\) and \(r=r_{cd,dd}\), \(\pi _i^{i(D)j(D)}=\pi _i^{i(C)j(D)}\). Next, we can compute the difference in the total chain profit under a coordinated or decentralized channel structure given that the rival supply chain is coordinated. The difference between \(\pi _i^{i(C)j(C)}\) and \(\pi _i^{i(D)j(C)}\) is
where
It can be calculated that if \(0\le r<0.9194\) and \(0<t\le t_0\), or \(0.9194<r<1\) and \(t_{cc,cd}< t\le t_0\), then \(G_4>0\), which indicates that \(\pi _i^{i(C)j(C)}>\pi _i^{i(D)j(C)}\); otherwise, \(\pi _i^{i(C)j(C)}\le \pi _i^{i(D)j(C)}\). Moreover, iff \(0.9194<r<1\) and \(t=t_{cc,cd}\), \(\pi _i^{i(C)j(C)}=\pi _i^{i(D)j(C)}\). \(\square \)
Proof of Theorem 3
Based on the calculations given in Sects. 3.1 and 3.2, we can compute
Again, we can compute
where
It can be concluded that if \(0\le r<\min \{r_{cc,dd}, \sqrt{1-\frac{t}{2d}}\}\) (i.e.,\(0\le r<r_{cc,dd}\) and \(0<t\le t_0\)), then \(G_6<0\), which indicates that \(\pi _i^{i(C)j(C)}>\pi _i^{i(D)j(D)}\); otherwise, \(\pi _i^{i(C)j(C)}\le \pi _i^{i(D)j(D)}\)( \(\pi _i^{i(C)j(C)}=\pi _i^{i(D)j(D)}\) only if \(0<t<1.3764\) and \(r=r_{cc,dd}\)). \(\square \)
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Ma, J., Ai, X., Yang, W. et al. Decentralization versus coordination in competing supply chains under retailers’ extended warranties. Ann Oper Res 275, 485–510 (2019). https://doi.org/10.1007/s10479-018-2871-6
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DOI: https://doi.org/10.1007/s10479-018-2871-6