Equilibrium supply chain structures in the presence of asymmetric manufacturer capabilities in service efficacy and provision

Abstract

In 2012, Tesla Motors announced that it would pursue company owned stores, while major automobile manufacturers, such as Ford and Honda, employ the traditional dealership model. Adding ‘service’ to the McGuire-Staelin duopoly game as another competitive instrument to ‘price’, this paper studies the role of service in shaping an equilibrium supply chain structure to show if and when a mixed supply chain structure of one integrated supply chain and one decentralized supply chain becomes an equilibrium outcome. Our model incorporates asymmetric manufacturer capabilities in service efficacy and provision, where service efficacy refers to the effectiveness of generating a higher demand for a given service level and service provision the cost-efficiency in producing service. Our results show that a mixed supply chain structure emerges as a Nash equilibrium outcome only if two products are moderately substitutable and one manufacturer is superior to the other in service provision with the former downward integrating and the latter decentralizing. Under this scenario, the superior manufacturer raises its profits by investing in service provision capabilities, widening the gap with its opponent, and furthermore, the superior manufacturer compensates for a less differentiated product if it is capable of providing service far more cheaply than its opponent.

Keywords:

• Supply chain management
• asymmetric manufacturer capabilities
• service efficacy
• service provision

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Bruce et al. (2004) and Bhardwaj and Fairhurst (2010) document the sources of asymmetric manufacturer capabilities in the fashion channel, where Zara is a significant player.

2 Other types of asymmetries previously considered in the literature include asymmetric price leadership situations (Chung & Lee, 2017; Edirisinghe et al., 2011) between supply chains and information asymmetry in horizontal (Li et al., 2013) or vertical (Chen et al., 2019) relationships within supply chains.

3 As early as 1985, Coughlan (1985) documents the empirical evidence of a mixed supply chain structure in the international semiconductor industry, but she concludes that a mixed supply chain structure is unstable, eventually evolving into an integrated one.

4 1985 Our results are presented using T = 1 but they hold for other values of T.

5 Using another demand function, $Q_{\mathrm{i}}=T+d_{\mathrm{i}}{a}_{\mathrm{i}}-{\mathrm{\beta }·d_{\mathrm{j}}·a}_{\mathrm{j}}-p_{\mathrm{i}}+\mathrm{\beta }{·p}_{\mathrm{j}},$ produces similar results.

6 Details of the results, including numerical evidences, are available upon request.

7 Our figures are drawn for d = 1 and c = 0.5, but the results hold for other parameter values.

8 The threshold values of β where ${\mathrm{\Pi }}_{{\mathrm{M}}_1}^{DD}={\mathrm{\Pi }}_{{\mathrm{M}}_1}^{ID}$ and ${\mathrm{\Pi }}_{{\mathrm{M}}_2}^{DD}={\mathrm{\Pi }}_{{\mathrm{M}}_2}^{DI}$ differ, and (D,D) becomes an equilibrium supply chain structure for the values of β satisfying both ${\mathrm{\Pi }}_{{\mathrm{M}}_1}^{DD}>{\mathrm{\Pi }}_{{\mathrm{M}}_1}^{ID}$ and ${\mathrm{\Pi }}_{{\mathrm{M}}_2}^{DD}>{\mathrm{\Pi }}_{{\mathrm{M}}_2}^{DI}.$

9 Our figures in the case of supply-side asymmetry are drawn for d = 1 and c = 0.5 but the results hold for other parameter values.

10 The higher the ratio ($\left(c_1·{\left(a_1\right)}^2\right)/{\Pi }_{M_1}$), the larger the service-provision cost to earn the same amount of profits, and this ratio is the highest under (I,I) regardless of parameter values. The proof of our analysis is available upon request.

11 The border between Regions A and D is the threshold values of β where ${\mathrm{\Pi }}_{{\mathrm{M}}_1}^{DD}={\mathrm{\Pi }}_{{\mathrm{M}}_1}^{ID},$ which differ from those where ${\mathrm{\Pi }}_{{\mathrm{M}}_2}^{DD}={\mathrm{\Pi }}_{{\mathrm{M}}_2}^{DI}$ as seen in Table 4. So there is a very narrow zone between Regions B and C (e.g., 0.9461 < β < 0.951 when d = 1, c = 0.5 and $\mathrm{\gamma }$=0.6) without any equilibrium supply chain structure.

12 In the case of demand-side asymmetry, as $\mathrm{\eta }$ decreases, the range of product substitutability over which (D,D) is a Nash equilibrium expands, because service fails to mitigate price competition, as the inferior manufacturer, for whom service becomes a less effective instrument, relies more heavily on price to compete with its opponent. Table C-2 in Appendix C shows how the range of β where (D,D) is an equilibrium outcome changes with $\eta .$

13 All the mathematical derivations in this section are available upon request.

14 Think of the extreme case where $\mathrm{\eta }$→1 and $\mathrm{\gamma }$→0. In this case the demand-side asymmetry is almost nil, while the supply-side asymmetry is maximal.

15 Interestingly, Xiao et al. (2014) have found other kinds of costs (for example, unit production cost and the retailer’s marginal selling cost) play an important role in determining an equilibrium supply chain structure.

16 “Tesla is looking for new locations ‘immediately available’ to expand service”, Fred Lambert, electrek., July 16, 2020.

17 “Tesla, too, sees service as central”, Jamie Butters, Automotive News, August 03, 2019.

18 https://www.tesla.com/support/do-it-yourself-model-3