The optimal channel structure with retail costs in a dual-channel supply chain

Abstract

This paper considers a dual-channel supply chain consisting of a monopoly manufacturer, an independent retailer and a continuum of heterogeneous consumers who are classified into two segments according to their channel preferences. Due to various activities undertaken in different channels leading to retail costs, we highlight the effect of retail costs (i.e. fixed, linear and quadratic costs) on the optimal channel structures for the manufacturer, consumers and society. Our results show that the retail cost greatly influences the optimal channel structures for different parties. First, the manufacturer's channel selection varies considerably across retail costs. Specifically, when there are variable costs (linear and quadratic costs): on the one hand, the manufacturer might give up the grocery encroachment strategy; on the other hand, some profitable strategies which are missed in the case with fixed cost are likely to be implemented. Second, both consumer surplus and social welfare are maximised in the manufacturer-owned online channel unless the linear costs are sufficiently high or the cost gap between different channels is large. Collectively, the optimal channel structure for the manufacturer is not always optimal for consumer surplus or social welfare.

Keywords:

• multi-channel management
• game theory
• retail costs
• consumer surplus
• social welfare

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jianghua Zhang  http://orcid.org/0000-0002-6734-3492

Notes

1 Since the fixed, linear and quadratic cost functions are representative functions that reflect different laws of change in marginal cost (i.e. zero, constant and incremental, respectively), we take these three cost types into account.

2 The bilateral monopoly assumption in our model follows Hsiao and Chen (2014) which allows us to isolate the effects of the retail cost on different parties.

3 We remain this assumption of Hsiao and Chen (2014) to isolate the effect of variable retail costs. Notably, f is sufficiently small to avoid the trivial result: if the introduction cost were prohibitively high, the manufacturer would have no incentive to introduce its own online channel.

4 Both assumptions are adopted by many related literatures, e.g. Hsiao and Chen (2014).

5 This setup follows Hsiao and Chen (2014) so as to show the different impact of variable costs from that of the fixed cost on the equilibrium solutions.

6 Due to space limitation, we put Figures 2–7 in the Appendix.

7 This result is based on the study of Hsiao and Chen (2014).

8 Comparing Figure 3 and Figure 2(a), we find that when $c\in [0,1],$ the channel selections are similar to the case with fixed cost. This finding is intuitive: the retail cost has an effect on the channel selection, but such effect is not too large to change firms' channel selections when $c\in [0,1]$. We omit $c\in [0,1]$ here for brevity, and focus only on the differences in results between the two cases. In addition, it is verifiable that the channel selections of the manufacturer and the retailer remain unchanged when $c\in (1,3)$ and the subsequent cases. The Mathematica codes are available upon request.

9 The well-known ‘double marginalisation’, first published by Spengler (1950), is the phenomenon in which different firms in the same industry that have their respective market powers but at different vertical levels in the supply chain (e.g. upstream and downstream) apply their own markups in prices.

Additional information

Funding

The work was supported by a grant from National Natural Science Foundation of China (Grant No. 71571111); Innovation Method Fund of China (Grant No. 2018IM020200); Fundamental Research Funds for Central Universities (Grant No. 2018JC055); China Postdoctoral Science Foundation (Grant No. 2019M662380). The authors also would like to thank the Qilu Young Scholars and Tang Scholars of Shandong University for financial and technical support.