Price and Service Competition of Dual-Channel Supply Chain with Consumer Returns

Table 1

The Stackelberg equilibriums.

	Case C1: 𝑡≤𝑡^𝑆1	Case C2: 𝑡^𝑆1≤𝑡≤𝑡^𝑆2	Case C3: 𝑡≥𝑡^𝑆2
𝑝^𝑆𝑑	12𝑀(1−𝛽)(2−𝜃)−𝛼𝜃−𝑡	(1−𝜃+𝑤)𝜃2−𝜃−𝑡	𝑐−𝑤+𝑤𝛼−𝛼𝑡+𝛼𝜃2𝛼
𝑝^𝑆𝑟	14𝑀2(1−𝜃+𝑤)+𝑡+(1−𝛽)(2−𝜃)−𝛼𝜃	1−𝜃+𝑤2−𝜃	𝑐−𝑤+𝑤𝛼+𝛼𝑡+𝛼𝜃2𝛼𝜃

𝑀=(𝛽−1−𝛼)𝜃²+(1+2𝑤+𝛼+𝑙𝛽−2𝑐−2𝑤𝛼−𝛽−𝑤𝛽)𝜃+2𝑐−2𝑙𝛽,
𝑡^𝑆₁=(2𝜃(1−𝜃+𝑤))/(2−𝜃)−𝑀/((1−𝛽)(2−𝜃)−𝛼𝜃), and
𝑡^𝑆₂=(2𝜃(1+𝑤−𝜃))/(2−𝜃)−(𝑐+𝑤𝛼−𝑤+𝛼𝜃)/𝛼.