Table 3.

Optimal decisions of five modes.

Modes	Pure PYO Mode (PP)	Self-Operated Dual-Channel Mode (SD)	Decentralized Dual-Channel Mode (DD)	Centralized Dual-Channel Mode (CD)	Contractual Cooperation Mode (CC)
Offline price	$p_f^{b*}=\frac{1}{2}(1+\overline{\theta }+c_f-h)$	$p_f^{s*}=\frac{1}{2}(1+\overline{\theta }+c_f-h)$	$p_f^{d*}=\frac{1}{2}(1+\overline{\theta }+c_f-h)$	$p_f^{*}=\frac{1}{2}(1+\overline{\theta }+c_f-h)$	$p_f^{N*}=\frac{1}{2}(1+\overline{\theta }+c_f-h)$
Online price	-	$p_o^{s*}=\frac{1}{2}(\alpha +\overline{\theta }-\frac{\eta t_o{}^2}{T^2})$	$\begin{array}{l}{p}_o^{d*}=\frac{1}{4}[\alpha (2+h+c_f-\overline{\theta })\\ \begin{array}{cc}& \end{array}+3\overline{\theta }-\frac{3\eta t_o{}^2}{T^2}]\end{array}$	$p_o^{*}=\frac{1}{2}(\alpha +\overline{\theta }-\frac{\eta t_o{}^2}{T^2})$	$p_o^{N*}=\frac{1}{2}(\alpha +\overline{\theta }-\frac{\eta t_o{}^2}{T^2})$
Wholesale price	-	-	$w^{d*}=\frac{1}{2}(\alpha +\overline{\theta }-\frac{\eta t_o{}^2}{T^2})$	-
Offline demand	$Q^{b*}=\frac{1}{2}(1+\overline{\theta }-h-c_f)$	$Q_f^{s*}=\frac{1}{2}\frac{(1-\alpha -h-c_f)T^2+\eta t_o{}^2}{(1-\alpha )T^2}$	$\begin{array}{l}{Q}_f^{d*}=\frac{1}{4}[h+c_f-\overline{\theta }-2-\frac{h+c_f}{1-\alpha }\\ \begin{array}{cc}& \end{array}-\frac{\eta t_o{}^2}{(1-\alpha )T^2}]\end{array}$	$Q_f^{*}=\frac{1}{2}\frac{(1-\alpha -h-c_f)T^2+\eta t_o{}^2}{(1-\alpha )T^2}$	$Q_f^{N*}=\frac{1}{2}\frac{(1-\alpha -h-c_f)T^2+\eta t_o{}^2}{(1-\alpha )T^2}$
Online demand	-	$Q_o^{s*}=\frac{1}{2}\frac{(h+c_f-\overline{\theta })\alpha T^2+\overline{\theta }{T}^2-\eta t_o{}^2}{(1-\alpha )\alpha T^2}$	$Q_o^{d*}=\frac{1}{4}[\frac{\overline{\theta }}{\alpha }+\frac{h+c_f}{(1-\alpha )\alpha }-\frac{\eta t_o{}^2}{(1-\alpha )\alpha T^2}]$	$Q_o^{*}=\frac{1}{2}\frac{(h+c_f-\overline{\theta })\alpha T^2+\overline{\theta }{T}^2-\eta t_o{}^2}{(1-\alpha )\alpha T^2}$	$Q_o^{N*}=\frac{1}{2}\frac{(h+c_f-\overline{\theta })\alpha T^2+\overline{\theta }{T}^2-\eta t_o{}^2}{(1-\alpha )\alpha T^2}$
Total demand	$Q^{b*}=\frac{1}{2}(1+\overline{\theta }-h-c_f)$	$Q_{}^{s*}=\frac{1}{2}\frac{(\alpha +\overline{\theta })T^2-\eta t_o{}^2}{\alpha T^2}$	$Q_{}^{d*}=\frac{[(2-h-c_f+\overline{\theta })\alpha +\overline{\theta }]T^2-\eta t_o{}^2}{4\alpha T^2}$	$Q_{}^{*}=\frac{1}{2}\frac{(\alpha +\overline{\theta })T^2-\eta t_o{}^2}{\alpha T^2}$	$Q_{}^{N*}=\frac{1}{2}\frac{(\alpha +\overline{\theta })T^2-\eta t_o{}^2}{\alpha T^2}$
Farmer cooperative’s profit	${\pi }_f^{b*}=\frac{1}{4}{(1+\overline{\theta }-h-c_f)}^2$	$\begin{array}{l}{\pi }_f^{\mathrm{s}*}=\frac{1}{4}[(1-2h-2c_f+2\overline{\theta })+\frac{{(h+c_f)}^2}{1-\alpha }\\ \begin{array}{l}\hfill \end{array}\begin{array}{l}\begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}\begin{array}{l}\begin{array}{l}+\frac{(\overline{\theta }-2\eta t_o{}^2)\overline{\theta }}{\alpha }-\frac{(h+c_f)2\eta t_o{}^2}{(1-\alpha )T^2}\\ +\frac{{\eta }^2{t}_o{}^4}{(1-\alpha )\alpha T^4}]-M\end{array}\hfill \end{array}\hfill \end{array}\end{array}$	$\begin{array}{l}{\pi }_f^{d*}=\hfill \end{array}\frac{{[(h+c_f-\overline{\theta })\alpha T^2+\overline{\theta }{T}^2-\eta t_o{}^2]}^2}{16(1-\alpha )\alpha T^4}$	-	${\pi }_f^{N*}={\pi }_f^N+M>{\pi }_f^{d*}$
Online retailer’s profit	-	-	$\begin{array}{l}\begin{array}{l}{\pi }_o^{d*}=\frac{1}{16}\hfill \end{array}[{(h+c_f-\overline{\theta })}^2+4(h-\overline{\theta }-c_f)+2\\ \begin{array}{cc}& \end{array}+\frac{{(h+c_f)}^2}{1-\alpha }+\frac{{\overline{\theta }}^2}{\alpha }+\frac{{\eta }^2{t}_o{}^4-2\eta t_o{}^2\overline{\theta }{T}^2}{(1-\alpha )\alpha T^4}]\end{array}$	-	${\pi }_o^{N*}={\pi }_o^N-M>{\pi }_o^{d*}$
Total profit	${\pi }_{}^{b*}=\frac{1}{4}{(1+\overline{\theta }-h-c_f)}^2$	$\begin{array}{l}{\pi }_{}^{\mathrm{s}*}=\frac{1}{4}[(1-2h-2c_f+2\overline{\theta })+\frac{{(h+c_f)}^2}{1-\alpha }\\ \begin{array}{l}\hfill \end{array}\begin{array}{l}\begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}\begin{array}{l}\begin{array}{l}+\frac{(\overline{\theta }-2\eta t_o{}^2)\overline{\theta }}{\alpha }-\frac{(h+c_f)2\eta t_o{}^2}{(1-\alpha )T^2}\\ +\frac{{\eta }^2{t}_o{}^4}{(1-\alpha )\alpha T^4}]-M\end{array}\hfill \end{array}\hfill \end{array}\end{array}$	$\begin{array}{l}{\pi }^{d*}=\frac{1}{16}\begin{array}{l}[{(h+c_f-\overline{\theta })}^2+4(h-\overline{\theta }-c_f)\hfill \end{array}\\ \begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}+\frac{{(h+c_f)}^2}{1-\alpha }]+\frac{{\overline{\theta }}^2}{16\alpha }+\frac{2{\eta }^2{t}_o{}^4}{(1-\alpha )\alpha T^4}\\ \begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}-\frac{2[(h+c_f-\overline{\theta })\alpha +2\overline{\theta }]\eta t_o{}^2}{(1-\alpha )\alpha T^2}\\ \begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}+\frac{{[(h+c_f-\overline{\theta })\alpha +\overline{\theta }]}^2}{(1-\alpha )\alpha }+\frac{1}{8}\end{array}$	$\begin{array}{l}{\pi }^{*}=\frac{1}{4}[(1-2h-2c_f+2\overline{\theta })+\frac{{(h+c_f)}^2}{1-\alpha }\\ \begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}-\frac{(h+c_f)2\eta t_o{}^2}{(1-\alpha )T^2}+\frac{{\eta }^2{t}_o{}^4}{(1-\alpha )\alpha T^4}\\ \begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}+\frac{(\overline{\theta }-2\eta t_o{}^2)\overline{\theta }}{\alpha }]\end{array}$	$\begin{array}{l}{\pi }^{\mathrm{N}*}=\frac{1}{4}[(1-2h-2c_f+2\overline{\theta })+\frac{{(h+c_f)}^2}{1-\alpha }\\ \begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}-\frac{(h+c_f)2\eta t_o{}^2}{(1-\alpha )T^2}+\frac{{\eta }^2{t}_o{}^4}{(1-\alpha )\alpha T^4}\\ \begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}\begin{array}{l}\hfill \end{array}+\frac{(\overline{\theta }-2\eta t_o{}^2)\overline{\theta }}{\alpha }]\end{array}$

* The specific profit functions of the online retailer and farmer cooperative under the revenue sharing contract are not presented due to its complexity. The range of the fixed transfer payment is $M\in [\frac{[(E-B+h^2)\alpha -(2h\overline{\theta }-B)]\alpha A{T}^4-DA}{8\alpha T^4(A+2c_f{T}^2)\left(1-\alpha \right)},\frac{[(E-2B+3h^2)\alpha -(2{\overline{\theta }}^2-2B+2h\overline{\theta }-2{c_f}^2)]\alpha A{T}^4-3DA}{16\alpha T^4(A+2c_f{T}^2)\left(1-\alpha \right)}]$.