Table 1 Symbol notation Decision...

Table 1

Symbol notation

Decision variables
$d$	The level of digital investment
$s$	Service level
$w$	Wholesale price
$p_{m}$	Online price
$p_{r}$	Offline price
Parameters
$c$	Unit production cost
$τ$	Unit transportation cost
θ	The sensitivity parameter of the service level (θ > 0)
δ	Perceived discount factor (0<δ < 1)
$v$	Perceived value follows U[0,1]
$λ$	Social work donation
$ρ$	Sensitivity parameters for CSR
$γ$	Sensitivity parameters for digital investment(⁠ $γ$ >0)
$k_{1}$	Investment cost factor for digital technology (⁠ $k_{1}$ >0)
$k_{2}$	Investment cost factor for service level (⁠ $k_{2}$ >0)
$U_{r}$	Consumer utility from the offline channel
$U_{m}$	Consumer utility from the online channel
$Π_{m}^{D} 、 Π_{r}^{D}$	Manufacturers' profit and retailers' profit under decentralized decision-making
$Π^{c}$	Profit of the supply chain under centralized decision-making
$Π_{m}^{H} 、 Π_{r}^{H}$	Manufacturers' profit and retailers' profit after coordination
$Π_{m}^{R} 、 Π_{r}^{R}$	Manufacturers' profit and retailers' profit under the retailer's CSR strategy

Decision variables
$d$	The level of digital investment
$s$	Service level
$w$	Wholesale price
$p_{m}$	Online price
$p_{r}$	Offline price
Parameters
$c$	Unit production cost
$τ$	Unit transportation cost
θ	The sensitivity parameter of the service level (θ > 0)
δ	Perceived discount factor (0<δ < 1)
$v$	Perceived value follows U[0,1]
$λ$	Social work donation
$ρ$	Sensitivity parameters for CSR
$γ$	Sensitivity parameters for digital investment( $γ$ >0)
$k_{1}$	Investment cost factor for digital technology ( $k_{1}$ >0)
$k_{2}$	Investment cost factor for service level ( $k_{2}$ >0)
$U_{r}$	Consumer utility from the offline channel
$U_{m}$	Consumer utility from the online channel
$Π_{m}^{D} 、 Π_{r}^{D}$	Manufacturers' profit and retailers' profit under decentralized decision-making
$Π^{c}$	Profit of the supply chain under centralized decision-making
$Π_{m}^{H} 、 Π_{r}^{H}$	Manufacturers' profit and retailers' profit after coordination
$Π_{m}^{R} 、 Π_{r}^{R}$	Manufacturers' profit and retailers' profit under the retailer's CSR strategy

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