# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2021047

## Assembly system with omnichannel coordination

 1 Business School, Nanjing Normal University, Qixia District, Nanjing 210023, China 2 Stern School of Business, New York University, 44 West Fourth Street, New York, NY 10012, USA 3 Supply Chain and Logistics Management Research Lab, Department of Business Administration, School of Business, Soochow University, Taipei, Taiwan

* Corresponding author: Zhisong Chen

Received  May 2020 Revised  December 2020 Published  March 2021

Fund Project: This work is supported by the National Natural Science Foundation of China (Grant No. 71603125), China Scholarship Council (Grant No. 201706865020), the National Key R & D Program of China (Grant No. 2017YFC0404600), China Postdoctoral Science Foundation (Grant No. 2019M651833), Social Science Foundation of Jiangsu Province in China (Grant No. 19GLC003), and Young Leading Talent Program of Nanjing Normal University

Assembly system with omnichannel is rarely studied in literature. This paper explores the equilibrium and coordination issues for an omnichannel assembly system. Four different game-theoretical model types applying four operational strategies - a total of sixteen analytical models - are developed and analyzed for both omnichannel and pure channel modes. The numerical analysis of an electronic product assembly system provides a clearer understanding of the solutions and their effects on the profits in the assembly system for different model types and operational strategies. A further sensitivity analysis with focus on an omnichannel with offline channel subsidy (OMS) creates better insights regarding how changes of key parameters affect the assembly system profits. It is found that the omnichannel mode with or without offline channel subsidy can deliver much better operational performance to the assembly system via mutual fusion effect than that of a pure online- or offline-channel mode. Furthermore, the offline channel subsidy can amplify to a very large extent the mutual fusion effect to increase the product demand dramatically and thus improving the operational performance of the assembly system in the omnichannel business scenario. The best operational strategy for the assembly system in the omnichannel business scenario is the coordination strategy with offline channel subsidy.

Citation: Zhisong Chen, Shong-Iee Ivan Su. Assembly system with omnichannel coordination. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021047
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##### References:
A Generic Assembly System with Omnichannel
Impact of Offline Channel Subsidy Factor ($\delta$) Change on Profits
Impact of Price Elasticity Index of the Expected Demand ($b$) Change on Profits
Impact of Mutual fusion Coefficient ($\theta$) Change on Profits
Modelling Notations and Explanations
 Parameter/Variable Explanations $c$ Unit assembly cost of the final product $c_i$ Unit cost of the $i^{\text {th }}$ module $w_i$ Wholesale price of the $i^{\text {th }}$ module $c_e$ Operational cost of the online channel $c_s$ Operational cost of the offline channel $p$ Retail price of the final product in the online/offline channel $z$ Stock factor $a$ Positive constant number $b$ Price-elasticity index of the expected demand $\theta$ Mutual fusion coefficient between channels $\eta$ Clearance discount price factor, and $0<\eta<1$ ${\lambda _0}$ Market demand share of the online channel, and $0<\lambda_{0}<1$ $\delta$ The offline channel subsidy factor, and $0<\delta<1$ $\kappa$ The offline channel discount price factor, and $\kappa=1-\delta$ $h$ The reaction extent of $\lambda(\kappa)$ w.r.t. the change of $\kappa$ $\phi$ Revenue keeping rate, and $0<\phi<1$ $x$ The random factor defined in the range $[A, B]$ with $B>A>0$ $\mu$ Mean value of random factor $\sigma$ Standard deviation of random factor
 Parameter/Variable Explanations $c$ Unit assembly cost of the final product $c_i$ Unit cost of the $i^{\text {th }}$ module $w_i$ Wholesale price of the $i^{\text {th }}$ module $c_e$ Operational cost of the online channel $c_s$ Operational cost of the offline channel $p$ Retail price of the final product in the online/offline channel $z$ Stock factor $a$ Positive constant number $b$ Price-elasticity index of the expected demand $\theta$ Mutual fusion coefficient between channels $\eta$ Clearance discount price factor, and $0<\eta<1$ ${\lambda _0}$ Market demand share of the online channel, and $0<\lambda_{0}<1$ $\delta$ The offline channel subsidy factor, and $0<\delta<1$ $\kappa$ The offline channel discount price factor, and $\kappa=1-\delta$ $h$ The reaction extent of $\lambda(\kappa)$ w.r.t. the change of $\kappa$ $\phi$ Revenue keeping rate, and $0<\phi<1$ $x$ The random factor defined in the range $[A, B]$ with $B>A>0$ $\mu$ Mean value of random factor $\sigma$ Standard deviation of random factor
Framework of Game-Theoretical Decision Models
 Section Channel Strategy Game-Theoretical Decision Models Theories Applied 4.1 Omnichannel mode without offline channel subsidy (OMO mode) 4.1.1 Centralized Decision Model OT & BC 4.1.2 Decentralized Decision Model SG & BC 4.1.2.1 Assembler's Decision SG & BC 4.1.2.2 Suppliers' Simultaneous Decision SG & BC 4.1.2.3 Suppliers' Sequential Decision SG & BC 4.1.3 Coordination Decision Model RSC & BC 4.2 Omnichannel OT+SG+RSC+BC mode with offline Centralized/Decentralized/Coordination channel subsidy Decision Models under OMS mode (OMS mode) 4.3 Pure online/offline Centralized/Decentralized/Coordination Decision Models under POC/PFC mode OT+SG+RSC+BC channel mode (POC/PFC mode) Notation: OT: Optimization Theory; BC: Bertrand Competition; SG: Stackelberg Game; RSC: Revenue Sharing Contract
 Section Channel Strategy Game-Theoretical Decision Models Theories Applied 4.1 Omnichannel mode without offline channel subsidy (OMO mode) 4.1.1 Centralized Decision Model OT & BC 4.1.2 Decentralized Decision Model SG & BC 4.1.2.1 Assembler's Decision SG & BC 4.1.2.2 Suppliers' Simultaneous Decision SG & BC 4.1.2.3 Suppliers' Sequential Decision SG & BC 4.1.3 Coordination Decision Model RSC & BC 4.2 Omnichannel OT+SG+RSC+BC mode with offline Centralized/Decentralized/Coordination channel subsidy Decision Models under OMS mode (OMS mode) 4.3 Pure online/offline Centralized/Decentralized/Coordination Decision Models under POC/PFC mode OT+SG+RSC+BC channel mode (POC/PFC mode) Notation: OT: Optimization Theory; BC: Bertrand Competition; SG: Stackelberg Game; RSC: Revenue Sharing Contract
Analytical Results under the OMO Mode
 Decentralized (Equilibrium) strategy Coordination strategy Suppliers' Simultaneous Actions Suppliers' Sequential Actions $F\left(z_{*}\right)$ $F\left(z_{d}\right)=F\left(z_{c}\right)$ $F\left(z_{d^{\prime}}\right)=F\left(z_{c}\right)$ $F\left(z_{c}\right)=\frac{1}{(1-\eta)(b-\theta)}+\frac{(b-\theta-1) \Lambda\left(z_{c}\right)}{(b-\theta) z_{c}}$ $p_{*}$ $p_{d}=\frac{b-\theta}{b-\theta-n} p_{c}$ $p_{d^{\prime}}=\left(\frac{b-\theta}{b-\theta-1}\right)^{n} p_{c}$ $p_{c}=\frac{b-\theta}{b-\theta-1} \frac{\left[c+\lambda_{0} c_{e}+\left(1-\lambda_{0}\right) c_{s}+\sum_{i=1}^{n} c_{i}\right] z_{c}}{z_{c}-(1-\eta) \Lambda\left(z_{c}\right)}$ $q_{*}$ $q_{d}=\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta} q_{c}$ $q_{d^{\prime}}=\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)} q_{c}$ $q_{c}=y\left(p_{c}\right) z_{c}$ $w_{i}^{*}$ $w_{i}^{d}=\frac{1}{b-\theta-n}\left[c+\lambda_{0} c_{e}+\left(1-\lambda_{0}\right) c_{s}+\sum_{i=1}^{n} c_{i}\right]+c_{i}$ $w_{i}^{d^{\prime}}=\frac{(b-\theta)^{i-1}}{(b-\theta-1)^{i}}\left[c+\lambda_{0} c_{e}+\left(1-\lambda_{0}\right) c_{s}+\sum_{i=1}^{n} c_{i}\right]+c_{i}$ $w_{i}^{c}=\phi^{*} c_{i}$ $\Pi_{S_{i}}^{*}$ $\Pi_{S_{i}}^{d}=\frac{b-\theta-1}{b-\theta}\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1} \Pi_{S C}^{c}$ $\Pi_{S_{i}}^{d^{\prime}}=\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)-i+1} \Pi_{S C}^{c}$ $\Pi_{S_{i}}^{c}=\frac{c_{i}}{\sum_{i=1}^{n} c_{i}}\left(1-\phi^{*}\right) \Pi_{S C}^{c}$ $\Pi_{A}^{*}$ $\Pi_{A}^{d}=\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1} \Pi_{S C}^{c}$ $\Pi_{A}^{d^{\prime}}=\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta-1)} \Pi_{S C}^{c}$ $\Pi_{A}^{c}=\phi^{*} \Pi_{S C}^{c}$ $\Pi_{S C}^{*}$ $\Pi_{S C}^{d}=\left[(n+1)-\frac{n}{b-\theta}\right]\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1} \Pi_{S C}^{c}$ $\Pi_{S C}^{d^{\prime}}=\left[(b-\theta)\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta-1)}-(b-\theta-1)\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)}\right] \Pi_{S C}^{c}$ $\Pi_{S C}^{c}=\frac{1}{b-\theta-1}\left[c+\lambda_{0} c_{e}+\left(1-\lambda_{0}\right) c_{s}+\sum_{i=1}^{n} c_{i}\right] q_{c}$ $\phi^{*}$ - - ${\phi ^*} \in [\underline \phi ,\bar \phi ]$ note: $\underline{\phi}=\max \left\{\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1}, \left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta-1)}\right\}$, $\bar{\phi}=\min _{i \in N}\left\{1-\frac{\sum_{i=1}^{n} c_{i}}{c_{i}} \max \left\{\frac{b-\theta-1}{b-\theta-n}\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta}, \left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)-i+1}\right\}\right\}$
 Decentralized (Equilibrium) strategy Coordination strategy Suppliers' Simultaneous Actions Suppliers' Sequential Actions $F\left(z_{*}\right)$ $F\left(z_{d}\right)=F\left(z_{c}\right)$ $F\left(z_{d^{\prime}}\right)=F\left(z_{c}\right)$ $F\left(z_{c}\right)=\frac{1}{(1-\eta)(b-\theta)}+\frac{(b-\theta-1) \Lambda\left(z_{c}\right)}{(b-\theta) z_{c}}$ $p_{*}$ $p_{d}=\frac{b-\theta}{b-\theta-n} p_{c}$ $p_{d^{\prime}}=\left(\frac{b-\theta}{b-\theta-1}\right)^{n} p_{c}$ $p_{c}=\frac{b-\theta}{b-\theta-1} \frac{\left[c+\lambda_{0} c_{e}+\left(1-\lambda_{0}\right) c_{s}+\sum_{i=1}^{n} c_{i}\right] z_{c}}{z_{c}-(1-\eta) \Lambda\left(z_{c}\right)}$ $q_{*}$ $q_{d}=\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta} q_{c}$ $q_{d^{\prime}}=\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)} q_{c}$ $q_{c}=y\left(p_{c}\right) z_{c}$ $w_{i}^{*}$ $w_{i}^{d}=\frac{1}{b-\theta-n}\left[c+\lambda_{0} c_{e}+\left(1-\lambda_{0}\right) c_{s}+\sum_{i=1}^{n} c_{i}\right]+c_{i}$ $w_{i}^{d^{\prime}}=\frac{(b-\theta)^{i-1}}{(b-\theta-1)^{i}}\left[c+\lambda_{0} c_{e}+\left(1-\lambda_{0}\right) c_{s}+\sum_{i=1}^{n} c_{i}\right]+c_{i}$ $w_{i}^{c}=\phi^{*} c_{i}$ $\Pi_{S_{i}}^{*}$ $\Pi_{S_{i}}^{d}=\frac{b-\theta-1}{b-\theta}\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1} \Pi_{S C}^{c}$ $\Pi_{S_{i}}^{d^{\prime}}=\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)-i+1} \Pi_{S C}^{c}$ $\Pi_{S_{i}}^{c}=\frac{c_{i}}{\sum_{i=1}^{n} c_{i}}\left(1-\phi^{*}\right) \Pi_{S C}^{c}$ $\Pi_{A}^{*}$ $\Pi_{A}^{d}=\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1} \Pi_{S C}^{c}$ $\Pi_{A}^{d^{\prime}}=\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta-1)} \Pi_{S C}^{c}$ $\Pi_{A}^{c}=\phi^{*} \Pi_{S C}^{c}$ $\Pi_{S C}^{*}$ $\Pi_{S C}^{d}=\left[(n+1)-\frac{n}{b-\theta}\right]\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1} \Pi_{S C}^{c}$ $\Pi_{S C}^{d^{\prime}}=\left[(b-\theta)\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta-1)}-(b-\theta-1)\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)}\right] \Pi_{S C}^{c}$ $\Pi_{S C}^{c}=\frac{1}{b-\theta-1}\left[c+\lambda_{0} c_{e}+\left(1-\lambda_{0}\right) c_{s}+\sum_{i=1}^{n} c_{i}\right] q_{c}$ $\phi^{*}$ - - ${\phi ^*} \in [\underline \phi ,\bar \phi ]$ note: $\underline{\phi}=\max \left\{\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1}, \left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta-1)}\right\}$, $\bar{\phi}=\min _{i \in N}\left\{1-\frac{\sum_{i=1}^{n} c_{i}}{c_{i}} \max \left\{\frac{b-\theta-1}{b-\theta-n}\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta}, \left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)-i+1}\right\}\right\}$
Analytical Results under the OMS Mode
 Decentralized (Equilibrium) strategy Coordination strategy Suppliers' Simultaneous Actions Suppliers' Sequential Actions $F\left(z_{*}\right)$ $F\left(z_{sd}\right)=F\left(z_{sc}\right)$ $F\left(z_{sd^{\prime}}\right)=F\left(z_{sc}\right)$ $F\left(z_{s c}\right)=\frac{1}{(1-\eta)(b-\theta)}+\frac{(b-\theta-1) \Lambda\left(z_{s c}\right)}{(b-\theta) z_{s c}}$ $p_{*}$ $p_{sd}=\frac{b-\theta}{b-\theta-n} p_{sc}$ $p_{sd^{\prime}}=\left(\frac{b-\theta}{b-\theta-1}\right)^{n} p_{sc}$ $p_{s c}=\frac{b-\theta}{b-\theta-1} \frac{\left\{c+\lambda(\kappa) c_{e}+[1-\lambda(\kappa)] c_{s}+\sum_{i=1}^{n} c_{i}\right\} z_{s c}}{z_{s c}-(1-\eta) \Lambda\left(z_{s c}\right)}$ $q_{*}$ $q_{sd}=\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta} q_{sc}$ $q_{sd^{\prime}}=\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)} q_{sc}$ $q_{s c}=\left\{\lambda(\kappa) \kappa^{\theta}+[1-\lambda(\kappa)] \kappa^{-b}\right\} y\left(p_{s c}\right) z_{x}$ $w_{i}^{*}$ $w_i^{sd} = \frac{1}{{b - \theta - n}}\left\{ {c + \lambda (\kappa ){c_e} + [1 - \lambda (\kappa )]{c_s} + \sum\nolimits_{i = 1}^n {{c_i}} } \right\} + {c_i}$ $w_{i}^{s d^{\prime}}=\frac{(b-\theta)^{i-1}}{(b-\theta-1)^{i}}\left\{c+\lambda(\kappa) c_{e}+[1-\lambda(\kappa)] c_{s}+\sum\nolimits_{i=1}^{n} c_{i}\right\}+c_{i}$ $w_{i}^{sc}=\phi^{*} c_{i}$ $\Pi_{S_{i}}^{*}$ $\Pi_{S_{i}}^{s d}=\frac{b-\theta-1}{b-\theta}\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1} \Pi_{S C}^{s c}$ $\Pi_{S_{i}}^{s d^{\prime}}=\left(\frac{b-\theta-1}{b-\theta}\right)^{n{(b-\theta)-i+1}} \Pi_{S C}^{s c}$ $\Pi_{S_{i}}^{s c}=\frac{c_{i}}{\sum_{i=1}^{n} c_{i}}\left(1-\phi^{*}\right) \Pi_{S C}^{s c}$ $\Pi_{A}^{*}$ $\Pi_{A}^{s d}=\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1} \Pi_{S C}^{s c}$ $\Pi_{A}^{s d^{\prime}}=\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta-1)} \Pi_{S C}^{s c}$ $\Pi_{A}^{s c}=\phi^{*} \Pi_{S C}^{s c}$ $\Pi_{S C}^{*}$ $\Pi_{S C}^{s d}=\left[(n+1)-\frac{n}{b-\theta}\right]\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1} \Pi_{S C}^{s c}$ $\Pi_{S C}^{s d^{\prime}}=\left[(b-\theta)\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta-1)}-(b-\theta-1)\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)}\right] \Pi_{S C}^{s c}$ $\Pi_{S C}^{s c}=\frac{1}{b-\theta-1}\left\{c+\lambda(\kappa) c_{e}+[1-\lambda(\kappa)] c_{s}+\sum_{i=1}^{n} c_{i}\right\} q_{s c}$ $\phi^{*}$ - - ${\phi ^*} \in [\underline \phi ,\bar \phi ]$ note: $\underline{\phi}=\max \left\{\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1},\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta-1)}\right\}$, $\bar{\phi}=\min _{i=N}\left\{1-\frac{\sum_{i=1}^{n} c_{i}}{c_{i}} \max \left\{\frac{b-\theta-1}{b-\theta-n}\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta},\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)-i+1}\right\}\right\}$
 Decentralized (Equilibrium) strategy Coordination strategy Suppliers' Simultaneous Actions Suppliers' Sequential Actions $F\left(z_{*}\right)$ $F\left(z_{sd}\right)=F\left(z_{sc}\right)$ $F\left(z_{sd^{\prime}}\right)=F\left(z_{sc}\right)$ $F\left(z_{s c}\right)=\frac{1}{(1-\eta)(b-\theta)}+\frac{(b-\theta-1) \Lambda\left(z_{s c}\right)}{(b-\theta) z_{s c}}$ $p_{*}$ $p_{sd}=\frac{b-\theta}{b-\theta-n} p_{sc}$ $p_{sd^{\prime}}=\left(\frac{b-\theta}{b-\theta-1}\right)^{n} p_{sc}$ $p_{s c}=\frac{b-\theta}{b-\theta-1} \frac{\left\{c+\lambda(\kappa) c_{e}+[1-\lambda(\kappa)] c_{s}+\sum_{i=1}^{n} c_{i}\right\} z_{s c}}{z_{s c}-(1-\eta) \Lambda\left(z_{s c}\right)}$ $q_{*}$ $q_{sd}=\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta} q_{sc}$ $q_{sd^{\prime}}=\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)} q_{sc}$ $q_{s c}=\left\{\lambda(\kappa) \kappa^{\theta}+[1-\lambda(\kappa)] \kappa^{-b}\right\} y\left(p_{s c}\right) z_{x}$ $w_{i}^{*}$ $w_i^{sd} = \frac{1}{{b - \theta - n}}\left\{ {c + \lambda (\kappa ){c_e} + [1 - \lambda (\kappa )]{c_s} + \sum\nolimits_{i = 1}^n {{c_i}} } \right\} + {c_i}$ $w_{i}^{s d^{\prime}}=\frac{(b-\theta)^{i-1}}{(b-\theta-1)^{i}}\left\{c+\lambda(\kappa) c_{e}+[1-\lambda(\kappa)] c_{s}+\sum\nolimits_{i=1}^{n} c_{i}\right\}+c_{i}$ $w_{i}^{sc}=\phi^{*} c_{i}$ $\Pi_{S_{i}}^{*}$ $\Pi_{S_{i}}^{s d}=\frac{b-\theta-1}{b-\theta}\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1} \Pi_{S C}^{s c}$ $\Pi_{S_{i}}^{s d^{\prime}}=\left(\frac{b-\theta-1}{b-\theta}\right)^{n{(b-\theta)-i+1}} \Pi_{S C}^{s c}$ $\Pi_{S_{i}}^{s c}=\frac{c_{i}}{\sum_{i=1}^{n} c_{i}}\left(1-\phi^{*}\right) \Pi_{S C}^{s c}$ $\Pi_{A}^{*}$ $\Pi_{A}^{s d}=\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1} \Pi_{S C}^{s c}$ $\Pi_{A}^{s d^{\prime}}=\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta-1)} \Pi_{S C}^{s c}$ $\Pi_{A}^{s c}=\phi^{*} \Pi_{S C}^{s c}$ $\Pi_{S C}^{*}$ $\Pi_{S C}^{s d}=\left[(n+1)-\frac{n}{b-\theta}\right]\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1} \Pi_{S C}^{s c}$ $\Pi_{S C}^{s d^{\prime}}=\left[(b-\theta)\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta-1)}-(b-\theta-1)\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)}\right] \Pi_{S C}^{s c}$ $\Pi_{S C}^{s c}=\frac{1}{b-\theta-1}\left\{c+\lambda(\kappa) c_{e}+[1-\lambda(\kappa)] c_{s}+\sum_{i=1}^{n} c_{i}\right\} q_{s c}$ $\phi^{*}$ - - ${\phi ^*} \in [\underline \phi ,\bar \phi ]$ note: $\underline{\phi}=\max \left\{\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta-1},\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta-1)}\right\}$, $\bar{\phi}=\min _{i=N}\left\{1-\frac{\sum_{i=1}^{n} c_{i}}{c_{i}} \max \left\{\frac{b-\theta-1}{b-\theta-n}\left(\frac{b-\theta-n}{b-\theta}\right)^{b-\theta},\left(\frac{b-\theta-1}{b-\theta}\right)^{n(b-\theta)-i+1}\right\}\right\}$
Analytical Results under the POC Mode
 Decentralized (Equilibrium) strategy Coordination strategy Suppliers' Simultaneous Actions Suppliers' Sequential Actions $F\left(z_{*}\right)$ $F\left(z_{o d}\right)=F\left(z_{o c}\right)$ $F\left(z_{o d^{\prime}}\right)=F\left(z_{o c}\right)$ $F\left(z_{o c}\right)=\frac{1}{(1-\eta) b}+\frac{(b-1) \Lambda\left(z_{o c}\right)}{b z_{o c}}$ $p_{*}$ $p_{o d}=\frac{b}{b-n} p_{oc}$ $p_{o d^{\prime}}=\left(\frac{b}{b-1}\right)^{n} p_{o c}$ $p_{o c}=\frac{b}{b-1} \frac{\left(c+c_{e}+\sum_{i=1}^{n} c_{i}\right) z_{o c}}{z_{o c}-(1-\eta) \Lambda\left(z_{o c}\right)}$ $q_{*}$ $q_{o d}=\left(\frac{b-n}{b}\right)^{b} q_{o c}$ $q_{o d^{\prime}}=\left(\frac{b-1}{b}\right)^{n(b-\theta)} q_{o c}$ $q_{o c}=y\left(p_{o c}\right) z_{o c}$ $w_{i}^{*}$ $w_{i}^{o d}=\frac{1}{b-n}\left(c+c_{e}+\sum_{i=1}^{n} c_{i}\right)+c_{i}$ $w_{i}^{o d^{\prime}}=\frac{b^{i-1}}{(b-1)^{i}}\left(c+c_{e}+\sum_{i=1}^{n} c_{i}\right)+c_{i}$ $w_{i}^{o c}=\phi^{*} c_{i}$ $\Pi_{S_{i}}^{*}$ $\Pi_{S_{i}}^{o d}=\frac{b-1}{b}\left(\frac{b-n}{b}\right)^{b-1} \Pi_{S C}^{o c}$ $\Pi_{S_{i}}^{o d^{\prime}}=\left(\frac{b-1}{b}\right)^{n b-i+1} \Pi_{S C}^{o c}$ $\Pi_{S_{i}}^{oc}=\frac{c_{i}}{\sum_{i=1}^{n} c_{i}}\left(1-\phi^{*}\right) \Pi_{S C}^{o c}$ $\Pi_{A}^{*}$ $\Pi_{A}^{o d}=\left(\frac{b-n}{b}\right)^{b-1} \Pi_{S C}^{o c}$ $\Pi_{A}^{o d^{\prime}}=\left(\frac{b-1}{b}\right)^{n(b-1)} \Pi_{S C}^{o c}$ $\Pi_{A}^{o c}=\phi^{*} \Pi_{S C}^{o c}$ $\Pi_{S C}^{*}$ $\Pi_{S C}^{o d}=\left[(n+1)-\frac{n}{b}\right]\left(\frac{b-n}{b}\right)^{b-1} \Pi_{S C}^{o c}$ $\Pi_{S C}^{o d^{\prime}}=\left[b\left(\frac{b-1}{b}\right)^{n(b-1)}-(b-1)\left(\frac{b-1}{b}\right)^{n b}\right] \Pi_{S C}^{o c}$ $\Pi_{S C}^{o c}=\frac{1}{b-1}\left(c+c_{e}+\sum_{i=1}^{n} c_{i}\right) q_{o c}$ $\phi^{*}$ - - ${\phi ^*} \in [\underline \phi ,\bar \phi ]$ note: $\underline \phi = \max \left\{ {{{\left( {\frac{{b - n}}{b}} \right)}^{b - 1}},{{\left( {\frac{{b - 1}}{b}} \right)}^{n(b - 1)}}} \right\},\bar \phi = {\min _{i \in N}}\left\{ {1 - \frac{{\sum\nolimits_{i = 1}^n {{c_i}} }}{{{c_i}}}\max \left\{ {\frac{{b - 1}}{{b - n}}{{\left( {\frac{{b - n}}{b}} \right)}^b},{{\left( {\frac{{b - 1}}{b}} \right)}^{nb - i + 1}}} \right\}} \right\}$
 Decentralized (Equilibrium) strategy Coordination strategy Suppliers' Simultaneous Actions Suppliers' Sequential Actions $F\left(z_{*}\right)$ $F\left(z_{o d}\right)=F\left(z_{o c}\right)$ $F\left(z_{o d^{\prime}}\right)=F\left(z_{o c}\right)$ $F\left(z_{o c}\right)=\frac{1}{(1-\eta) b}+\frac{(b-1) \Lambda\left(z_{o c}\right)}{b z_{o c}}$ $p_{*}$ $p_{o d}=\frac{b}{b-n} p_{oc}$ $p_{o d^{\prime}}=\left(\frac{b}{b-1}\right)^{n} p_{o c}$ $p_{o c}=\frac{b}{b-1} \frac{\left(c+c_{e}+\sum_{i=1}^{n} c_{i}\right) z_{o c}}{z_{o c}-(1-\eta) \Lambda\left(z_{o c}\right)}$ $q_{*}$ $q_{o d}=\left(\frac{b-n}{b}\right)^{b} q_{o c}$ $q_{o d^{\prime}}=\left(\frac{b-1}{b}\right)^{n(b-\theta)} q_{o c}$ $q_{o c}=y\left(p_{o c}\right) z_{o c}$ $w_{i}^{*}$ $w_{i}^{o d}=\frac{1}{b-n}\left(c+c_{e}+\sum_{i=1}^{n} c_{i}\right)+c_{i}$ $w_{i}^{o d^{\prime}}=\frac{b^{i-1}}{(b-1)^{i}}\left(c+c_{e}+\sum_{i=1}^{n} c_{i}\right)+c_{i}$ $w_{i}^{o c}=\phi^{*} c_{i}$ $\Pi_{S_{i}}^{*}$ $\Pi_{S_{i}}^{o d}=\frac{b-1}{b}\left(\frac{b-n}{b}\right)^{b-1} \Pi_{S C}^{o c}$ $\Pi_{S_{i}}^{o d^{\prime}}=\left(\frac{b-1}{b}\right)^{n b-i+1} \Pi_{S C}^{o c}$ $\Pi_{S_{i}}^{oc}=\frac{c_{i}}{\sum_{i=1}^{n} c_{i}}\left(1-\phi^{*}\right) \Pi_{S C}^{o c}$ $\Pi_{A}^{*}$ $\Pi_{A}^{o d}=\left(\frac{b-n}{b}\right)^{b-1} \Pi_{S C}^{o c}$ $\Pi_{A}^{o d^{\prime}}=\left(\frac{b-1}{b}\right)^{n(b-1)} \Pi_{S C}^{o c}$ $\Pi_{A}^{o c}=\phi^{*} \Pi_{S C}^{o c}$ $\Pi_{S C}^{*}$ $\Pi_{S C}^{o d}=\left[(n+1)-\frac{n}{b}\right]\left(\frac{b-n}{b}\right)^{b-1} \Pi_{S C}^{o c}$ $\Pi_{S C}^{o d^{\prime}}=\left[b\left(\frac{b-1}{b}\right)^{n(b-1)}-(b-1)\left(\frac{b-1}{b}\right)^{n b}\right] \Pi_{S C}^{o c}$ $\Pi_{S C}^{o c}=\frac{1}{b-1}\left(c+c_{e}+\sum_{i=1}^{n} c_{i}\right) q_{o c}$ $\phi^{*}$ - - ${\phi ^*} \in [\underline \phi ,\bar \phi ]$ note: $\underline \phi = \max \left\{ {{{\left( {\frac{{b - n}}{b}} \right)}^{b - 1}},{{\left( {\frac{{b - 1}}{b}} \right)}^{n(b - 1)}}} \right\},\bar \phi = {\min _{i \in N}}\left\{ {1 - \frac{{\sum\nolimits_{i = 1}^n {{c_i}} }}{{{c_i}}}\max \left\{ {\frac{{b - 1}}{{b - n}}{{\left( {\frac{{b - n}}{b}} \right)}^b},{{\left( {\frac{{b - 1}}{b}} \right)}^{nb - i + 1}}} \right\}} \right\}$
Analytical Results under the PFC Mode
 Decentralized (Equilibrium) strategy Coordination strategy Suppliers' Simultaneous Actions Suppliers' Sequential Actions $F\left(z_{*}\right)$ $F\left(z_{f d}\right)=F\left(z_{f c}\right)$ $F\left(z_{f d^{\prime}}\right)=F\left(z_{f c}\right)$ $F\left(z_{f c}\right)=\frac{1}{(1-\eta) b}+\frac{(b-1) \Lambda\left(z_{f c}\right)}{b z_{fc}}$ $p_{*}$ $p_{f d}=\frac{b}{b-n} p_{f c}$ $p_{f d^{\prime}}=\left(\frac{b}{b-1}\right)^{n} p_{f c}$ $p_{f c}=\frac{b}{b-1} \frac{\left(c+c_{s}+\sum_{i=1}^{n} c_{i}\right) z_{f c}}{z_{f c}-(1-\eta) \Lambda\left(z_{f c}\right)}$ $q_{*}$ $q_{f d}=\left(\frac{b-n}{b}\right)^{b} q_{f c}$ $q_{f d^{\prime}}=\left(\frac{b-1}{b}\right)^{n(b-\theta)} q_{f c}$ $q_{f c}=y\left(p_{f c}\right) z_{f c}$ $w_{i}^{*}$ $w_i^{fd} = \frac{1}{{b - n}}\left( {c + {c_s} + \sum\nolimits_{i = 1}^n {{c_i}} } \right) + {c_i}$ $w_i^{f{d^\prime }} = \frac{{{b^{i - 1}}}}{{{{(b - 1)}^i}}}\left( {c + {c_s} + \sum\nolimits_{i = 1}^n {{c_i}} } \right) + {c_i}$ $w_i^{fc} = {\phi ^*}{c_i}$ $\Pi_{S_{i}}^{*}$ $\Pi_{S_{i}}^{f d}=\frac{b-1}{b}\left(\frac{b-n}{b}\right)^{b-1} \Pi_{S C}^{f{c}}$ $\Pi_{S_{i}}^{f d^{\prime}}=\left(\frac{b-1}{b}\right)^{n b-i+1} \Pi_{S C}^{f_{c}}$ $\Pi_{S_{i}}^{f c}=\frac{c_{i}}{\sum_{i=1}^{n} c_{i}}\left(1-\phi^{*}\right) \Pi_{S C}^{f c}$ $\Pi_{A}^{*}$ $\Pi_{A}^{f d}=\left(\frac{b-n}{b}\right)^{b-1} \Pi_{S C}^{f c}$ $\Pi_{A}^{f d^{\prime}}=\left(\frac{b-1}{b}\right)^{n(b-1)} \Pi_{S C}^{f c}$ $\Pi_{A}^{f_{c}}=\phi^{*} \Pi_{S C}^{f c}$ $\Pi_{S C}^{*}$ $\Pi _{SC}^{fd} = \left[ {(n + 1) - \frac{n}{b}} \right]{\left( {\frac{{b - n}}{b}} \right)^{b - 1}}\Pi _{SC}^{{fc}}$ $\Pi _{SC}^{f{d^{\prime}}} = \left[ {b{{\left( {\frac{{b - 1}}{b}} \right)}^{n(b - 1)}} - (b - 1){{\left( {\frac{{b - 1}}{b}} \right)}^{nb}}} \right]\Pi _{SC}^{fc}$ $\Pi _{SC}^{{fc}} = \frac{1}{{b - 1}}\left( {c + {c_s} + \sum\nolimits_{i = 1}^n {{c_i}} } \right){q_{fc}}$ $\phi^{*}$ - - ${\phi ^*} \in [\underline \phi ,\bar \phi ]$ note: $\underline{\phi}=\max \left\{\left(\frac{b-n}{b}\right)^{b-1},\left(\frac{b-1}{b}\right)^{n(b-1)}\right\}, \bar{\phi}=\min _{i \in N}\left\{1-\frac{\sum_{i=1}^{n} c_{i}}{c_{i}} \max \left\{\frac{b-1}{b-n}\left(\frac{b-n}{b}\right)^{b},\left(\frac{b-1}{b}\right)^{n b-i+1}\right\}\right\}$
 Decentralized (Equilibrium) strategy Coordination strategy Suppliers' Simultaneous Actions Suppliers' Sequential Actions $F\left(z_{*}\right)$ $F\left(z_{f d}\right)=F\left(z_{f c}\right)$ $F\left(z_{f d^{\prime}}\right)=F\left(z_{f c}\right)$ $F\left(z_{f c}\right)=\frac{1}{(1-\eta) b}+\frac{(b-1) \Lambda\left(z_{f c}\right)}{b z_{fc}}$ $p_{*}$ $p_{f d}=\frac{b}{b-n} p_{f c}$ $p_{f d^{\prime}}=\left(\frac{b}{b-1}\right)^{n} p_{f c}$ $p_{f c}=\frac{b}{b-1} \frac{\left(c+c_{s}+\sum_{i=1}^{n} c_{i}\right) z_{f c}}{z_{f c}-(1-\eta) \Lambda\left(z_{f c}\right)}$ $q_{*}$ $q_{f d}=\left(\frac{b-n}{b}\right)^{b} q_{f c}$ $q_{f d^{\prime}}=\left(\frac{b-1}{b}\right)^{n(b-\theta)} q_{f c}$ $q_{f c}=y\left(p_{f c}\right) z_{f c}$ $w_{i}^{*}$ $w_i^{fd} = \frac{1}{{b - n}}\left( {c + {c_s} + \sum\nolimits_{i = 1}^n {{c_i}} } \right) + {c_i}$ $w_i^{f{d^\prime }} = \frac{{{b^{i - 1}}}}{{{{(b - 1)}^i}}}\left( {c + {c_s} + \sum\nolimits_{i = 1}^n {{c_i}} } \right) + {c_i}$ $w_i^{fc} = {\phi ^*}{c_i}$ $\Pi_{S_{i}}^{*}$ $\Pi_{S_{i}}^{f d}=\frac{b-1}{b}\left(\frac{b-n}{b}\right)^{b-1} \Pi_{S C}^{f{c}}$ $\Pi_{S_{i}}^{f d^{\prime}}=\left(\frac{b-1}{b}\right)^{n b-i+1} \Pi_{S C}^{f_{c}}$ $\Pi_{S_{i}}^{f c}=\frac{c_{i}}{\sum_{i=1}^{n} c_{i}}\left(1-\phi^{*}\right) \Pi_{S C}^{f c}$ $\Pi_{A}^{*}$ $\Pi_{A}^{f d}=\left(\frac{b-n}{b}\right)^{b-1} \Pi_{S C}^{f c}$ $\Pi_{A}^{f d^{\prime}}=\left(\frac{b-1}{b}\right)^{n(b-1)} \Pi_{S C}^{f c}$ $\Pi_{A}^{f_{c}}=\phi^{*} \Pi_{S C}^{f c}$ $\Pi_{S C}^{*}$ $\Pi _{SC}^{fd} = \left[ {(n + 1) - \frac{n}{b}} \right]{\left( {\frac{{b - n}}{b}} \right)^{b - 1}}\Pi _{SC}^{{fc}}$ $\Pi _{SC}^{f{d^{\prime}}} = \left[ {b{{\left( {\frac{{b - 1}}{b}} \right)}^{n(b - 1)}} - (b - 1){{\left( {\frac{{b - 1}}{b}} \right)}^{nb}}} \right]\Pi _{SC}^{fc}$ $\Pi _{SC}^{{fc}} = \frac{1}{{b - 1}}\left( {c + {c_s} + \sum\nolimits_{i = 1}^n {{c_i}} } \right){q_{fc}}$ $\phi^{*}$ - - ${\phi ^*} \in [\underline \phi ,\bar \phi ]$ note: $\underline{\phi}=\max \left\{\left(\frac{b-n}{b}\right)^{b-1},\left(\frac{b-1}{b}\right)^{n(b-1)}\right\}, \bar{\phi}=\min _{i \in N}\left\{1-\frac{\sum_{i=1}^{n} c_{i}}{c_{i}} \max \left\{\frac{b-1}{b-n}\left(\frac{b-n}{b}\right)^{b},\left(\frac{b-1}{b}\right)^{n b-i+1}\right\}\right\}$
Parameter Values for Numerical Analysis
 Parameters Value $c$ Assembly cost (USD/unit) 50 $c_1$ $1^{\text {st }}$ module cost (USD/unit) 149 $c_2$ $2^{\text {nd }}$ module cost (USD/unit) 53 $c_3$ $3^{\text {rd }}$ module cost (USD/unit) 80 $c_4$ $4^{\text {th }}$ module cost (USD/unit) 60 $c_e$ Operational cost of the online channel (USD/unit) 26 $c_s$ Operational cost of offline channel (USD/unit) 39 $a$ Positive constant number 1E+18 $b$ Price-elasticity index of the expected demand 5.0 $\theta$ Mutual fusion coefficient between channels 0.5 $\eta$ Clearance discount price factor 50% ${\lambda _0}$ Market demand share of the online channel 0.6 $\delta$ The offline channel subsidy factor, and $0< \delta< 1$ 0.1 $\kappa$ The offline channel discount price factor, and $\kappa = 1 - \delta$ 0.9 $h$ the reaction extent of $\lambda \left( \kappa \right)$ w.r.t. the change of $\kappa$ 0.5 $\phi$ Revenue keeping rate 0.7 $\mu$ Mean value of random factor 100 $\sigma$ Standard deviation of random factor 10
 Parameters Value $c$ Assembly cost (USD/unit) 50 $c_1$ $1^{\text {st }}$ module cost (USD/unit) 149 $c_2$ $2^{\text {nd }}$ module cost (USD/unit) 53 $c_3$ $3^{\text {rd }}$ module cost (USD/unit) 80 $c_4$ $4^{\text {th }}$ module cost (USD/unit) 60 $c_e$ Operational cost of the online channel (USD/unit) 26 $c_s$ Operational cost of offline channel (USD/unit) 39 $a$ Positive constant number 1E+18 $b$ Price-elasticity index of the expected demand 5.0 $\theta$ Mutual fusion coefficient between channels 0.5 $\eta$ Clearance discount price factor 50% ${\lambda _0}$ Market demand share of the online channel 0.6 $\delta$ The offline channel subsidy factor, and $0< \delta< 1$ 0.1 $\kappa$ The offline channel discount price factor, and $\kappa = 1 - \delta$ 0.9 $h$ the reaction extent of $\lambda \left( \kappa \right)$ w.r.t. the change of $\kappa$ 0.5 $\phi$ Revenue keeping rate 0.7 $\mu$ Mean value of random factor 100 $\sigma$ Standard deviation of random factor 10
Numerical Analysis Results for the Omnichannel mode
 OMO Mode OMS Mode Decentralized strategy Coordination strategy Decentralized strategy Coordination strategy Simultaneous actions Sequential actions Simultaneous actions Sequential actions ${z_ * }$ 99 99 99 99 99 99 ${p_ * }$ 6, 418 1, 949 713 6, 604 2, 005 734 ${q_ * }$ 731 156, 071 14, 385, 462 825 176, 168 16, 237, 802 $w_1^ *$ 1, 238 305 104 1, 269 309 104 $w_2^ *$ 1, 142 253 37 1, 173 259 37 $w_3^ *$ 1, 169 337 56 1, 200 345 56 $w_4^ *$ 1, 149 391 42 1, 180 400 42 $\Pi_{A}^{*}$ 1, 023, 117 66, 336, 309 1, 566, 289, 055 1, 188, 375 77, 051, 259 1, 819, 283, 383 $\Pi_{S_{1}}^{*}$ 795, 757 24, 275, 793 292, 452, 468 924, 292 28, 196, 932 339, 690, 757 $\Pi_{S_{2}}^{*}$ 795, 757 31, 211, 734 104, 026, 717 924, 292 36, 253, 199 120, 829, 598 $\Pi_{S_{3}}^{*}$ 795, 757 40, 129, 372 157, 021, 459 924, 292 46, 611, 256 182, 384, 299 $\Pi_{S_{4}}^{*}$ 795, 757 51, 594, 907 117, 766, 094 924, 292 59, 928, 757 136, 788, 224 $\Pi_{S C}^{*}$ 4, 206, 146 213, 548, 114 2, 237, 555, 793 4, 885, 542 248, 041, 403 2, 598, 976, 261 Range of $\phi^{*}$ [0.029646773, 0.868565973]; set at 0.7 [0.029646773, 0.868565973]; set at 0.7
 OMO Mode OMS Mode Decentralized strategy Coordination strategy Decentralized strategy Coordination strategy Simultaneous actions Sequential actions Simultaneous actions Sequential actions ${z_ * }$ 99 99 99 99 99 99 ${p_ * }$ 6, 418 1, 949 713 6, 604 2, 005 734 ${q_ * }$ 731 156, 071 14, 385, 462 825 176, 168 16, 237, 802 $w_1^ *$ 1, 238 305 104 1, 269 309 104 $w_2^ *$ 1, 142 253 37 1, 173 259 37 $w_3^ *$ 1, 169 337 56 1, 200 345 56 $w_4^ *$ 1, 149 391 42 1, 180 400 42 $\Pi_{A}^{*}$ 1, 023, 117 66, 336, 309 1, 566, 289, 055 1, 188, 375 77, 051, 259 1, 819, 283, 383 $\Pi_{S_{1}}^{*}$ 795, 757 24, 275, 793 292, 452, 468 924, 292 28, 196, 932 339, 690, 757 $\Pi_{S_{2}}^{*}$ 795, 757 31, 211, 734 104, 026, 717 924, 292 36, 253, 199 120, 829, 598 $\Pi_{S_{3}}^{*}$ 795, 757 40, 129, 372 157, 021, 459 924, 292 46, 611, 256 182, 384, 299 $\Pi_{S_{4}}^{*}$ 795, 757 51, 594, 907 117, 766, 094 924, 292 59, 928, 757 136, 788, 224 $\Pi_{S C}^{*}$ 4, 206, 146 213, 548, 114 2, 237, 555, 793 4, 885, 542 248, 041, 403 2, 598, 976, 261 Range of $\phi^{*}$ [0.029646773, 0.868565973]; set at 0.7 [0.029646773, 0.868565973]; set at 0.7
Numerical Analysis Results for the Pure Channel Mode
 POC Mode PFC Mode Decentralized strategy Coordination strategy Decentralized strategy Coordination strategy Simultaneous actions Sequential actions Simultaneous actions Sequential actions ${z_ * }$ 98 98 98 98 98 98 ${p_ * }$ 2, 655 1, 296 531 4, 662 2, 276 932 ${q_ * }$ 744 26, 812 2, 325, 562 45 1, 606 139, 293 $w_1^ *$ 567 254 104 883 333 104 $w_2^ *$ 471 184 37 787 282 37 $w_3^ *$ 498 243 56 814 367 56 $w_4^ *$ 478 264 42 794 418 42 $\Pi_{A}^{*}$ 388, 834 6, 840, 438 170, 114, 826 40, 896 719, 457 17, 892, 172 $\Pi_{S_{1}}^{*}$ 311, 067 2, 801, 843 31, 763, 295 32, 717 294, 690 3, 340, 769 $\Pi_{S_{2}}^{*}$ 311, 067 3, 502, 304 11, 298, 353 32, 717 368, 362 1, 188, 327 $\Pi_{S_{3}}^{*}$ 311, 067 4, 377, 880 17, 054, 118 32, 717 460, 452 1, 793, 701 $\Pi_{S_{4}}^{*}$ 311, 067 5, 472, 350 12, 790, 588 32, 717 575, 566 1, 345, 276 $\Pi_{S C}^{*}$ 1, 633, 102 22, 994, 817 243, 021, 181 171, 765 2, 418, 526 25, 560, 245 Range of $\phi^{*}$ [0.028147498, 0.871647411]; set at 0.7 [0.028147498, 0.871647411]; set at 0.7
 POC Mode PFC Mode Decentralized strategy Coordination strategy Decentralized strategy Coordination strategy Simultaneous actions Sequential actions Simultaneous actions Sequential actions ${z_ * }$ 98 98 98 98 98 98 ${p_ * }$ 2, 655 1, 296 531 4, 662 2, 276 932 ${q_ * }$ 744 26, 812 2, 325, 562 45 1, 606 139, 293 $w_1^ *$ 567 254 104 883 333 104 $w_2^ *$ 471 184 37 787 282 37 $w_3^ *$ 498 243 56 814 367 56 $w_4^ *$ 478 264 42 794 418 42 $\Pi_{A}^{*}$ 388, 834 6, 840, 438 170, 114, 826 40, 896 719, 457 17, 892, 172 $\Pi_{S_{1}}^{*}$ 311, 067 2, 801, 843 31, 763, 295 32, 717 294, 690 3, 340, 769 $\Pi_{S_{2}}^{*}$ 311, 067 3, 502, 304 11, 298, 353 32, 717 368, 362 1, 188, 327 $\Pi_{S_{3}}^{*}$ 311, 067 4, 377, 880 17, 054, 118 32, 717 460, 452 1, 793, 701 $\Pi_{S_{4}}^{*}$ 311, 067 5, 472, 350 12, 790, 588 32, 717 575, 566 1, 345, 276 $\Pi_{S C}^{*}$ 1, 633, 102 22, 994, 817 243, 021, 181 171, 765 2, 418, 526 25, 560, 245 Range of $\phi^{*}$ [0.028147498, 0.871647411]; set at 0.7 [0.028147498, 0.871647411]; set at 0.7
Numerical Analysis Results for the Pure Channel Mode
 Parameters Original Value $\pm$ Increment Range $\delta$ Offline channel subsidy factor 0.1 0.01 [0, 0.5] $b$ Price-elasticity index of the expected demand 5.0 0.01 [4.5, 5.5] $\theta$ Mutual fusion coefficient between channels 0.5 0.01 [0.1, 0.9]
 Parameters Original Value $\pm$ Increment Range $\delta$ Offline channel subsidy factor 0.1 0.01 [0, 0.5] $b$ Price-elasticity index of the expected demand 5.0 0.01 [4.5, 5.5] $\theta$ Mutual fusion coefficient between channels 0.5 0.01 [0.1, 0.9]
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