Assembly system with omnichannel coordination

Zhisong Chen; Shong-Iee Ivan Su

doi:10.3934/jimo.2021047

Article Contents

2022, Volume 18, Issue 3: 1863-1889. Doi: 10.3934/jimo.2021047

This issue Previous Article Quadratic surface support vector machine with L1 norm regularization Next Article Optimal lot-sizing policy for a failure prone production system with investment in process quality improvement and lead time variance reduction

Assembly system with omnichannel coordination

Zhisong Chen^1,2, , and
Shong-Iee Ivan Su^3,

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
^* Corresponding author: Zhisong Chen

Received: April 30, 2020

Revised: November 30, 2020

Published: May 2022

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 90B06, 91A10; Secondary: 91A12.

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Figure 1. A Generic Assembly System with Omnichannel

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Figure 2. Impact of Offline Channel Subsidy Factor ($ \delta $) Change on Profits

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Figure 3. Impact of Price Elasticity Index of the Expected Demand ($ b $) Change on Profits

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Figure 4. Impact of Mutual fusion Coefficient ($ \theta $) Change on Profits

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Table 1. 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

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Table 2. 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

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Table 3. Analytical Results under the OMO Mode

	Decentralized (Equilibrium) strategy		Coordination strategy
	Suppliers' Simultaneous Actions	Suppliers' Sequential Actions	Coordination strategy
$ 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\} $

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Table 4. Analytical Results under the OMS Mode

	Decentralized (Equilibrium) strategy		Coordination strategy
	Suppliers' Simultaneous Actions	Suppliers' Sequential Actions	Coordination strategy
$ 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\} $

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Table 5. Analytical Results under the POC Mode

	Decentralized (Equilibrium) strategy		Coordination strategy
	Suppliers' Simultaneous Actions	Suppliers' Sequential Actions	Coordination strategy
$ 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\} $

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Table 6. Analytical Results under the PFC Mode

	Decentralized (Equilibrium) strategy		Coordination strategy
	Suppliers' Simultaneous Actions	Suppliers' Sequential Actions	Coordination strategy
$ 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\} $

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Table 7. 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

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Table 8. Numerical Analysis Results for the Omnichannel mode

	OMO Mode			OMS Mode
	Decentralized strategy		Coordination strategy	Decentralized strategy		Coordination strategy
	Simultaneous actions	Sequential actions	Coordination strategy	Simultaneous actions	Sequential actions	Coordination strategy
$ {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

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Table 9. Numerical Analysis Results for the Pure Channel Mode

	POC Mode			PFC Mode
	Decentralized strategy		Coordination strategy	Decentralized strategy		Coordination strategy
	Simultaneous actions	Sequential actions	Coordination strategy	Simultaneous actions	Sequential actions	Coordination strategy
$ {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

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Table 10. 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]

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