# Strategic Integration Decision under Supply Chain Competition in the Presence of Online Channel

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

- (a)
- competing manufacturers’ and retailers’ strategies in equilibrium;
- (b)
- the equilibrium price in the online and retail channels, and wholesale prices;
- (c)
- the total profits for each SCs?

## 2. Problem Statement

## 3. Main Analytical Results

#### 3.1. Benchmark Models

#### 3.1.1. Optimal Decisions in Scenario BM

**Proposition**

**1.**

**Remark**

**1.**

#### 3.1.2. Optimal Decisions in Scenario DD

**Proposition**

**2.**

**Remark 2.**

- 1.
- Market price of product from ${M}_{1}$ is always higher compared to ${M}_{2}$, because ${p}_{1}^{dd}-{p}_{2}^{dd}=\frac{a{\beta}_{2}(2(1-\alpha )(4-{\beta}_{1}-2{\beta}_{1}^{2})+\alpha (7+4{\beta}_{1}){\beta}_{2})}{2{\Delta}_{dd}}>0$.
- 2.
- Wholesale price for first product is less compared to product at online channel, i.e., ${p}_{0}^{dd}\ge {w}_{1}^{dd}$, if ${\alpha}_{p}^{dd}=\frac{32(1-{\beta}_{2})-2{\beta}_{1}(17{\beta}_{1}-4{\beta}_{1}^{3}+10{\beta}_{2}-7{\beta}_{1}{\beta}_{2}-4{\beta}_{1}^{2}{\beta}_{2})}{4(3-{\beta}_{1}^{2}){{\rm Y}}_{3}-(5+4{\beta}_{1})(12-{\beta}_{1}-4{\beta}_{1}^{2}){\beta}_{2}+(2+{\beta}_{1}){\beta}_{2}^{2}}\ge \alpha $.

**Proposition**

**3.**

#### 3.2. Vertical Integration

#### Optimal Decision in Scenario II

**Proposition**

**4.**

**Remark 3.**

- 1.
- Total profit for the first SC is always higher compared to Second SC because ${\pi}_{c1}^{ii}-{\pi}_{c2}^{ii}=\frac{{a}^{2}(4{(1-\alpha )}^{2}(4-{\beta}_{1}^{2})+4(1-\alpha )\alpha (4+{\beta}_{1}){\beta}_{2}+3{\alpha}^{2}{\beta}_{2}^{2})}{4{(4-{\beta}_{1}^{2}-(5+2{\beta}_{1}){\beta}_{2}^{2})}^{2}}>0$.
- 2.
- Market price for the first product in an online channel is higher compared to price of that in the retail channel if $\alpha \ge \frac{2(4-{\beta}_{1}^{2}-(4+{\beta}_{1}){\beta}_{2})}{12-2{\beta}_{1}^{2}-(14-{\beta}_{2}){\beta}_{2}-{\beta}_{1}(2-5{\beta}_{2})}$, because ${p}_{0}^{ii}-{p}_{1}^{ii}=\frac{a(8(1-{\beta}_{2})+2{\beta}_{1}({\beta}_{1}+{\beta}_{2})+\alpha (12-2{\beta}_{1}^{2}+{\beta}_{1}(2-5{\beta}_{2})-(14-{\beta}_{2}){\beta}_{2}))}{2(4-{\beta}_{1}^{2}-(5+2{\beta}_{1}){\beta}_{2}^{2})}>0$.
- 3.
- Price of the first product is always higher compared to the second product in retail channel, because ${p}_{1}^{ii}-{p}_{2}^{ii}=\frac{a{\beta}_{2}(2(1-\alpha )(2-{\beta}_{1})+3x{\beta}_{2})}{4-{\beta}_{1}^{2}-(5+2{\beta}_{1}){\beta}_{2}^{2}}>0$.
- 4.
- Profits in the first retail channel is always less compared to the second retail channel because ${p}_{1}^{ii}{D}_{1}^{ii}-{p}_{2}^{ii}{D}_{2}^{ii}=\frac{-{a}^{2}{\beta}_{2}}{4{(4-{\beta}_{1}^{2}-(5+2{\beta}_{1}){\beta}_{2}^{2})}^{2}}(2{{\rm Y}}_{2}+3\alpha {\beta}_{2})(2\alpha {\beta}_{1}(2+{\beta}_{1})+2(1-\alpha )(1+{\beta}_{1})(2+{\beta}_{1}){\beta}_{2}+\alpha (3+{\beta}_{1}){\beta}_{2}^{2})<0$.

#### 3.3. Optimal Decision in Scenario ID

**Proposition**

**5.**

**Remark 4.**

- 1.
- Retail price for the first retail channel remains higher compared to the second retail channel because ${p}_{1}^{id}\ge {p}_{2}^{id}$ if $\alpha \le \frac{2(2-{\beta}_{1}){\beta}_{2}}{4-3{\beta}_{1}^{2}+2(2-{\beta}_{1}){\beta}_{2}-2(5+3{\beta}_{1}){\beta}_{2}^{2}}$. Sales volume for first retail channel is also less compared to second retail channel because ${Q}_{2}^{id}-{Q}_{1}^{id}=\frac{a(1+{\beta}_{1})(\alpha (4-3{\beta}_{1}^{2})+2(1-\alpha )(4-{\beta}_{1}-2{\beta}_{1}^{2}){\beta}_{2}+\alpha (1+{\beta}_{1}^{2}){\beta}_{2}^{2})}{2(8-5{\beta}_{1}^{2}-(10+{\beta}_{1}(4-3{\beta}_{1})){\beta}_{2}^{2}))}>0.$
- 2.
- Price of the first product in retail channel will be higher compared to the online channel, ${p}_{1}^{id}>{p}_{o}^{id}$ if $\alpha \le \frac{(2(8-8{\beta}_{2}-3{\beta}_{1}{\beta}_{2}-{\beta}_{1}^{2}(5-2{\beta}_{2}))}{28+6{\beta}_{1}-13{\beta}_{1}^{2}-(7-2{\beta}_{1})(4+3{\beta}_{1}){\beta}_{2}-(3-{\beta}_{1})(1+{\beta}_{1}){\beta}_{2}^{2})}$

**Proposition**

**6.**

- (1)
- Total profit for the first SC is higher in Scenario II compared to BM, i.e., ${\pi}_{c1}^{ii}\ge {\pi}_{c1}^{bm}$ if $\alpha \in \left(max\left\{0,\frac{2(2-{\beta}_{2})(4-{\beta}_{2}-2{\beta}_{2}^{2}){\varphi}_{5}-4(1+{\beta}_{2})(2-2{\beta}_{2}-{\beta}_{2}^{2})\sqrt{{\varphi}_{6}}}{(2-{\beta}_{2})(4-{\beta}_{2}-2{\beta}_{2}^{2})(40-80{\beta}_{2}+44{\beta}_{2}^{3}+5{\beta}_{2}^{4})}\right\},min\left\{1,\frac{2(2-{\beta}_{2})(4-{\beta}_{2}-2{\beta}_{2}^{2}){\varphi}_{5}+4(1+{\beta}_{2})(2-2{\beta}_{2}-{\beta}_{2}^{2})\sqrt{{\varphi}_{6}}}{(2-{\beta}_{2})(4-{\beta}_{2}-2{\beta}_{2}^{2})(40-80{\beta}_{2}+44{\beta}_{2}^{3}+5{\beta}_{2}^{4})}\right\}\right)$
- (2)
- Total profit for the first SC is higher in Scenario II compared to DD, i.e., ${\pi}_{c1}^{ii}\ge {\pi}_{c1}^{dd}$ if $\alpha \in \left(max\left\{0,\frac{-(2-{\beta}_{2}){\beta}_{2}{\varphi}_{7}+4(2-{\beta}_{2}){\beta}_{2}(2-2{\beta}_{2}-{\beta}_{2}^{2}){\varphi}_{2}\sqrt{{\varphi}_{8}}}{{\varphi}_{9}}\right\},min\left\{1,\frac{(2-{\beta}_{2}){\beta}_{2}{\varphi}_{7}+4(2-{\beta}_{2}){\beta}_{2}(2-2{\beta}_{2}-{\beta}_{2}^{2}){\varphi}_{2}\sqrt{{\varphi}_{8}}}{{\varphi}_{9}}\right\}\right)$
- (3)
- Total profit for the first SC is higher in Scenario ID compared to Scenario BM, i.e., ${\pi}_{c1}^{id}\ge {\pi}_{c1}^{bm}$ $\alpha \in \left(max\left\{0,\frac{2(2-{\beta}_{2})(4-{\beta}_{2}-2{\beta}_{2}^{2}){\varphi}_{10}+4(4-4{\beta}_{2}-5{\beta}_{2}^{2})\sqrt{(1+{\beta}_{2}){\varphi}_{11}}}{(2-{\beta}_{2})(4-{\beta}_{2}-2{\beta}_{2}^{2}){\varphi}_{12}}\right\},min\left\{1,\frac{2(2-{\beta}_{2})(4-{\beta}_{2}-2{\beta}_{2}^{2}){\varphi}_{10}+4(4-4{\beta}_{2}-5{\beta}_{2}^{2})\sqrt{(1+{\beta}_{2}){\varphi}_{11}}}{(2-{\beta}_{2})(4-{\beta}_{2}-2{\beta}_{2}^{2}){\varphi}_{12}}\right\}\right)$
- (4)
- Total profit for the first SC is higher in Scenario ID compared to Scenario DD, i.e., ${\pi}_{c1}^{id}\ge {\pi}_{c1}^{dd}$$\alpha \in \left(max\left\{0,\frac{2(2-{\beta}_{2}){\beta}_{2}^{2}{\varphi}_{13}+4(2-{\beta}_{2}){\beta}_{2}^{2}(4-4{\beta}_{2}-5{\beta}_{2}^{2}){\varphi}_{2}\sqrt{(1-{\beta}_{2}-{\beta}_{2}^{2}){\varphi}_{14}}}{{\varphi}_{15}}\right\},min\left\{1,\frac{2(2-{\beta}_{2}){\beta}_{2}^{2}{\varphi}_{13}+4(2-{\beta}_{2}){\beta}_{2}^{2}(4-4{\beta}_{2}-5{\beta}_{2}^{2}){\varphi}_{2}\sqrt{(1-{\beta}_{2}-{\beta}_{2}^{2}){\varphi}_{14}}}{{\varphi}_{15}}\right\}\right)$

#### 3.4. Optimal Decision in Scenario UC

**Proposition**

**7.**

**Remark 5.**

- 1.
- Unlike all four scenarios in the presence of an online channel, market prices, profits for two retailers, and wholesale prices remain identical for two competing SCs.
- 2.
- Market price of the first product is always higher in an online channel compared to a retail channel, i.e., ${p}_{0}^{uc}\ge {p}_{1}^{uc}$ if $\frac{2(2-{\beta}_{1})(1-{\beta}_{1}-{\beta}_{2})}{7+2{\beta}_{1}^{2}-4{\beta}_{1}(2-{\beta}_{2})-2{\beta}_{2}(4+{\beta}_{2})}\ge \alpha $
- 3.
- Wholesale price for the first product is less compared to its price at online channel, i.e., ${p}_{0}^{uc}\ge {w}_{1}^{uc}$, if $\alpha \le \frac{2(1-{\beta}_{1}-{\beta}_{2})}{3-2{\beta}_{1}-4{\beta}_{2}}$

**Proposition**

**8.**

- If a competing manufacturer opens an online channel, then consumers can receive the first products at a lower price.
- If an upstream manufacturer opens an online channel, then the retailer in that SC may lose a significant amount of profit, as well as consumers in the future. Due to easy access to the internet, if consumers continuously find the product available online at a cheaper price or similar types of products in other retail outlets at a lower price, they may intend to buy the product online or change their minds in the future.
- All the competing members have the opportunity to receive a higher profit in the presence of an online channel compared to Scenario BM. Due to the additional price option and consumer cross-price elasticity, members are somehow bound to reduce the price for the products. Consequently, demand increases and total profit also increases.
- Both horizontal and vertical integration decisions can improve total profits for each competing SCs.

## 4. Result Analysis and Discussion

#### 4.1. Nature of Retail Prices in Different Scenarios

#### 4.2. Nature Profits for Two Competing SCs in Five Scenarios

**Proposition**

**9.**

#### 4.3. Managerial Insights

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Derivation of the Optimal Decision in Scenario BM

## Appendix B. Derivation of the Optimal Decision in Scenario DD

## Appendix C. Derivation of the Optimal Decision in Scenario II

## Appendix D. Derivation of the Optimal Decision in Scenario ID

## Appendix E. Derivation of the Optimal Decision in Scenario UC

## Appendix F. Prof of Proposition 3

## Appendix G. Optimal Decision in the Absence of Online Channel

Decision | Scenario BM/DD | Scenario II | Scenario UC | Scenario ID |
---|---|---|---|---|

${w}_{i1}^{k}$ | $\frac{a(2+{\beta}_{1})}{4-{\beta}_{1}-2{\beta}_{1}^{2}}$ | - | $\frac{a}{2-2{\beta}_{1}}$ | - |

${w}_{i2}^{k}$ | $\frac{a(2+{\beta}_{1})}{4-{\beta}_{1}-2{\beta}_{1}^{2}}$ | - | $\frac{a}{2-2{\beta}_{1}}$ | $\frac{a(4+(2-{\beta}_{1}){\beta}_{1})}{8-5{\beta}_{1}^{2}}$ |

${p}_{i1}^{k}$ | $\frac{2a(3-{\beta}_{1}^{2})}{(2-{\beta}_{1})(4-{\beta}_{1}-2{\beta}_{1}^{2})}$ | $\frac{a}{2-{\beta}_{1}}$ | $\frac{a(3-2{\beta}_{1})}{2(2-3{\beta}_{1}+{\beta}_{1}^{2})}$ | $\frac{a(4+3{\beta}_{1})}{8-5{\beta}_{1}^{2}}$ |

${p}_{i2}^{k}$ | $\frac{2a(3-{\beta}_{1}^{2})}{(2-{\beta}_{1})(4-{\beta}_{1}-2{\beta}_{1}^{2})}$ | $\frac{a}{2-{\beta}_{1}}$ | $\frac{a(3-2{\beta}_{1})}{2(2-3{\beta}_{1}+{\beta}_{1}^{2})}$ | $\frac{3a(4+(2-{\beta}_{1}){\beta}_{1})}{2(8-5{\beta}_{1}^{2})}$ |

${\pi}_{r1}^{k}$ | $\frac{{a}^{2}{(2-{\beta}_{1}^{2})}^{2}}{{(2-{\beta}_{1})}^{2}{(4-{\beta}_{1}-2{\beta}_{1}^{2})}^{2}}$ | - | $\frac{{a}^{2}}{4{(2-{\beta}_{1})}^{2}}$ | - |

${\pi}_{r2}^{k}$ | $\frac{{a}^{2}{(2-{\beta}_{1}^{2})}^{2}}{{(2-{\beta}_{1})}^{2}{(4-{\beta}_{1}-2{\beta}_{1}^{2})}^{2}}$ | - | $\frac{{a}^{2}}{4{(2-{\beta}_{1})}^{2}}$ | $\frac{{a}^{2}{(4+(2-{\beta}_{1}){\beta}_{1})}^{2}}{4{(8-5{\beta}_{1}^{2})}^{2}}$ |

${\pi}_{m1}^{k}$ | $\frac{{a}^{2}(2+{\beta}_{1})(2-{\beta}_{1}^{2})}{(2-{\beta}_{1}){(4-{\beta}_{1}-2{\beta}_{1}^{2})}^{2}}$ | - | $\frac{{a}^{2}}{4(2-3{\beta}_{1}+{\beta}_{1}^{2}}$ | - |

${\pi}_{m2}^{k}$ | $\frac{{a}^{2}(2+{\beta}_{1})(2-{\beta}_{1}^{2})}{(2-{\beta}_{1}){(4-{\beta}_{1}-2{\beta}_{1}^{2})}^{2}}$ | - | $\frac{{a}^{2}}{4(2-3{\beta}_{1}+{\beta}_{1}^{2}}$ | $\frac{{a}^{2}{(4+(2-{\beta}_{1}){\beta}_{1})}^{2}}{2{(8-5{\beta}_{1}^{2})}^{2}}$ |

${\pi}_{c1}^{k}$ | $\frac{2{a}^{2}(6-5{\beta}_{1}^{2}+{\beta}_{1}^{4})}{{(2-{\beta}_{1})}^{2}{(4-{\beta}_{1}-2{\beta}_{1}^{2})}^{2}}$ | $\frac{{a}^{2}}{{(2-{\beta}_{1})}^{2}}$ | $\frac{{a}^{2}(3-2{\beta}_{1})}{4{(2-{\beta}_{1})}^{2}(1-{\beta}_{1})}$ | $\frac{{a}^{2}{(4+3{\beta}_{1})}^{2}(2-{\beta}_{1}^{2})}{2{(8-5{\beta}_{1}^{2})}^{2})}$ |

${\pi}_{c2}^{k}$ | $\frac{2{a}^{2}(6-5{\beta}_{1}^{2}+{\beta}_{1}^{4})}{{(2-{\beta}_{1})}^{2}{(4-{\beta}_{1}-2{\beta}_{1}^{2})}^{2}}$ | $\frac{{a}^{2}}{{(2-{\beta}_{1})}^{2}}$ | $\frac{{a}^{2}(3-2{\beta}_{1})}{4{(2-{\beta}_{1})}^{2}(1-{\beta}_{1})}$ | $\frac{3{a}^{2}{(4+(2-{\beta}_{1}){\beta}_{1})}^{2}}{4{(8-5{\beta}_{1}^{2})}^{2}}$ |

## Appendix H. List of Symbols

## References

- Netessine, S.; Rudi, N. Supply chain choice on the internet. Manag. Sci.
**2006**, 52, 844–864. [Google Scholar] [CrossRef] [Green Version] - Ofek, E.; Katona, Z.; Sarvary, M. “Bricks and clicks”: The impact of product returns on the strategies of multichannel retailers. Mark. Sci.
**2011**, 30, 42–60. [Google Scholar] [CrossRef] [Green Version] - Yan, R.; Pei, Z.; Myers, C. Do channel members value the multiple-cooperation strategy? J. Retail. Consum. Serv.
**2016**, 30, 84–95. [Google Scholar] [CrossRef] - Young, Y. US Ecommerce Sales Grow 14.9% in 2019. 2020. Available online: www.digitalcommerce360.com/article/us-ecommerce-sales/ (accessed on 5 July 2020).
- Chiang, W.Y.K.; Chhajed, D.; Hess, J.D. Direct marketing, indirect profits: A strategic analysis of dual-channel supply-chain design. Manag. Sci.
**2003**, 49, 1–20. [Google Scholar] [CrossRef] [Green Version] - Arya, A.; Mittendorf, B.; Sappington, D.E. The bright side of supplier encroachment. Mark. Sci.
**2007**, 26, 651–659. [Google Scholar] [CrossRef] - Yan, R.; Ghose, S. Forecast information and traditional retailer performance in a dual-channel competitive market. J. Bus. Res.
**2010**, 63, 77–83. [Google Scholar] [CrossRef] - Huang, T.; Van Mieghem, J.A. Clickstream data and inventory management: Model and empirical analysis. Prod. Oper. Manag.
**2014**, 23, 333–347. [Google Scholar] [CrossRef] [Green Version] - Kalnins, A. Pricing variation within dual-distribution chains: The different implications of externalities and signaling for high-and low-quality brands. Manag. Sci.
**2017**, 63, 139–152. [Google Scholar] [CrossRef] - Xiao, T.; Shi, J.J. Pricing and supply priority in a dual-channel supply chain. Eur. J. Oper. Res.
**2016**, 254, 813–823. [Google Scholar] [CrossRef] - Moon, I.; Sarmah, S.P.; Saha, S. The impact of online sales on centralised and decentralised dual-channel supply chains. Eur. J. Ind. Eng.
**2018**, 12, 67–92. [Google Scholar] [CrossRef] - Chen, J.; Liang, L.; Yao, D.Q.; Sun, S. Price and quality decisions in dual-channel supply chains. Eur. J. Oper. Res.
**2017**, 259, 935–948. [Google Scholar] [CrossRef] - Dan, B.; Liu, C.; Xu, G.; Zhang, X. Pareto improvement strategy for service-based free-riding in a dual-channel supply chain. Asia Pac. J. Oper. Res.
**2014**, 31, 1450050. [Google Scholar] [CrossRef] - Rodriguez, B.; Aydın, G. Pricing and assortment decisions for a manufacturer selling through dual channels. Eur. J. Oper. Res.
**2015**, 242, 901–909. [Google Scholar] [CrossRef] - Yan, R.; Pei, Z. Retail services and firm profit in a dual-channel market. J. Retail. Consum. Serv.
**2009**, 16, 306–314. [Google Scholar] [CrossRef] - Pei, Z.; Toombs, L.; Yan, R. How does the added new online channel impact the supporting advertising expenditure? J. Retail. Consum. Serv.
**2014**, 21, 229–238. [Google Scholar] [CrossRef] - Chen, T.H. Effects of the pricing and cooperative advertising policies in a two-echelon dual-channel supply chain. Comput. Ind. Eng.
**2015**, 87, 250–259. [Google Scholar] [CrossRef] - He, Y.; Huang, H.; Li, D. Inventory and pricing decisions for a dual-channel supply chain with deteriorating products. Oper. Res.
**2018**, 1–43. [Google Scholar] [CrossRef] - Jamali, M.B.; Rasti-Barzoki, M. A game theoretic approach for green and non-green product pricing in chain-to-chain competitive sustainable and regular dual-channel supply chains. J. Clean. Prod.
**2018**, 170, 1029–1043. [Google Scholar] [CrossRef] - Basiri, Z.; Heydari, J. A mathematical model for green supply chain coordination with substitutable products. J. Clean. Prod.
**2017**, 145, 232–249. [Google Scholar] [CrossRef] [Green Version] - Fang, D.; Ren, Q. Optimal decision in a dual-channel supply chain under potential information leakage. Symmetry
**2019**, 11, 308. [Google Scholar] [CrossRef] [Green Version] - Zhou, J.; Zhao, R.; Wang, W. Pricing decision of a manufacturer in a dual-channel supply chain with asymmetric information. Eur. J. Oper. Res.
**2019**, 278, 809–820. [Google Scholar] [CrossRef] - Wang, J.; Jiang, H.; Yu, M. Pricing decisions in a dual-channel green supply chain with product customization. J. Clean. Prod.
**2020**, 247, 119101. [Google Scholar] [CrossRef] - Saha, S.; Sarmah, S.P.; Moon, I. Dual channel closed-loop supply chain coordination with a reward-driven remanufacturing policy. Int. J. Prod. Res.
**2016**, 54, 1503–1517. [Google Scholar] [CrossRef] - Choi, S.C. Price competition in a duopoly common retailer channel. J. Retail.
**1996**, 72, 117–134. [Google Scholar] [CrossRef] - Ha, A.Y.; Tong, S. Contracting and Information Sharing Under Supply Chain Competition. Manag. Sci.
**2008**, 54, 701–715. [Google Scholar] [CrossRef] - Anderson, E.J.; Bao, Y. Price competition with integrated and decentralized supply chains. Eur. J. Oper. Res.
**2010**, 200, 227–234. [Google Scholar] [CrossRef] - Xie, G. Modeling decision processes of a green supply chain with regulation on energy saving level. Comput. Oper. Res.
**2015**, 54, 266–273. [Google Scholar] [CrossRef] - Zhang, G.; Dai, G.; Sun, H.; Zhang, G.; Yang, Z. Equilibrium in supply chain network with competition and service level between channels considering consumers’ channel preferences. J. Retail. Consum. Serv.
**2020**, 57, 102199. [Google Scholar] [CrossRef] - Garrett, B. Why Collaborating with Your Competition Can Be a Great Idea. 2019. Available online: www.forbes.com/sites/briannegarrett/2019/09/19/why-collaborating-with-your-competition-can-be-a-great-idea/?sh=4e77f3dedf86 (accessed on 5 July 2020).
- Wei, J.; Zhao, J.; Hou, X. Integration strategies of two supply chains with complementary products. Int. J. Prod. Res.
**2019**, 57, 1972–1989. [Google Scholar] [CrossRef] - Bian, J.; Zhao, X.; Liu, Y. Single vs. cross distribution channels with manufacturers’ dynamic tacit collusion. Int. J. Prod. Econ.
**2020**, 220, 107456. [Google Scholar] [CrossRef] - Colombo, S. Mixed oligopolies and collusion. J. Econ.
**2016**, 118, 167–184. [Google Scholar] [CrossRef] - Zhou, Y.W.; Cao, Z.H. Equilibrium structures of two supply chains with price and displayed-quantity competition. J. Oper. Res. Soc.
**2014**, 65, 1544–1554. [Google Scholar] [CrossRef] - Wang, L.; Song, H.; Wang, Y. Pricing and service decisions of complementary products in a dual-channel supply chain. Comput. Ind. Eng.
**2017**, 105, 223–233. [Google Scholar] [CrossRef] - Saha, S. Channel characteristics and coordination in three-echelon dual-channel supply chain. Int. J. Syst. Sci.
**2016**, 47, 740–754. [Google Scholar] [CrossRef] - Eriksen, P.S.; Nielsen, P. Order quantity distributions: Estimating an adequate aggregation horizonautomotive industries: A SEM analysis. Manag. Prod. Eng. Rev.
**2016**, 7, 39–48. [Google Scholar] - Jafari, H.; Hejazi, S.R.; Rasti-Barzoki, M. Sustainable development by waste recycling under a three-echelon supply chain: A game-theoretic approach. J. Clean. Prod.
**2017**, 142, 2252–2261. [Google Scholar] [CrossRef] - Song, Z.; He, S.; An, B. Decision and coordination in a dual-channel three-layered green supply chain. Symmetry
**2018**, 10, 549. [Google Scholar] [CrossRef] [Green Version] - Nielsen, I.E.; Majumder, S.; Saha, S. Exploring the intervention of intermediary in a green supply chain. J. Clean. Prod.
**2019**, 233, 1525–1544. [Google Scholar] [CrossRef] - Nielsen, I.E.; Majumder, S.; Szwarc, E.; Saha, S. Impact of Strategic Cooperation under Competition on Green Product Manufacturing. Sustainability
**2020**, 12, 248. [Google Scholar] [CrossRef] - Saha, S.; Sarmah, S.P. Supply chain coordination under ramp-type price and effort induced demand considering revenue sharing contract. Asia Pac. J. Oper. Res.
**2015**, 32, 1550004. [Google Scholar] [CrossRef] - Michna, Z.; Disney, S.M.; Nielsen, P. The impact of stochastic lead times on the bullwhip effect under correlated demand and moving average forecasts. Omega
**2020**, 93, 102033. [Google Scholar] [CrossRef] [Green Version]

**Figure 2.**Profits for (

**a**) M1 and (

**b**) M2 for ${\beta}_{1}=0.15$, ${\beta}_{2}\in \{0.0,0.15,0.3\}$ in Scenarios DD and BM.

**Figure 3.**Profits for (

**a**) $S{C}_{1}$ and (

**b**) $S{C}_{2}$ for ${\beta}_{1}=0.15$, ${\beta}_{2}\in \{0.0,0.15,0.3\}$ in Scenarios II, ID, and BM.

**Figure 4.**Profits for (

**a**) ${M}_{1}$ and (

**b**) ${M}_{2}$ for ${\beta}_{1}=0.15$, ${\beta}_{2}\in \{0.0,0.15,0.3\}$ in Scenarios UC and BM.

**Figure 5.**(

**a**) Prices in retail channels in five scenarios for two products and (

**b**) prices in online channels for the first product along with Scenario BM for ${\beta}_{1}=15$ and ${\beta}_{2}=0.15$.

**Figure 6.**Total profits for (

**a**) SC1, (

**b**) SC2 in between Scenarios II, UC, DD, ID and BM; for ${\beta}_{2}=0.1$, respectively. Total profits for (

**c**) SC1, (

**d**) SC2 in between Scenarios II, UC, DD, ID and BM; for ${\beta}_{2}=0.4$, respectively ($\alpha \in (0.8,1)$, and ${\beta}_{1}\in (0,1)$).

Notations | Descriptions |
---|---|

Indices | |

i | index for ith SC, $i\in \{1,2\}$ |

j | index for decision scenarios, $j\in \{BM,DD,II,ID,UC\}$ |

Parameters | |

a | market potential for each SC |

${\beta}_{1}$ | the cross-price sensitivity of consumers between two retail channels, ${\beta}_{1}\in [0,1)$ |

${\beta}_{2}$ | the cross-price sensitivity of consumers between retail and online channels, ${\beta}_{2}\in [0,1)$ |

Variables | |

${w}_{i}^{j}$ | wholesale price of per unit ith product |

${p}_{i}^{j}$ | retail price of per unit ith product in the traditional retail channel |

${p}_{o}^{j}$ | retail price of per unit first product in the online channel |

${\Pi}_{ri}^{j}$ | profit of the ith retailer |

${\Pi}_{m1}^{j}$ | profit of the first manufacturer, i.e., sum of profits from the retail channel (${\Pi}_{m1r}^{j}$) and online channel(${\Pi}_{m1o}^{j}$), and ${\Pi}_{m1}^{j}={\Pi}_{m1r}^{j}+{\Pi}_{m1o}^{j}$ |

${\Pi}_{m2}^{j}$ | profit of the second manufacturer |

${\Pi}_{c1}^{j}$ | profit of the first SC, i.e., sum of profits form the retail channel(${\Pi}_{c1r}^{j}={\Pi}_{m1r}^{j}+{\Pi}_{r1}^{j}$) and online channel(${\Pi}_{m1o}^{j}$), and ${\Pi}_{c1}^{j}={\Pi}_{c1r}^{j}+{\Pi}_{m1o}^{j}$ |

${\Pi}_{c2}^{j}$ | total profit of the second SC |

${Q}_{i}^{j}$ | sales volume of ith SC |

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**MDPI and ACS Style**

Saha, S.; Nielsen, I.
Strategic Integration Decision under Supply Chain Competition in the Presence of Online Channel. *Symmetry* **2021**, *13*, 58.
https://doi.org/10.3390/sym13010058

**AMA Style**

Saha S, Nielsen I.
Strategic Integration Decision under Supply Chain Competition in the Presence of Online Channel. *Symmetry*. 2021; 13(1):58.
https://doi.org/10.3390/sym13010058

**Chicago/Turabian Style**

Saha, Subrata, and Izabela Nielsen.
2021. "Strategic Integration Decision under Supply Chain Competition in the Presence of Online Channel" *Symmetry* 13, no. 1: 58.
https://doi.org/10.3390/sym13010058