# Online Retailer’s Contingent Free-Shipping Decisions under Large-Scale Promotions Considering Delayed Delivery

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. The CFS Policy

#### 2.2. Demand Postponement Strategy

#### 2.3. Firms’ Operational Decisions during Price Promotions

## 3. Model

#### 3.1. Notations and Assumptions

**Notations:**

**Assumptions:**

#### 3.2. The Basic Model

#### 3.2.1. Consumer’s Purchasing Decision

**Case 1:**${x}_{0}\ge {V}_{h}$

**Case 2:**${x}_{0}<{V}_{h}$

**Theorem**

**1.**

#### 3.2.2. Online Retailer’s Decision

**Theorem**

**2.**

**Corollary**

**1.**

#### 3.3. The Developed Model with Delayed Delivery

#### 3.3.1. Consumer’s Purchasing Decision

**Case 1:**${x}_{0}\ge {V}_{h}$

**Case 2:**${V}_{l}\le {x}_{0}<{V}_{h}$

**Case 3:**${x}_{0}<{V}_{l}$

**Theorem**

**3.**

#### 3.3.2. Online Retailer’s Decision

**Theorem**

**4.**

**Corollary**

**2.**

## 4. Numerical Example

#### 4.1. Numerical Results

#### 4.2. Sensitivity Analysis

#### 4.2.1. The Impact of T

**Result**

**1.**

#### 4.2.2. The Impact of C

**Result**

**2.**

#### 4.2.3. The Impact of $\omega $

**Result**

**3.**

#### 4.2.4. The Impact of $\beta $

**Result**

**4.**

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Cyber Monday: Brisk Sales, Fewer Discounts and Plenty of Out-of-Stock Problems. Available online: https://edition.cnn.com/2021/11/30/business/cyber-monday-sales-total-2021/index.html (accessed on 30 November 2021).
- Alibaba Posts Record Sales for Singles Day, but Growth Is Slowing. Available online: https://edition.cnn.com/2021/11/10/business/china-singles-day-intl-hnk/index.html (accessed on 12 November 2021).
- Shu, L.; Wu, F.; Chu, L.K. Risk-averse procurement strategy under large-scale promotion online considering strategic customer. Comput. Ind. Eng.
**2017**, 112, 576–585. [Google Scholar] [CrossRef] - Fang, Z.; Ho, Y.; Tan, X.; Tan, Y. Show Me the Money: The Economic Impact of Membership-based Free Shipping Programs on e-Tailers. Inform. Syst. Res.
**2021**, 32, 1115–1127. [Google Scholar] [CrossRef] - Lewis, M. The effect of shipping fees on customer acquisition, customer retention, and purchase quantities. J. Retail.
**2006**, 82, 13–23. [Google Scholar] [CrossRef] - Lewis, M.; Singh, V.; Fay, S. An Empirical Study of the Impact of Nonlinear Shipping and Handling Fees on Purchase Incidence and Expenditure Decisions. Market. Sci.
**2006**, 25, 51–64. [Google Scholar] [CrossRef] - Koukova, N.T.; Srivastava, J.; Steul-Fischer, M. The effect of shipping fee structure on consumers’ online evaluations and choice. J. Acad. Market. Sci.
**2012**, 40, 759–770. [Google Scholar] [CrossRef] - Huang, W.; Cheng, Y. Threshold free shipping policies for internet shoppers. Transport. Res. A Pol.
**2015**, 82, 193–203. [Google Scholar] [CrossRef] - Huang, W.H.; Shen, G.C.; Liang, C.L. The effect of threshold free shipping policies on online shoppers’ willingness to pay for shipping. J. Retail. Consum. Serv.
**2019**, 48, 105–112. [Google Scholar] [CrossRef] - Jiang, Y.; Shang, J.; Liu, Y. Optimizing shipping-fee schedules to maximize e-tailer profits. Int. J. Prod. Econ.
**2013**, 146, 634–645. [Google Scholar] [CrossRef] - Zhou, B.; Michael, N.K.; Zhao, Y. Managing stochastic inventory systems with free shipping option. Eur. J. Oper. Res.
**2009**, 196, 186–197. [Google Scholar] [CrossRef] - Kwon, K.; Cheong, T. A minimax distribution-free procedure for a newsvendor problem with free shipping. Eur. J. Oper. Res.
**2014**, 232, 234–240. [Google Scholar] [CrossRef] - Leng, M.; Parlar, M. Free shipping and purchasing decisions in B2B transactions: A game-theoretic analysis. IIE. Trans.
**2005**, 37, 1119–1128. [Google Scholar] [CrossRef] - Hua, G.; Wang, S.; Cheng, T.C.E. Optimal order lot sizing and pricing with free shipping. Eur. J. Oper. Res.
**2012**, 218, 435–441. [Google Scholar] [CrossRef] - Leng, M.; Becerril-Arreola, R. Joint Pricing and Contingent Free-Shipping Decisions in B2C Transactions. Prod. Oper. Manag.
**2010**, 19, 390–405. [Google Scholar] [CrossRef] - Boone, T.; Ganeshan, R. Exploratory analysis of free shipping policies of online retailers. Int. J. Prod. Econ.
**2013**, 143, 627–632. [Google Scholar] [CrossRef] - Becerril-Arreola, R.; Leng, M.; Parlar, M. Online retailers’ promotional pricing, free-shipping threshold, and inventory decisions: A simulation-based analysis. Eur. J. Oper. Res.
**2013**, 230, 272–283. [Google Scholar] [CrossRef] - Song, J.; Yin, Y.; Huang, Y. A coordination mechanism for optimizing the contingent-free shipping threshold in online retailing. Electron. Commer. Res. Appl.
**2017**, 26, 73–80. [Google Scholar] [CrossRef] - Iyer, A.V.; Wu, D.Z. A Postponement Model for Demand Management. Manag. Sci.
**2003**, 49, 983–1002. [Google Scholar] [CrossRef] - Wu, Z.; Wu, J. Price Discount and Capacity Planning under Demand Postponement with Opaque Selling. Decis. Support. Syst.
**2015**, 76, 24–34. [Google Scholar] [CrossRef] - Alim, M.; Beullens, P. Joint inventory and distribution strategy for online sales with a flexible delivery option. Int. J. Prod. Econ.
**2020**, 222, 1–12. [Google Scholar] [CrossRef] - Shin, Y.; Lee, S.; Moon, I. Robust multiperiod inventory model with a new type of buy one get one promotion: “My Own Refrigerator”. Omega
**2021**, 99, 102170. [Google Scholar] [CrossRef] - Papanastasiou, Y.; Savva, N. Dynamic Pricing in the Presence of Social Learning and Strategic Consumers. Manag. Sci.
**2017**, 63, 919–939. [Google Scholar] [CrossRef] - Dong, J.; Wu, D.D. Two-period pricing and quick response with strategic customers. Int. J. Prod. Econ.
**2019**, 215, 165–173. [Google Scholar] [CrossRef] - Chen, K.; Zha, Y.; Alwan, L.C.; Zhang, L. Dynamic pricing in the presence of reference price effect and consumer strategic behaviour. Int. J. Prod. Res.
**2020**, 58, 546–561. [Google Scholar] [CrossRef] - Chen, P.; Zhao, R.; Yan, Y.; Li, X. Promotional pricing and online business model choice in the presence of retail competition. Omega
**2020**, 94, 102085. [Google Scholar] [CrossRef] - Li, C.; Chu, M.; Zhou, C.; Zhao, L. Two-period discount pricing strategies for an e-commerce platform with strategic consumers. Comput. Ind. Eng.
**2020**, 147, 106640. [Google Scholar] [CrossRef] - Maihami, R.; Karimi, B. Optimizing the pricing and replenishment policy for non-instantaneous deteriorating items with stochastic demand and promotional efforts. Comput. Oper. Res.
**2014**, 51, 302–312. [Google Scholar] [CrossRef] - Zhang, J.L.; Chen, J.; Lee, C.Y. Joint optimization on pricing, promotion and inventory control with stochastic demand. Int. J. Prod. Econ.
**2008**, 116, 190–198. [Google Scholar] [CrossRef] - Chen, Z. Optimization of production inventory with pricing and promotion effort for a single-vendor multi-buyer system of perishable products. Int. J. Prod. Econ.
**2018**, 203, 333–349. [Google Scholar] [CrossRef] - Tsao, Y.C.; Sheen, G.J. Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments. Comput. Oper. Res.
**2008**, 35, 3562–3580. [Google Scholar] [CrossRef] - Lin, Z. Price promotion with reference price effects in supply chain. Transp. Res. E
**2016**, 85, 52–68. [Google Scholar] [CrossRef] - Su, Y.; Geunes, J. Price promotions, operations cost, and profit in a two-stage supply chain. Omega
**2012**, 40, 891–905. [Google Scholar] [CrossRef] - Kurata, H.; Liu, J. Optimal promotion planning-depth and frequency-for a two-stage supply chain under Markov switching demand. Eur. J. Oper. Res.
**2007**, 177, 1026–1043. [Google Scholar] [CrossRef] - Wu, F.; Shu, L.; Zhao, S.S.; Jiang, B. Risk-Averse Portfolio Procurement Strategy Under Large-Scale Promotion Online. IEEE. Trans. Eng. Manag.
**2022**, 69, 1252–1261. [Google Scholar] [CrossRef] - Zeng, M.; Cao, H.; Chen, M.; Li, Y. User behaviour modeling, recommendations, and purchase prediction during shopping festivals. Electron. Market.
**2019**, 29, 263–274. [Google Scholar] [CrossRef] - Xu, X.; Li, Q.; Peng, L.; Hsia, T.L.; Huang, C.J.; Wu, J.H. The impact of informational incentives and social influence on consumer behavior during Alibaba’s online shopping carnival. Comput. Hum. Behav.
**2017**, 76, 245–254. [Google Scholar] [CrossRef] - Xu, X.; Wang, L.; Zhao, K. Exploring Determinants of Consumers’ Platform Usage in “Double Eleven” Shopping Carnival in China: Cognition and Emotion from an Integrated Perspective. Sustainability
**2020**, 12, 2790. [Google Scholar] [CrossRef] - Yu, H.; Zeng, A.Z.; Zhao, L. Single or dual sourcing: Decision-making in the presence of supply chain disruption risks. Omega
**2009**, 37, 788–800. [Google Scholar] [CrossRef] - Khouja, M.; Pan, J.; Ratchford, B.T. Analysis of free gift card program effectiveness. J. Retail.
**2011**, 87, 444–461. [Google Scholar] [CrossRef]

**Figure 7.**The impact of the potential market size a on the online retailer’s CFS threshold values and profit.

**Figure 8.**The impact of T on the online retailer’s optimal CFS threshold, profit, and the value of the delayed delivery.

**Figure 9.**The impact of C on the online retailer’s optimal CFS threshold, profit, and the value of the delayed delivery.

**Figure 10.**The impact of $\omega $ on the online retailer’s optimal CFS threshold, profit, and the value of the delayed delivery.

**Figure 11.**The impact of $\beta $ on the online retailer’s optimal CFS threshold, profit, and the value of the delayed delivery.

Notations | |
---|---|

m | The online retailer’s profit margin |

C | The shipping fee of the unit order |

T | The length of the delivery delay time |

a | Potential market size |

$\theta $ | Consumer sensitivity to the shipping fee |

$\delta $ | Consumer sensitivity to CFS threshold |

${Q}_{1}$ | The demand for consumer orders in the basic model |

${Q}_{2}$ | The demand for consumer orders in the developed model |

${x}_{0}$ | The consumer’s planned purchase amount (in dollars), which follows the uniform distribution $U[0,b]$ |

v | Consumer’s marginal utility when the real purchase amount is less than the planned purchase amount, $v>1$ |

d | Consumer’s marginal utility when the real purchase amount is not less than the planned purchase amount, $0<d<1$ |

$\beta $ | Indicator of consumers’ negative attitude toward the shipping fee, $\beta >0$ |

$\eta $ | Indicator of consumers’ negative attitude toward the delayed delivery time, which follows the uniform distribution $U[0,\omega ]$ |

k | The discount on the shipping fee for the delayed delivery |

R | The total shipping fees |

E | The total expected revenues |

$\pi $ | The online retailer’s total expected profit |

Subscript | |

n | The shipping-fee-sensitive consumer |

s | The on-time delivery required consumer |

Decision variables | |

x | Consumer’s real purchase amount (in dollars) |

${V}_{h}$ | The high CFS threshold value |

${V}_{l}$ | The low CFS threshold value |

CFS Threshold | Demand | The Expected Profit | |
---|---|---|---|

The basic model | ${V}_{h}^{*}=108.11$ | $8.2253\times {10}^{5}$ | $7.1746\times {10}^{5}$ |

The developed model | ${V}_{l}^{*}=59.73$ | $1.9630\times {10}^{6}$ | $7.8459\times {10}^{5}$ |

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**MDPI and ACS Style**

Ma, X.; Bian, W.; Yang, X.; Niu, S.; Cai, Y.; Guan, J.; Wang, W.
Online Retailer’s Contingent Free-Shipping Decisions under Large-Scale Promotions Considering Delayed Delivery. *Sustainability* **2022**, *14*, 10773.
https://doi.org/10.3390/su141710773

**AMA Style**

Ma X, Bian W, Yang X, Niu S, Cai Y, Guan J, Wang W.
Online Retailer’s Contingent Free-Shipping Decisions under Large-Scale Promotions Considering Delayed Delivery. *Sustainability*. 2022; 14(17):10773.
https://doi.org/10.3390/su141710773

**Chicago/Turabian Style**

Ma, Xiaxia, Wenliang Bian, Xiqing Yang, Shengnan Niu, Yongming Cai, Jie Guan, and Wenbin Wang.
2022. "Online Retailer’s Contingent Free-Shipping Decisions under Large-Scale Promotions Considering Delayed Delivery" *Sustainability* 14, no. 17: 10773.
https://doi.org/10.3390/su141710773