# Sustainable Investment in a Supply Chain in the Big Data Era: An Information Updating Approach

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Modelling

#### 3.1. Basic Modelling Framework

#### 3.2. Bayesian Information Updating

#### 3.3. Objective Functions

## 4. A Benchmark

**Proposition 1.**

**Proposition 2.**

## 5. With Bayesian Information Updating

**Proposition 3.**

## 6. Comparison

**Proposition 4.**

**Proposition 5.**

**Proposition 6.**

## 7. Impact of the Number of the Observations

**Proposition 7.**

## 8. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A.

**Proof of Proposition 1.**

**Proof of Proposition 2.**

**Proof of Proposition 3.**

**Proof of Proposition 4.**

**Proof of Proposition 5.**

**Proof of Proposition 6.**

**Proof of Proposition 7.**

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**Figure 1.**The relationships of ${\mathsf{\Pi}}_{r}^{W}$ and ${\mathsf{\Pi}}_{r}^{N}$. (

**a**) r ≤ 0.5; (

**b**) r > 0.5.

Papers | Sustainability Issues | Big Data Applications | Bayesian Information Updating | ||
---|---|---|---|---|---|

Carbon Emission | Sustainable Investment | Consumer Environment Awareness | |||

Letmathe and Balakrishnan [12], Bouchery et al. [13], Rosič and Jammernegg [16], Zhang and Xu [14], Shen and Li [17], Chen and Wang [15] | √ | ||||

Benjaafar et al. [21], Toptal et al. [22], Drake et al. [23] | √ | √ | |||

Yalabik and Fairchild [24], Liu et al. [25], Nouira et al. [26], Du et al. [27], Li and Shen [28], Dong et al. [4], Shi et al. [11] | √ | √ | √ | ||

Feng and Shanthikumar [1], Liu and Yi [3], See-To and Ngai [37] | √ | ||||

Iyer and Bergen [40], Choi et al. [41], Wu [42], Choi and Chow [43], Yang et al. [44], Chan et al. [45] | √ | ||||

Choi [46] | √ | √ | |||

Chan et al. [47] | √ | √ | √ | ||

Shen et al. [48] | √ | √ | √ | ||

This paper | √ | √ | √ | √ | √ |

Notation | Meaning |
---|---|

$p$ | Unit retail price of the products |

$w$ | Unit wholesale price of the products |

$c$ | Unit production cost of the products |

$v$ | Unit salvage price of the unsold products |

$r$ | Service level, i.e., $r=\left(p-w\right)/\left(p-v\right)$ |

$s$ | Sustainable level of the products |

$e$ | Sensitivity parameter of environmental tax reduction by the sustainable investment |

${c}_{I}$ | Coefficient of investment cost |

$\beta $ | Sensitivity parameter of the effect of the sustainable level on the demand |

$D$ | Demand function of the products |

${x}_{0}$ | Forecasted base demand of the product at Stage 0, a random variable $~N\left({\mu}_{0},{\sigma}_{0}^{2}\right)$ |

${x}_{1}$ | Forecasted base demand of the product at Stage 1, a random variable $~N\left({\mu}_{1},{\sigma}_{1}^{2}\right)$ |

$n$ | Number of the market observation |

${d}_{0}$ | Mean of market observation |

$q$ | Order quantity of the products |

${C}_{B}$ | Fixed cost of using the big data technology |

${\mathsf{\Pi}}_{\mathrm{r}}$ | Retailer’s expected profit |

${\mathsf{\Pi}}_{\mathrm{m}}$ | Manufacturer’s profit |

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## Share and Cite

**MDPI and ACS Style**

Cheng, Y.; Kuang, Y.; Shi, X.; Dong, C. Sustainable Investment in a Supply Chain in the Big Data Era: An Information Updating Approach. *Sustainability* **2018**, *10*, 403.
https://doi.org/10.3390/su10020403

**AMA Style**

Cheng Y, Kuang Y, Shi X, Dong C. Sustainable Investment in a Supply Chain in the Big Data Era: An Information Updating Approach. *Sustainability*. 2018; 10(2):403.
https://doi.org/10.3390/su10020403

**Chicago/Turabian Style**

Cheng, Yanping, Yunjuan Kuang, Xiutian Shi, and Ciwei Dong. 2018. "Sustainable Investment in a Supply Chain in the Big Data Era: An Information Updating Approach" *Sustainability* 10, no. 2: 403.
https://doi.org/10.3390/su10020403