# American Institute of Mathematical Sciences

July  2020, 16(4): 1769-1781. doi: 10.3934/jimo.2019028

## Optimal inventory policy for fast-moving consumer goods under e-commerce environment

 1 School of Management, Huazhong University of Science and Technology, Wuhan, Hubei, China 2 School of Economics and Management, Wuhan University, Wuhan, Hubei, China

* Corresponding author: Zhiyuan Chen

Received  January 2018 Revised  August 2018 Published  May 2019

Fund Project: This work is partially supported by the Key Program of National Natural Science Foundation of China (NSFC) under grant No.71831007 and the General Programs of NSFC under grant Nos. 71571079, 71871166, and by the Ministry of Education Innovation Century Talents Support Fund (NCET-13-0228) and the Fundamental Research Funds for the Central Universities

Coming up with effective inventory-ordering strategies for fast-moving consumer goods (FMCGs) through online channels has a major characteristic that the goods are promoted frequently. In this paper, a multi-period inventory model is employed wherein each period represents the promotion period, and the inventory level can be adjusted by replenishing or salvaging the inventory at the beginning of each promotion period. A two-threshold ordering policy is proven to be optimal for each promotion period. The benefits of salvaging can be significantly high for decision makers. This study contributes to the literature of inventory management that products are frequently promoted under an e-commerce environment.

Citation: Jianbin Li, Mengcheng Guan, Zhiyuan Chen. Optimal inventory policy for fast-moving consumer goods under e-commerce environment. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1769-1781. doi: 10.3934/jimo.2019028
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##### References:
Policy structure
The relationship of the benefit of salvaging $\Delta$ and model parameters
SKU of FMCGs from YihaoDian
 Categories 27th Week 28th Week 28th Week 30th Week Food and beverage 12,949 12,926 12,799 12,811 Maternal and infant products 5,936 5,301 5,296 5,291 Kitchen and cleaning products 5,217 5,231 5,155 5,188
 Categories 27th Week 28th Week 28th Week 30th Week Food and beverage 12,949 12,926 12,799 12,811 Maternal and infant products 5,936 5,301 5,296 5,291 Kitchen and cleaning products 5,217 5,231 5,155 5,188
Benefit of salvaging vs. salvaging frequency
 k 1 2 5 10 x0 = 60 4.5483 2.0535 0.1946 0.0085 x0 = 80 32.613 16.7936 2.4027 0.076 x0 = 100 84.8075 49.5771 9.946 0.3748
 k 1 2 5 10 x0 = 60 4.5483 2.0535 0.1946 0.0085 x0 = 80 32.613 16.7936 2.4027 0.076 x0 = 100 84.8075 49.5771 9.946 0.3748
Average gap between two thresholds varies with covariance
 $\tau$ $T=4$ $T=10$ $T=20$ $T=100$ $\tau= \; 0.99$ $7.50$ $7.60$ $7.05$ $7.34$ $\tau= \; 0.50$ $7.50$ $7.20$ $7.35$ $7.17$ $\tau= \; 0.00$ $7.25$ $7.10$ $6.80$ $7.00$ $\tau=-0.50$ $7.00$ $7.60$ $7.10$ $6.99$ $\tau=-0.99$ $7.50$ $7.70$ $6.80$ $6.97$
 $\tau$ $T=4$ $T=10$ $T=20$ $T=100$ $\tau= \; 0.99$ $7.50$ $7.60$ $7.05$ $7.34$ $\tau= \; 0.50$ $7.50$ $7.20$ $7.35$ $7.17$ $\tau= \; 0.00$ $7.25$ $7.10$ $6.80$ $7.00$ $\tau=-0.50$ $7.00$ $7.60$ $7.10$ $6.99$ $\tau=-0.99$ $7.50$ $7.70$ $6.80$ $6.97$
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