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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, doi: 10.3934/jimo.2019028
##### References:
 [1] N. A. H. Agatz, M. Fleischmann and J. A. E. E. van Nunen, E-fulfillment and multi- channel distribution-A review, European Journal of Operational Research, 187 (2008), 339-356. [2] Y. Aviv and A. Pazgal, Optimal pricing of seasonal products in the presence of forward-looking consumers, Manufacturing & Service Operations Management, 10 (2008), 339-359. [3] G. R. Bitran and S. V. Mondschein, Periodic pricing of seasonal products in retailing, Management Science, 43 (1997), 64-79. [4] E. Bottani and A. Rizzi, Economical assessment of the impact of RFID technology and EPC system on the fast-moving consumer goods supply chain, International Journal of Production Economics, 112 (2008), 548-569. [5] K. K. Boyer and M. T. Frohlich, Analysis of effects of operational execution on repeat purchasing for heterogeneous customer segments, Production and Operations Management, 15 (2006), 229-242. [6] B. A. Chaouch, Analysis of the stochastic cash balance problem using a level crossing technique, Annals of Operations Research, 271 (2018), 429-444. doi: 10.1007/s10479-018-2822-2. [7] F. Y. Chen, J. Chen and Y. Xiao, Optimal control of selling channels for an online retailer with cost-per-click payments and seasonal products, Production and Operations Management, 16 (2007), 292-305. [8] X. Chen and D. Simchi-Levi, A new approach for the stochastic cash balance problem with fixed costs, Probability in the Engineering and Informational Sciences, 23 (2009), 545-562. doi: 10.1017/S0269964809000242. [9] X. Chen, S. X. Zhou and Y. Chen, Integration of inventory and pricing decisions with costly price adjustments, Operations Research, 59 (2011), 1144-1158. doi: 10.1287/opre.1110.0946. [10] M. A. Cohen, W. P. Pierskalla and S. Nahmias, A dynamic inventory system with recycling, Naval Research Logistics Quarterly, 27 (1980), 289-296. [11] G. A. Decroix and P. H. Zipkin, Inventory management for an assembly system with product or component returns, Management Science, 51 (2005), 1250-1265. [12] G. A. Decroix, J. S. Song and P. H. Zipkin, Managing an assemble-to-order system with returns, Manufacturing & Service Operations Management, 11 (2009), 144-159. [13] M. Fleischmann, R. Kuik and R. Dekker, Controlling inventories with stochastic item returns: A basic model, European Journal of Operational Research, 138 (2002), 63-75. doi: 10.1016/S0377-2217(01)00100-X. [14] J. Goh and E. L. Porteus, Multi-echelon inventory management under short-term take-or-pay contracts, Production and Operations Management, 25 (2016), 1415-1429. [15] Gu ide Jr, R. V. Daniel and L. N. Van Wassenhove, OR Forum-The evolution of closed-loop supply chain research, Operations Research, 57 (2009), 10-18. [16] A. Gunasekaran, H. B. Marri, R. E. Mcgaughey and M. D. Nebhwani, E-commerce and its impact on operations management, International Journal of Production Economics, 75 (2002), 185-197. [17] D. Heyman and M. Sobel, Stochastic Models in Operations Research, Volume II, McGraw-Hill, New York, 1982. [18] B. A. Pasternack, Optimal pricing and return policies for perishable commodities, Marketing Science, 27 (2008), 133-140. [19] K. Pauwels, How retailer and competitor decisions drive the long-term effectiveness of manufacturer promotions for fast moving consumer goods, Journal of Retailing, 83 (2007), 297-308. [20] M. Pourakbar, A. Sleptchenko and R. Dekker, The floating stock policy in fast moving consumer goods supply chains, Transportation Research Part E: Logistics and Transportation Review, 45 (2009), 39-49. [21] D. Simchi-Levi, X. Chen and J. Bramel, The Logic of Logistics: Theory, Algorithms, and Applications for Logistics Management, 3rd edition, Springer-Verlag, New York, 2014. doi: 10.1007/978-1-4614-9149-1. [22] J. S. Song and P. Zipkin, Inventory control in a fluctuating demand environment, Operations Research, 41 (1993), 351-370. [23] Y. Wang, S. W. Wallace, B. Shen and T. M. Choi, Service supply chain management: A review of operational models, European Journal of Operational Research, 247 (2015), 685-698. [24] Q. Ye and I. Duenyas, Optimal capacity investment decisions with two-sided fixed-capacity adjustment costs, Operations Research, 55 (2007), 272-283. doi: 10.1287/opre.1060.0386. [25] S. X. Zhou, Z. Tao and X. Chao, Optimal control of inventory systems with multiple types of remanufacturable products, Manufacturing & Service Operations Management, 13 (2011), 20-34. [26] S. X. Zhou and Y. Yu, Technical note-optimal product acquisition, pricing, and inventory management for systems with remanufacturing, Operations Research, 59 (2011), 514-521. doi: 10.1287/opre.1100.0898.

show all references

##### References:
 [1] N. A. H. Agatz, M. Fleischmann and J. A. E. E. van Nunen, E-fulfillment and multi- channel distribution-A review, European Journal of Operational Research, 187 (2008), 339-356. [2] Y. Aviv and A. Pazgal, Optimal pricing of seasonal products in the presence of forward-looking consumers, Manufacturing & Service Operations Management, 10 (2008), 339-359. [3] G. R. Bitran and S. V. Mondschein, Periodic pricing of seasonal products in retailing, Management Science, 43 (1997), 64-79. [4] E. Bottani and A. Rizzi, Economical assessment of the impact of RFID technology and EPC system on the fast-moving consumer goods supply chain, International Journal of Production Economics, 112 (2008), 548-569. [5] K. K. Boyer and M. T. Frohlich, Analysis of effects of operational execution on repeat purchasing for heterogeneous customer segments, Production and Operations Management, 15 (2006), 229-242. [6] B. A. Chaouch, Analysis of the stochastic cash balance problem using a level crossing technique, Annals of Operations Research, 271 (2018), 429-444. doi: 10.1007/s10479-018-2822-2. [7] F. Y. Chen, J. Chen and Y. Xiao, Optimal control of selling channels for an online retailer with cost-per-click payments and seasonal products, Production and Operations Management, 16 (2007), 292-305. [8] X. Chen and D. Simchi-Levi, A new approach for the stochastic cash balance problem with fixed costs, Probability in the Engineering and Informational Sciences, 23 (2009), 545-562. doi: 10.1017/S0269964809000242. [9] X. Chen, S. X. Zhou and Y. Chen, Integration of inventory and pricing decisions with costly price adjustments, Operations Research, 59 (2011), 1144-1158. doi: 10.1287/opre.1110.0946. [10] M. A. Cohen, W. P. Pierskalla and S. Nahmias, A dynamic inventory system with recycling, Naval Research Logistics Quarterly, 27 (1980), 289-296. [11] G. A. Decroix and P. H. Zipkin, Inventory management for an assembly system with product or component returns, Management Science, 51 (2005), 1250-1265. [12] G. A. Decroix, J. S. Song and P. H. Zipkin, Managing an assemble-to-order system with returns, Manufacturing & Service Operations Management, 11 (2009), 144-159. [13] M. Fleischmann, R. Kuik and R. Dekker, Controlling inventories with stochastic item returns: A basic model, European Journal of Operational Research, 138 (2002), 63-75. doi: 10.1016/S0377-2217(01)00100-X. [14] J. Goh and E. L. Porteus, Multi-echelon inventory management under short-term take-or-pay contracts, Production and Operations Management, 25 (2016), 1415-1429. [15] Gu ide Jr, R. V. Daniel and L. N. Van Wassenhove, OR Forum-The evolution of closed-loop supply chain research, Operations Research, 57 (2009), 10-18. [16] A. Gunasekaran, H. B. Marri, R. E. Mcgaughey and M. D. Nebhwani, E-commerce and its impact on operations management, International Journal of Production Economics, 75 (2002), 185-197. [17] D. Heyman and M. Sobel, Stochastic Models in Operations Research, Volume II, McGraw-Hill, New York, 1982. [18] B. A. Pasternack, Optimal pricing and return policies for perishable commodities, Marketing Science, 27 (2008), 133-140. [19] K. Pauwels, How retailer and competitor decisions drive the long-term effectiveness of manufacturer promotions for fast moving consumer goods, Journal of Retailing, 83 (2007), 297-308. [20] M. Pourakbar, A. Sleptchenko and R. Dekker, The floating stock policy in fast moving consumer goods supply chains, Transportation Research Part E: Logistics and Transportation Review, 45 (2009), 39-49. [21] D. Simchi-Levi, X. Chen and J. Bramel, The Logic of Logistics: Theory, Algorithms, and Applications for Logistics Management, 3rd edition, Springer-Verlag, New York, 2014. doi: 10.1007/978-1-4614-9149-1. [22] J. S. Song and P. Zipkin, Inventory control in a fluctuating demand environment, Operations Research, 41 (1993), 351-370. [23] Y. Wang, S. W. Wallace, B. Shen and T. M. Choi, Service supply chain management: A review of operational models, European Journal of Operational Research, 247 (2015), 685-698. [24] Q. Ye and I. Duenyas, Optimal capacity investment decisions with two-sided fixed-capacity adjustment costs, Operations Research, 55 (2007), 272-283. doi: 10.1287/opre.1060.0386. [25] S. X. Zhou, Z. Tao and X. Chao, Optimal control of inventory systems with multiple types of remanufacturable products, Manufacturing & Service Operations Management, 13 (2011), 20-34. [26] S. X. Zhou and Y. Yu, Technical note-optimal product acquisition, pricing, and inventory management for systems with remanufacturing, Operations Research, 59 (2011), 514-521. doi: 10.1287/opre.1100.0898.
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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