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doi: 10.3934/jimo.2019028

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

Jianbin Li 1, , Mengcheng Guan 1, and  Zhiyuan Chen 2,,

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.

Keywords: Dynamic programming, inventory policy, fast-moving consumer goods.
Mathematics Subject Classification: Primary: 90B05, 90B60.
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:
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[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.   Google Scholar

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G. R. Bitran and S. V. Mondschein, Periodic pricing of seasonal products in retailing, Management Science, 43 (1997), 64-79.   Google Scholar

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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.   Google Scholar

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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.   Google Scholar

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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.  Google Scholar

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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.   Google Scholar

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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.  Google Scholar

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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.  Google Scholar

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M. A. Cohen, W. P. Pierskalla and S. Nahmias, A dynamic inventory system with recycling, Naval Research Logistics Quarterly, 27 (1980), 289-296.   Google Scholar

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G. A. Decroix and P. H. Zipkin, Inventory management for an assembly system with product or component returns, Management Science, 51 (2005), 1250-1265.   Google Scholar

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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.   Google Scholar

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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.  Google Scholar

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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.   Google Scholar

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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.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[22]

J. S. Song and P. Zipkin, Inventory control in a fluctuating demand environment, Operations Research, 41 (1993), 351-370.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

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.   Google Scholar

[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.   Google Scholar

[3]

G. R. Bitran and S. V. Mondschein, Periodic pricing of seasonal products in retailing, Management Science, 43 (1997), 64-79.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[10]

M. A. Cohen, W. P. Pierskalla and S. Nahmias, A dynamic inventory system with recycling, Naval Research Logistics Quarterly, 27 (1980), 289-296.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[17]

D. Heyman and M. Sobel, Stochastic Models in Operations Research, Volume II, McGraw-Hill, New York, 1982.  Google Scholar

[18]

B. A. Pasternack, Optimal pricing and return policies for perishable commodities, Marketing Science, 27 (2008), 133-140.   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[22]

J. S. Song and P. Zipkin, Inventory control in a fluctuating demand environment, Operations Research, 41 (1993), 351-370.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.   Google Scholar

[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.  Google Scholar

Figure 1.  Policy structure
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Figure 2.  The relationship of the benefit of salvaging $ \Delta $ and model parameters
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Table 1.  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
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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
Table 2.  Benefit of salvaging vs. salvaging frequency
k 1 2 5 10
x0 = 60 4.5483 2.0535 0.1946 0.0085
x0 = 80 32.6130 16.7936 2.4027 0.0760
x0 = 100 84.8075 49.5771 9.9460 0.3748
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k 1 2 5 10
x0 = 60 4.5483 2.0535 0.1946 0.0085
x0 = 80 32.6130 16.7936 2.4027 0.0760
x0 = 100 84.8075 49.5771 9.9460 0.3748
Table 3.  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 $
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$ \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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