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September  2020, 16(5): 2159-2173. doi: 10.3934/jimo.2019048

Strategic inventory under suppliers competition

Ganfu Wang , Xingzheng Ai , , Chen Zheng and  Li Zhong

School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, 611731, China

* Corresponding author: Xingzheng Ai

Received  March 2018 Revised  November 2018 Published  September 2020 Early access  May 2019

This paper investigates the impact of competition and the strategic inventories on the performance of a supply chain comprising two competing suppliers and one retailer. Existing literature has shown that the retailer's optimal strategy in equilibrium is to carry inventories, and the suppliers are unable to prevent this. In contrast, our results show that the suppliers will prevent the retailer from carrying strategic inventories when the degree of competition between suppliers is high, and the retailer's carrying strategic inventory is not necessary to force suppliers to lower the future wholesale price. We also find the substitutable relationship between the effect of strategic inventories and the effect of competition. When the degree of competition increases, the suppliers are worse off but the retailer and the total supply chain are both better off when carrying strategic inventories. The retailer could introduce profit sharing contracts so as to encourage suppliers to support strategic inventories which enhance the entire performance of the supply chain.

Keywords: Strategic inventory, supplier competition, profit sharing, supply chain, multi-period.
Mathematics Subject Classification: Primary: 90B05, 90B50; Secondary: 90C40.
Citation: Ganfu Wang, Xingzheng Ai, Chen Zheng, Li Zhong. Strategic inventory under suppliers competition. Journal of Industrial and Management Optimization, 2020, 16 (5) : 2159-2173. doi: 10.3934/jimo.2019048
References:
[1]

K. Anand, R. Anupindi and Y. Bassok, Strategic inventories in vertical contracts, Management Science, 54 (2008), 1792-1804. 

[2]

A. Arya, H. Frimor and B. Mittendorf, Decentralized procurement in light of strategic inventories, Management Science, 61 (2015), 487-705.  doi: 10.1287/mnsc.2014.1908.

[3]

A. Arya and B. Mittendorf, Managing strategic inventories via supplier-to-consumer rebates, Management Science, 59 (2013), 813-818. 

[4]

G. P. Cachon, Supply chain coordination with contracts, A. G. des Kok, S. C. Graves. Eds, Supply chain management: design, coordination and operation, Esevier, Amsterdam, (2003), 223–339.

[5]

S. C. Choi, Price competition in a channel structure with a common retailer, Marketing Science, 10 (1991), 271-358.  doi: 10.1287/mksc.10.4.271.

[6]

Fr. Fitzroy and K. Kraft, Cooperation, productivity, and profit sharing, Quarterly Journal of Economics, 102 (1987), 23-35.  doi: 10.2307/1884678.

[7]

O. Foros, K. P. Hagen and H. J. Kind, Price-dependent profit sharing as a channel coordination device, Management Science, 55 (2009), 1280-1291. 

[8]

R. Hartwig, K. Inderfurth, A. Sadrieh and G. Voigt, Strategic inventory and supply chain behavior, Production and Operations Management, 24 (2015), 1329-1345.  doi: 10.1111/poms.12325.

[9]

B. Mantin and L. Jiang, Strategic inventories with quality deterioration, European Journal of Operational Research, 258 (2017), 155-164.  doi: 10.1016/j.ejor.2016.08.062.

[10]

J. J. Rotmeberg and G. Saloner, Cyclical behavior of strategic inventories, Quart. J. Econom., 104 (1989), 73-97. 

[11]

G. Saloner, The role of obsolescence and inventory costs in providing commitment, Internat. J. Indust. Organ., 4 (1986), 333-345.  doi: 10.1016/0167-7187(86)90025-1.

[12]

W. Shang, AY. Ha and S. Tong, Information sharing in a supply chain with a common retailer, Management Science, 62 (2016), 1-301.  doi: 10.1287/mnsc.2014.2127.

show all references

References:
[1]

K. Anand, R. Anupindi and Y. Bassok, Strategic inventories in vertical contracts, Management Science, 54 (2008), 1792-1804. 

[2]

A. Arya, H. Frimor and B. Mittendorf, Decentralized procurement in light of strategic inventories, Management Science, 61 (2015), 487-705.  doi: 10.1287/mnsc.2014.1908.

[3]

A. Arya and B. Mittendorf, Managing strategic inventories via supplier-to-consumer rebates, Management Science, 59 (2013), 813-818. 

[4]

G. P. Cachon, Supply chain coordination with contracts, A. G. des Kok, S. C. Graves. Eds, Supply chain management: design, coordination and operation, Esevier, Amsterdam, (2003), 223–339.

[5]

S. C. Choi, Price competition in a channel structure with a common retailer, Marketing Science, 10 (1991), 271-358.  doi: 10.1287/mksc.10.4.271.

[6]

Fr. Fitzroy and K. Kraft, Cooperation, productivity, and profit sharing, Quarterly Journal of Economics, 102 (1987), 23-35.  doi: 10.2307/1884678.

[7]

O. Foros, K. P. Hagen and H. J. Kind, Price-dependent profit sharing as a channel coordination device, Management Science, 55 (2009), 1280-1291. 

[8]

R. Hartwig, K. Inderfurth, A. Sadrieh and G. Voigt, Strategic inventory and supply chain behavior, Production and Operations Management, 24 (2015), 1329-1345.  doi: 10.1111/poms.12325.

[9]

B. Mantin and L. Jiang, Strategic inventories with quality deterioration, European Journal of Operational Research, 258 (2017), 155-164.  doi: 10.1016/j.ejor.2016.08.062.

[10]

J. J. Rotmeberg and G. Saloner, Cyclical behavior of strategic inventories, Quart. J. Econom., 104 (1989), 73-97. 

[11]

G. Saloner, The role of obsolescence and inventory costs in providing commitment, Internat. J. Indust. Organ., 4 (1986), 333-345.  doi: 10.1016/0167-7187(86)90025-1.

[12]

W. Shang, AY. Ha and S. Tong, Information sharing in a supply chain with a common retailer, Management Science, 62 (2016), 1-301.  doi: 10.1287/mnsc.2014.2127.

Figure 1.  The relationship between $ r $ and $ h_{0} $ when $ a = 10 $
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Figure 2.  The relationship between $ r $ and $ I^{i} $ when $ a = 10, h = 0.5 $
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Figure 3.  the relationship $ h $ and $ r $ with $ a = 1 $
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Figure 4.  Improvement performance
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Figure 5.  the relationship between $ \beta $ and $ r $ with $ a = 10, h = 0.2 $
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Table 1.  The Equilibrium Outcome
The Dynamic ContractThe Commitment Contract
$\left( {w_{1}^{\ast } , w_{2}^{\ast } } \right)$ $\left( {\begin{array}{l} \dfrac{2a(3-r)^{2}(3-2r-r^{2})-h(12-24r+9r^{2}+2r^{3}-r^{4})}{102-81r+9r^{2}+8r^{3}-2r^{4}}, \\ \dfrac{(2-r)(2a(3-r)(1-r)(3+r)+h(30-r(9+(3-r)r)))}{102-81r+9r^{2}+8r^{3}-2r^{4}}\end{array}} \right)$ $\left( {\dfrac{a(1-r)}{2-r}, \dfrac{a(1-r)}{2-r}} \right)$
$\left( {p_{1}^{\ast } , p_{2}^{\ast } } \right)$ $\left( {\begin{array}{l} \dfrac{a(156-153r+21r^{2}+16r^{3}-4r^{4})-h(2-r)(6-9r+r^{3})}{2(102-81r+9r^{2}+8r^{3}-2r^{4})}, \\ \dfrac{a(138-r(135-r(23+2r(7-2r)))) +h(2-r)(30-r(9+(3-r)r))}{2(102-81r+9r^{2}+8r^{3}-2r^{4})} \end{array}} \right)$ $\left( {\dfrac{a}{2(2-r)}, \dfrac{a}{2(2-r)}} \right)$
$I^{{\rm \ast }}$ $\dfrac{a(30-39r+8r^{2}+r^{3})-h(2-r)^{2}(30-9r-3r^{2}+r^{3})}{2(1-r^{2})(102-81r+9r^{2}+8r^{3}-2r^{4})}$ 0
$\left( {Q_{1}^{\ast } , Q_{2}^{\ast } } \right)$ $\left( {\begin{array}{l} \dfrac{2a(1-r)(39-r(9+2r))+h(2-r)(r(33+6r-4r^{2})-54)}{2(1-r^{2})(102-81r+9r^{2}+8r^{3}-2r^{4})}, \\\dfrac{(2-r)(2a(3-r)(1-r)(3+r)+h(30-r(9+(3-r)r)))}{2(1-r^{2})(102-81r+9r^{2}+8r^{3}-2r^{4})} \end{array}} \right)$ $\left( {\begin{array}{l} \dfrac{a}{2(2-r)(1+r)}, \\ \dfrac{a}{2(2-r)(1+r)}\end{array}} \right)$
$\pi_{m}^{\ast } $ $\dfrac{h^{2}(2-r)^{2}D-4ahE+4a^{2}K}{2(1-r^{2})(102-81r+9r^{2}+8r^{3}-2r^{4})^{2}}$ $\dfrac{a^{2}(1-r)}{(r+1)(2-r)^{2}}$
$\pi_{b}^{\ast } $ $\dfrac{h^{2}(2-r)^{2}A-2ahB+a^{2}C}{2(1-r^{2})(102-81r+9r^{2}+8r^{3}-2r^{4})^{2}}$ $\dfrac{a^{2}(1-r)}{(r+1)(2-r)^{2}}$
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The Dynamic ContractThe Commitment Contract
$\left( {w_{1}^{\ast } , w_{2}^{\ast } } \right)$ $\left( {\begin{array}{l} \dfrac{2a(3-r)^{2}(3-2r-r^{2})-h(12-24r+9r^{2}+2r^{3}-r^{4})}{102-81r+9r^{2}+8r^{3}-2r^{4}}, \\ \dfrac{(2-r)(2a(3-r)(1-r)(3+r)+h(30-r(9+(3-r)r)))}{102-81r+9r^{2}+8r^{3}-2r^{4}}\end{array}} \right)$ $\left( {\dfrac{a(1-r)}{2-r}, \dfrac{a(1-r)}{2-r}} \right)$
$\left( {p_{1}^{\ast } , p_{2}^{\ast } } \right)$ $\left( {\begin{array}{l} \dfrac{a(156-153r+21r^{2}+16r^{3}-4r^{4})-h(2-r)(6-9r+r^{3})}{2(102-81r+9r^{2}+8r^{3}-2r^{4})}, \\ \dfrac{a(138-r(135-r(23+2r(7-2r)))) +h(2-r)(30-r(9+(3-r)r))}{2(102-81r+9r^{2}+8r^{3}-2r^{4})} \end{array}} \right)$ $\left( {\dfrac{a}{2(2-r)}, \dfrac{a}{2(2-r)}} \right)$
$I^{{\rm \ast }}$ $\dfrac{a(30-39r+8r^{2}+r^{3})-h(2-r)^{2}(30-9r-3r^{2}+r^{3})}{2(1-r^{2})(102-81r+9r^{2}+8r^{3}-2r^{4})}$ 0
$\left( {Q_{1}^{\ast } , Q_{2}^{\ast } } \right)$ $\left( {\begin{array}{l} \dfrac{2a(1-r)(39-r(9+2r))+h(2-r)(r(33+6r-4r^{2})-54)}{2(1-r^{2})(102-81r+9r^{2}+8r^{3}-2r^{4})}, \\\dfrac{(2-r)(2a(3-r)(1-r)(3+r)+h(30-r(9+(3-r)r)))}{2(1-r^{2})(102-81r+9r^{2}+8r^{3}-2r^{4})} \end{array}} \right)$ $\left( {\begin{array}{l} \dfrac{a}{2(2-r)(1+r)}, \\ \dfrac{a}{2(2-r)(1+r)}\end{array}} \right)$
$\pi_{m}^{\ast } $ $\dfrac{h^{2}(2-r)^{2}D-4ahE+4a^{2}K}{2(1-r^{2})(102-81r+9r^{2}+8r^{3}-2r^{4})^{2}}$ $\dfrac{a^{2}(1-r)}{(r+1)(2-r)^{2}}$
$\pi_{b}^{\ast } $ $\dfrac{h^{2}(2-r)^{2}A-2ahB+a^{2}C}{2(1-r^{2})(102-81r+9r^{2}+8r^{3}-2r^{4})^{2}}$ $\dfrac{a^{2}(1-r)}{(r+1)(2-r)^{2}}$
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