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The impact of inventory sharing on the bullwhip effect in decentralized inventory systems

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Logistics Research

Abstract

The paper derives the impact of inventory sharing policy on the bullwhip effect in two-stage supply chains with two independent suppliers and two integrated retailers. There exists an inventory sharing policy between two retailers. Under inventory sharing policy, when demand in one retailer exceeds its inventory, this retailer can ask for a product sharing volume from the other in order to satisfy customer demand. With certain assumptions, the bullwhip effect is quantified in both cases, with inventory sharing policy and without inventory sharing policy. We found that inventory sharing has significant impact on the bullwhip effect in the supply system. However, inventory sharing policy does not synchronously reduce or increase the bullwhip effect in both suppliers in the same period. A numerical example is given to illustrate the study model.

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References

  1. Bassok Y, Anupindi R, Akella R (1999) Single-period multi-product inventory models with substitution. Oper Res 47(4):632–642

    Article  MATH  MathSciNet  Google Scholar 

  2. Bitran G, Dasu S (1992) Ordering policies in an environment of stochastic yields and substitutable demands. Oper Res 40(5):177–185

    Article  Google Scholar 

  3. Chen F, Ryan JK, Simchi-Levi D (2000) The impact of exponential smoothing forecasts on the bullwhip effect. Naval Res Logist 47(4):269–286

    Article  MATH  MathSciNet  Google Scholar 

  4. Chatfield DC, Kim JG, Harrison TP, Hayya JC (2004) The bullwhip effect—impact of stochastic lead time, information quality, and information sharing: a simulation study. Prod Oper Manag 13(4):340–353

    Article  Google Scholar 

  5. Drezner Z, Gurnani H, Pasternack BA (1995) An eoq model with substitutions between products. J Oper Res Soc 46(7):887–891

    Article  MATH  Google Scholar 

  6. Evers PT (2001) Heuristics for assessing emergency transshipments. Eur J Oper Res 129:311–316

    Article  MATH  Google Scholar 

  7. Kutanoglu E (2009) An inventory sharing and allocation method for a multi-location service parts logistics network with time-based service levels. Eur Oper Res 194(3):728–742

    Article  MATH  MathSciNet  Google Scholar 

  8. Forrester J (1958) Industrial dynamics, a major breakthrough for decision makers. Harvard Bus Rev 36:37–66

    Google Scholar 

  9. Chen F, Drezner Z, Ryan JK, Levi DS (2000) Quantifying the bullwhip effect in a simple supply chain. Manag Sci 46(3):436–443

    Article  MATH  Google Scholar 

  10. Gilbert K (2005) An ARIMA supply chain model. Manag Sci 51(2):305–310

    Article  MATH  Google Scholar 

  11. Luong HT, Phien NH (2010) Measure of bullwhip effect in supply chains: the case of high order autoregressive demand process. Eur J Oper Res 183(1):197–209

    Article  Google Scholar 

  12. Luong HT (2007) Measure of the bullwhip effect in supply chains with autoregressive demand process. Eur J Oper Res 180(3):1086–1097

    Article  MATH  MathSciNet  Google Scholar 

  13. Sun HX, Ren YT (2005) The impact of forecasting methods on bullwhip effect in supply chain management. Proc Eng Manage Conf 1:215–219

    Google Scholar 

  14. Zhao H, Deshpande V, Ryan K (2005) Inventory sharing and rationing in decentralized dealer networks. Manage Sci 51(4):531–547

    Article  MATH  Google Scholar 

  15. Kim JG, Chatfield D, Harrison TP, Hayya JC (2006) Quantifying the bullwhip effect in a supply chain with stochastic lead time. Eur J Oper Res 173:617–636

    Article  MATH  MathSciNet  Google Scholar 

  16. Heydari J, Karemzadeh RB, Chaharsooghi SK (2009) A study of lead time variation impact on supply chain performance. Int J Adv Manuf Technol 40:1206–1215

    Article  Google Scholar 

  17. Karaesmen I, van Ryzin G (2004) Overbooking with substitutable inventory classes. Oper Res 52(1):83–104

    Article  MATH  MathSciNet  Google Scholar 

  18. So KC, Zheng X (2003) Impact of supplier’s lead time and forecast demand updating on retailer’s order quantity variability in a two-level supply chain. Int J Prod Econ 86:169–179

    Article  Google Scholar 

  19. Xu K, Dong Y, Evers PT (2000) “Towards better coordination of the supply chain”, Transport. Res Part E Logist Trans Rev 37(1):35–54

    Article  Google Scholar 

  20. Lee HL, Padmanabhan V, Whang S (1997) Information distortion in a supply chain: the bullwhip effect. Manag Sci 43(4):546–558

    Article  MATH  Google Scholar 

  21. McGillivray AR, Silver EA (1978) Some concepts for inventory control under substitutable demand. Inf Syst Oper Res 16(1):47–63

    MATH  MathSciNet  Google Scholar 

  22. Netessine S, Rudi N (2003) Centralized and competitive inventory models with demand substitution. Oper Res 51(2):329–335

    Article  MATH  MathSciNet  Google Scholar 

  23. Rudi N, Kapur S, Pyke DF (2001) A two-location inventory model with transshipment and local decision making. Manage Sci 47(12):1668–1680

    Article  MATH  Google Scholar 

  24. Parlar M, Goyal S (1984) Optimal ordering decisions for twosubstitutable products with stochastic demands. Opsearch 21:1–15

    MATH  Google Scholar 

  25. Graves SC (1999) A single-item inventory model for a non-stationary demand process. Manuf Serv Oper Manage 1(1):50–61

    Google Scholar 

  26. Ryan JK (1997) Analysis of inventory models with limited demand information. PhD thesis, Northwestern University, Evanston

  27. Tagaras G (1989) Effects of pooling on the optimization and service levels of two-location inventory systems. IIE Trans 21:250–257

    Article  Google Scholar 

  28. Duc TTH, Luong HT, Kim YD (2008) A measure of bullwhip effect in supply chains with a mixed autore-gressive-moving average demand process. Eur J Oper Res 187(1):243–256

    Article  MATH  MathSciNet  Google Scholar 

  29. Duc TTH, Luong HT, Kim YD (2010) Investigate the impact of third-Party warehouse on bullwhip effect in supply chains with autoregressive demand process. SIMTech technical reports (STR_V11_N3_08_POM). 11(3)

  30. Zhang X (2004) The impact of forecasting methods on the bullwhip effect. Int J Prod Econ 88:15–27

    Article  Google Scholar 

  31. Li X, Song L, Zhao Z (2011) Quantifying the impact of demand substitution on the bullwhip effect in a supply chain. Logist Res 3:221–232

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Engineering and Technology, Asian Institute of Technology, Bangkok, Thailand

    Dang Van Le & Luong Trung Huynh

  2. Faculty of Engineering and Technology, Lucian Blaga University of Sibiu, Sibiu, Romania

    Kifor Vasile Claudiu & Muntean Achim

Authors
  1. Dang Van Le
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  2. Luong Trung Huynh
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  3. Kifor Vasile Claudiu
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  4. Muntean Achim
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Corresponding author

Correspondence to Dang Van Le.

Appendix

Appendix

  1. 1.

    The derivation process of E(Dt,i) and \( \text{var} (D_{t,i} ) \)When the autoregressive demand process is stationary, we have

    $$ E(D_{t,i} ) = E(D_{t - 1,i} ) = E(D_{t - 2,i} ) = \ldots = E(D_{i} ), $$

    and

    $$ \text{var} (D_{t,i} ) = \text{var} (D_{t - 1,i} ) = \text{var} (D_{t - 2,i} ) = \ldots = \text{var} (D_{i} ), $$

    where

    $$ \begin{aligned} & D_{t,1} = \mu_{1} + \rho_{1} D_{t - 1,1} + \varepsilon_{t,1} , \\ & E(D_{t,1} ) = E(\mu_{1} ) + \rho_{1} E(D_{t - 1,1} ) + E(\varepsilon_{t,1} ) \\ & E(D_{1} ) = \,\mu_{1} + \rho_{1} E(D_{1} ) + 0 \\ & \quad \Rightarrow E(D_{1} ) = \frac{{\mu_{1} }}{{1 - \rho_{1} }}. \\ & \,\text{var} (D_{t,1} ) = \text{var} (\mu_{1} ) + \rho_{1}^{2} \text{var} (D_{t - 1,1} ) + \text{var} (\varepsilon_{t,1} ) \\ \, & \text{var} (D_{1} ) = 0 + \rho_{1}^{2} \text{var} (D_{1} ) + \sigma_{1}^{2} \\ & \quad \Rightarrow \text{var} (D_{1} ) = \frac{{\sigma_{1}^{2} }}{{1 - \rho_{1}^{2} }}. \\ \end{aligned} $$

    Similarly, we have

    $$ \begin{aligned} E(D_{2} ) & = \frac{{\mu_{2} }}{{1 - \rho_{2} }}, \\ \text{var} (D_{1} ) & = \frac{{\sigma_{2}^{2} }}{{1 - \rho_{2}^{2} }}. \\ \end{aligned} $$
  2. 2.

    The derivation process of the further equation of qt,1.

    $$ \begin{aligned} q_{t,1} &= y_{t,1} - y_{t - 1,1} + D_{t -1,1} + \lambda q_{t,1} , \\ \Rightarrow q_{t,1} & = \frac{1}{1 -\lambda }\left[ {y_{t,1} - y_{t - 1,1} + D_{t - 1,1} } \right] \\& = \frac{1}{1 - \lambda }\left[ {\left({\widehat{D}_{t,1}^{{L_{1} }} + z_{1} \widehat{\sigma}_{t,1}^{{L_{1} }} } \right) - \left( {\widehat{D}_{t - 1,1}^{{L_{1}}} + z_{1} \widehat{\sigma }_{t - 1,1}^{{L_{1} }} } \right) + D_{t -1,1} } \right] \\ & = \frac{1}{1 - \lambda }\left[ {\left({\widehat{D}_{t,1}^{{L_{1} }} - \widehat{D}_{t - 1,1}^{{L_{1} }} }\right) + D_{t - 1,1} - z_{1} \left( {\widehat{\sigma}_{t,1}^{{L_{1} }} - \widehat{\sigma }_{t - 1,1}^{{L_{1} }} }\right)} \right] \\ & = \frac{L}{p(1 - \lambda )}\left({\sum\limits_{i = 1}^{p} {D_{t - i,1} - \sum\limits_{i = 1}^{p}{D_{t - 1 - i,1} } } } \right) \\ & \quad + \frac{{D_{t - 1,1}}}{1 - \lambda } + \frac{{z_{1} }}{1 - \lambda }\left({\widehat{\sigma }_{t,1}^{{L_{1} }} - \widehat{\sigma }_{t -1,1}^{{L_{1} }} } \right) \\ \, & = \frac{L}{p(1 - \lambda)}\left( {D_{t - 1,1} - D_{t - p - 1,1} } \right) + \frac{{D_{t -1,1} }}{1 - \lambda } + \frac{{z_{1} }}{1 - \lambda }\left({\widehat{\sigma }_{t,1}^{{L_{1} }} - \widehat{\sigma }_{t -1,1}^{{L_{1} }} } \right) \\ & = \frac{1}{1 - \lambda }\left(1 +\frac{{L_{1} }}{p}\right)D_{t - 1,1} - \frac{{L_{1} }}{p\left(1 - \lambda\right)}D_{t - p - 1,1} \\ & \quad + \frac{{z_{1} }}{1 - \lambda}\left( {\widehat{\sigma }_{t,1}^{{L_{1} }} - \widehat{\sigma }_{t -1,1}^{{L_{1} }} } \right), \\ \end{aligned} $$
    $$\text{var} (q_{t,1} ) = \text{var} \left( \begin{gathered}\frac{1}{1 - \lambda }\left(1 + \frac{{L_{1}}}{p}\right)D_{t - 1,1} -\frac{{L_{1} }}{p(1 - \lambda )}D_{t - p - 1,1} \hfill \\ \, +\frac{{z_{1} }}{1 - \lambda }\left( {\widehat{\sigma }_{t,1}^{{L_{1}}} - \widehat{\sigma }_{t - 1,1}^{{L_{1} }} } \right) \hfill \\\end{gathered} \right) $$
    $$\begin{aligned} &= \frac{1}{{(1 - \lambda )^{2} }}\left(\begin{gathered} \left(1 + \frac{{L_{1} }}{p}\right)^{2} \text{var} (D_{t -1,1} ) \hfill \\ - 2\left(\frac{{L_{1} }}{p}\right)\left(1 + \frac{{L_{1}}}{p}\right)\text{cov} (D_{t - 1,1} ,D_{t - p - 1,1} ) \hfill \\ +\left(\frac{{L_{1} }}{p}\right)^{2} \text{var} (D_{t - p - 1,1} ) + z_{1}^{2}\text{var} (\widehat{\sigma }_{t,1}^{{L_{1} }} - \widehat{\sigma}_{t - 1,1}^{{L_{1} }} ) \hfill \\ + 2z_{1} \left(1 + \frac{{2L_{1}}}{p}\right)\text{cov} (D_{t - 1,1} ,\widehat{\sigma }_{t,1}^{{L_{1} }} )\hfill \\ \end{gathered} \right) \\ & = \frac{1}{{\left(1 - \lambda\right)^{2} }}\left( \begin{gathered} \left(1 + \frac{{2L_{1} }}{p} +\left(\frac{{2L_{1} }}{p}\right)^{2} \right)\text{var} (D_{1} ) \hfill \\ -\left(\frac{{2L_{1} }}{p} + \frac{{2L_{1}^{2} }}{p}\right)\text{cov} (D_{t -1,1} ,D_{t - p - 1,1} ) \hfill \\ + z_{1}^{2} \text{var}(\widehat{\sigma }_{t,1}^{{L_{1} }} - \widehat{\sigma }_{t -1,1}^{{L_{1} }} ) \hfill \\ + 2z_{1} \left(1 + \frac{{2L_{1}}}{p}\right)\text{cov} (D_{t - 1,1} ,\widehat{\sigma }_{t,1}^{{L_{1} }} )\hfill \\ \end{gathered} \right). \\ \end{aligned} $$

    Now we will determine \( \text{cov} (D_{t - 1,1} ,D_{t - p - 1,1} ) \) and \( \text{cov} (D_{t - 1,1} ,\widehat{\sigma }_{t,1}^{{L_{1} }} ) \) We have

    $$ \begin{gathered} \text{cov} (D_{t - 1,1} ,D_{t - p - 1,1} ) \hfill \\ = \text{cov} \left( {(\mu_{1} + \rho_{1} D_{t - 2,1} + \varepsilon_{t,1} ),D_{t - p - 1,1} } \right) \hfill \\ = \text{cov} \left( {\mu_{1} ,D_{t - p - 1,1} } \right) + \rho_{1} \text{cov} \left( {D_{t - 2,1} ,D_{t - p - 1,1} } \right) \hfill \\ + \text{cov} \left( {\varepsilon_{t,1} ,D_{t - p - 1,1} } \right). \hfill \\ \end{gathered} $$
    $$ \begin{gathered} ({\text{Since}}\,\text{cov} \left( {\mu_{1} ,D_{t - p - 1,1} } \right) = 0\,{\text{and}}\,\text{cov} \left( {\varepsilon_{t,1} ,D_{t - p - 1,1} } \right) = 0), \hfill \\ \text{cov} (D_{t - 1,1} ,D_{t - p - 1,1} ) = \rho_{1} \text{cov} \left( {D_{t - 2,1} ,D_{t - p - 1,1} } \right) \hfill \\ \ldots \hfill \\ = \rho_{1}^{p} \text{cov} \left( {D_{t - p,1} ,D_{t - p - 1,1} } \right) \hfill \\ = \rho_{1}^{p} \text{var} (D_{1} ). \hfill \\ \end{gathered} $$

    We assume that forecasting customer demands by retailers are random variables of the form as \( D_{t} = \mu + \rho D_{t - 1} + \varepsilon_{t} \), and the error terms ɛ t are identically independent distribution with mean 0 and variance σ2. Let the estimate of the standard deviation of forecast error of the lead time demand be

    $$ \widehat{\sigma }_{t}^{L} = C_{L,p} \sqrt {\frac{{\sum\nolimits_{i = j}^{p} {(D_{t - j} - \widehat{D}_{t - j} )^{2} } }}{p}} . $$

    Applying the result proved in Ryan [21], we have

    $$ \text{cov} (D_{t - j} ,\widehat{\sigma }_{t}^{L} ) = 0,\quad \forall i = 1,2, \ldots ,p. $$

    Hence,

    $$ \begin{gathered} \text{var} (q_{t,1} ) \hfill \\ = \frac{1}{{(1 -\lambda )^{2} }}\left[ \begin{gathered} \left(1 + \frac{{2L_{1} }}{p} +2\left(\frac{{L_{1} }}{p}\right)^{2} \right)\text{var} (D_{1} ) \hfill \\ -\left(\frac{{2L_{1} }}{p} + \frac{{2L_{1}^{2} }}{p}\right)\text{cov} (D_{t -1,1} ,D_{t - p - 1,1} ) \hfill \\ + z_{1}^{2} \text{var}(\widehat{\sigma }_{t,1}^{{L_{1} }} - \widehat{\sigma }_{t -1,1}^{{L_{1} }} ) + \,2z_{1} \left(1 + \frac{{2L_{1} }}{p}\right)\text{cov}(D_{t - 1,1} ,\widehat{\sigma }_{t,1}^{{L_{1} }} ) \hfill \\\end{gathered} \right] \hfill \\ = \frac{1}{{(1 - \lambda )^{2}}}\left[ \begin{gathered} \left(1 + \frac{{2L_{1} }}{p} + 2\left(\frac{{L_{1}}}{p}\right)^{2} \right)\text{var} (D_{1} ) - \,\left(\frac{{2L_{1} }}{p} +\frac{{2L_{1}^{2} }}{p}\right)\rho_{1}^{p} \text{var} (D_{1} ) \hfill \\ +z_{1}^{2} \text{var} (\widehat{\sigma }_{t,1}^{{L_{1} }} -\widehat{\sigma }_{t - 1,1}^{{L_{1} }} ) \hfill \\ \end{gathered}\right] \hfill \\ = \frac{{\text{var} (D_{1} )}}{{(1 - \lambda )^{2}}}\left[ {1 + \left(\frac{{2L_{1} }}{p} + \frac{{2L_{1}^{2} }}{p}\right)(1 -\rho_{1}^{p} )} \right] + \frac{{z_{1}^{2} \text{var}(\widehat{\sigma }_{t,1}^{{L_{1} }} - \widehat{\sigma }_{t -1,1}^{{L_{1} }} )}}{{(1 - \lambda )^{2} }}. \hfill \\ \end{gathered}$$
  3. 3.

    The derivation process of the further expression of qt,2:

    $$ \begin{aligned} q_{t,2} & = \left(1 + \frac{{L_{2} }}{p}\right)D_{t -1,2} - \left(\frac{{L_{2} }}{p}\right)D_{t - p - 1,2} + z_{2} (\widehat{\sigma}_{t,2}^{{L_{2} }} - \widehat{\sigma }_{t - 1,2}^{{L_{2} }} ) -\lambda q_{t,1} , \\ \Rightarrow \text{var} (q_{t,2} ) \\ & =\text{var} \left[ {\left(1 + \frac{{L_{2} }}{p}\right)D_{t - 1,2} -\left(\frac{{L_{2} }}{p}\right)D_{t - p - 1,2} + z_{2} (\widehat{\sigma}_{t,2}^{{L_{2} }} - \widehat{\sigma }_{t - 1,2}^{{L_{2} }} )}\right] \\ & \quad - \lambda^{2} \text{var} (q_{t,1} ) \\ &= \left(1 + \frac{{L_{2} }}{p}\right)^{2} \text{var} (D_{t - 1,2} ) -2\left(\frac{{L_{2} }}{p}\right)\left(1 + \frac{{L_{2} }}{p}\right)\text{cov} (D_{t - 1,2},D_{t - p - 1,2} ) \\ & \quad + \left(\frac{{L_{2} }}{p}\right)^{2}\text{var} (D_{t - p - 1,2} ) + z_{2}^{2} \text{var}(\widehat{\sigma }_{t,2}^{{L_{2} }} - \widehat{\sigma }_{t -1,2}^{{L_{2} }} ) \\ & \quad + 2z_{2} \left(1 + 2\frac{{L_{2}}}{p}\right)\text{cov} (D_{t - 1,2} ,\widehat{\sigma }_{t,2}^{{L_{2} }} )- \lambda^{2} \text{var} (q_{t,1} ) \\ & = \left( {1 +2\frac{{L_{2} }}{p} + 2\left(\frac{{L_{2} }}{p}\right)^{2} } \right)\text{var}(D_{2} ) \\ & \quad - \left( {\frac{{2L_{2} }}{p} +2(\frac{{L_{2} }}{p})^{2} } \right)\text{cov} (D_{t - 1,2} ,D_{t - p- 1,2} ) \\ \,\quad + z_{2}^{2} \text{var} (\widehat{\sigma}_{t,2}^{{L_{2} }} - \widehat{\sigma }_{t - 1,2}^{{L_{2} }} ) +2z_{2} \left(1 + \frac{{2L_{2} }}{p}\right)\text{cov} (D_{t - 1,2},\widehat{\sigma }_{t,2}^{{L_{2} }} ) \\ & \quad - \lambda^{2}\text{var} (q_{t,1} ). \\ \end{aligned} $$

    Furthermore, we have \( \text{cov} (D_{t - 1,2} ,\widehat{\sigma }_{t,2}^{{L_{2} }} ) = 0 \) and

    $$ \begin{gathered} \text{cov} (D_{t - 1,2} ,D_{t - p - 1,2} ) \hfill \\ = \text{cov} (\mu_{2} + \rho_{2} D_{t - 2,2} + \varepsilon_{t - 1,2} ,D_{t - p - 1,2} ) \hfill \\ = \text{cov} (\mu_{2} ,D_{t - p - 1,2} ) + \rho_{2} \text{cov} (D_{t - 2,2} ,D_{t - p - 1,2} ) \hfill \\ \quad + \text{cov} (\varepsilon_{t - 1,2} ,D_{t - p - 1,2} ) \hfill \\ = \rho_{2} \text{cov} (D_{t - 1,2} ,D_{t - p - 1,2} ) \hfill \\ \ldots \hfill \\ = \rho_{2}^{p} \text{cov} (D_{t - p - 1,2} ,D_{t - p - 1,2} ) \hfill \\ = \rho_{2}^{p} \text{var} (D_{2} ). \hfill \\ \end{gathered}$$
    $$({\text{Note}}\,{\text{that}}\,\text{cov} (\mu_{2} ,D_{t - p - 1,2} ) = 0\quad {\text{and}}\quad \text{cov} (\varepsilon_{t - 1,2} ,D_{t - p - 1,2} ) = 0) $$

    Hence,

    $$ \begin{aligned} \text{var} (q_{t,2} ) & = \left( {1 + 2\frac{{L_{2} }}{p} + 2\left(\frac{{L_{2} }}{p}\right)^{2} } \right)\text{var} (D_{2} ) \\ & \quad - \left( {\frac{{2L_{2} }}{p} + 2\left(\frac{{L_{2} }}{p}\right)^{2} } \right)\rho_{2}^{2} \text{var} (D_{2} ) \\ & \quad + z_{2}^{2} \text{var} (\widehat{\sigma }_{t,2}^{{L_{2} }} - \widehat{\sigma }_{t - 1,2}^{{L_{2} }} )\, - \lambda^{2} \text{var} (q_{t,1} ) \\ & = \text{var} (D_{2} )\left[ {1 + \left( {2\frac{{L_{2} }}{p} + 2\left(\frac{{L_{2} }}{p}\right)^{2} } \right)(1 - \rho_{2}^{2} )} \right] \\ & \quad + z_{2}^{2} \text{var} (\widehat{\sigma }_{t,2}^{{L_{2} }} - \widehat{\sigma }_{t - 1,2}^{{L_{2} }} )\, - \lambda^{2} \text{var} (q_{t,1} ). \\ \end{aligned} $$

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Le, D.V., Huynh, L.T., Claudiu, K.V. et al. The impact of inventory sharing on the bullwhip effect in decentralized inventory systems. Logist. Res. 6, 89–98 (2013). https://doi.org/10.1007/s12159-012-0096-7

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