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Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
Bull whip effect
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Bull whip effect

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A brief explanation on Bullwhip effect. Presentation

A brief explanation on Bullwhip effect. Presentation

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  • 1. Bullwhip Effect and Risk Pooling Tokyo University of Marine Science and Technology Mikio Kubo
  • 2. Bullwhip effect• Key concept for understanding the SCM• Procter & Gamble noticed an interesting phenomenon that retail sales of the product were fairly uniform, but distributors’ orders placed to the factory fluctuated much more than retail sales.
  • 3. Why the bullwhip effect occurs? 1. Demand Forecasting• One day, the manager of a retailer observed a larger demand (sales) than expected.• He increased the inventory level because he expected more demand in the future (forecasting).• The manager of his wholesaler observed more demand (some of which are not actual demand) than usual and increased his inventory.• This caused more (non-real) demand to his maker; the manager of the maker increased his inventory, and so on. This is the basic reason of the bull whip effect.
  • 4. Why the bullwhip effect occurs? 2. Lead time• With longer lead times, a small change in the estimate of demand variability implies a significant change in safety stock, reorder level, and thus in order quantities.• Thus a longer lead time leads to an increase in variability and the bull whip effect.
  • 5. Why the bullwhip effect occurs? 3. Batch Ordering• When using a min-max inventory policy, then the wholesaler will observe a large order, followed by several periods of no orders, followed by another large order, and so on.• The wholesaler sees a distorted and highly variable pattern of orders.• Thus, batch ordering increases the bull whip effect.
  • 6. Why the bullwhip effect occurs? 4. Variability of Price• Retailers (or wholesalers or makers) offer promotions and discounts at certain times or for certain quantities.• Retailers (or customers) often attempt to stock up when prices are lower.• It increases the variability of demands and the bull whip effect.
  • 7. Why the bullwhip effect occurs?5. Lack of supply and supply allocation• When retailers suspect that a product will be in short supply, and therefore anticipate receiving supply proportional to the amount ordered (supply allocation).• When the period of shortage is over, the retailer goes back to its standard orders, leading to all kinds of distortions
  • 8. Quantifying the Bullwhip Effect One stage modelFor each period t=1,2…, let Retailer CustomerOrderingquantity q[t] Inventory I[t] Demand D[t]
  • 9. Discrete time model (Periodic ordering system) Lead time L Items ordered at the end of period t will arrive at the beginning of period t+L+1. 2) Demand D[t] occurs t t+1 t+2 t+3 t+41) Arrive the 3) Forecast demand F[t+1] items ordered 4) Order q[t] Arrive the itemsin period t-L-1 in period t+L+1 ( L=3)
  • 10. Demand process• d: a constant term of the demand process• ρ: a parameter that represents the correlation between two consecutive periods ρ  1 < ρ < 1) (−• ε t  = 1,2, ) : An error parameter in period t; it (t has an independent distribution with mean 0 and standard deviation σ• Dt: the demand in period t Dt = d + ρDt −1 + ε t
  • 11. An example of demand process d=80,ρ=0.5,ε[t]=[-10,10] =80+0.5*B2+(RAND()*(-20)+10) 250 需要量 D(t )=d +期 t ρ * D(t - 1 )+ε 2001 802 1 46.43491 073 1 66.2490253 1504 1 81 .9468235 200.6561 255 1006 21 0.03596447 202.0940006 508 200.3971 6979 1 93.98555510 1 94.6002961 0 3 5 7 9 1 15 19 25 27 33 37 39 13 17 23 29 35 11 21 41 31
  • 12. Ordering quantity q[t] • Forecasting ( p period moving average ) p ∑D j =1 t− j ˆ dt = p ˆWe denote d t and Dt by F [t ] and D[t ], respectively.     • Ordering quantity q[t] of period t is: q[t]=D[t]+L (F[t+1]-F[t]) ,t=1,2,…
  • 13. Inventory I[t]• Inventory flow conservation equation: Final inventory (period t)= Final inventory (period t-1)-Demand + Arrival Volume I[0]=A Safety Stock Level I[t] =I[t-1] –D[t] +q[t-L-1],t=1,2,…
  • 14. Excel Simulation (bull.xls) =E7-E6+B6 =(B5+B4+B3+B2)/4 =D6+1 =G5-B6+F3 =C6*2 リードタイム中の 発注量 在庫量 需要量 D(t )=d+ 移動平均法による 需要量予測 目標在庫レベル q(t )=y(t )- y(t - I(t )=I(t - 1 )-期 t ρ * D(t - 1 )+ε 予測 F(t ):p=4 F(t ) * :L, L=2 y(t )= F[t ]* L+ z *σ 1 )+D(t - 1 ) D(t )+q(t - 3)1 80 80 02 127.81847 80 03 144.8770316 80 04 152.9420471 80 3005 157.4258033 126.4093872 252.8187744 254.8187744 196.138705 222.57419676 151.3785902 145.765838 291.5316761 293.5316761 163.1586503 151.19560647 161.1899679 151.6558681 303.3117361 305.3117361 169.3464361 70.005638518 158.4760476 155.7341022 311.4682043 313.4682043 161.2430479 107.66829599 164.937867 157.1176023 314.2352046 316.2352046 168.6938988 105.889079210 156.4019926 158.9956182 317.9912364 319.9912364 158.9136938 118.8335227
  • 15. Demand, ordering quantity, and demand processes 350 300 250 200 需要量 D(t )=d+e * D(t - 1 )+e ps ilo n 1 50 発注量 q(t )=y(t )- y(t - 1 00 1 )+D(t - 1 ) 在庫量 I )=I - 1 )- (t (t 50 D(t )+q(t - 3) 0 5 9 13 17 29 25 33 37 1 21 41 - 50- 1 00
  • 16. Asymptotic analysis: expectation,variance, and Covariance) d E ( D[t ]) = By solving E[D]=d+ρE[D] 1− ρ σ 2 Var ( D[t ]) = By solving 1− ρ 2 Var[D]=ρ2 Var[D]+σ2 ρ σ p 2Cov ( D[t ], D[t − p ]) = 1− ρ 2
  • 17. Expansion of ordering quantityq[t ] = D[t ] + LF [t + 1] − LF [t ] p p L ∑ D[t + 1 − j ] L ∑ D[t − j ] j =1 j =1 = D[t ] + − p p L L = (1 + ) D[t ] − D[t − p ] p p
  • 18. Variance of ordering quantity L 2 L 2Var ( q[t ]) = (1 + ) Var ( D[t ]) + ( ) Var ( D[t − p ]) p p L L − 2(1 + )( )Cov ( D[t ], D[t − p ]) p p   2 L 2 L2   =  p + p 2 (1 − ρ ) Var ( D[t ]) 1 +  2      Var ( q[t ])  2 L 2 L2  =1+   p + 2 (1 − ρ ) 2  Var ( D[t ])  p 
  • 19. Observations Var (q[t ])  2 L 2 L2   = 1+  + 2  (1 − ρ ) 2 Var ( D[t ])  p p • When p is large, and L is small, the bullwhip effect due to forecasting error is negligible.• The bullwhip effect is magnified as we increase the lead time and decrease p.• A positive correlation DECRESES the bull whip effect.
  • 20. Coping with the Bullwhip Effect 1. Demand uncertainty• Adjust the forecasting parameters, e.g., larger p for the moving average method.• Centralizing demand information; by providing each stage of the supply chain with complete information on actual customer demand (POS: Point-Of- Sales data )• Continuous replenishment• VMI ( Vender Managed Inventory: VMI )
  • 21. Coping with the Bullwhip Effect 2. Lead time• Lead time reduction• Information lead time can be reduced ujsing EDI ( Electric Data Interchange ) or CAO ( Computer Assisted Ordering ) .• QR ( Quick Response ) in apparel industry
  • 22. Coping with the Bullwhip Effect 3. Batch ordering• Reduction of fixed ordering cost using EDI and CAO• 3PL ( Third Party Logistics )• VMI
  • 23. Coping with the Bullwhip Effect 4. Variability of Price• EDLP: Every Day Low Price ( P&G )• Remark that the same strategy does not work well in Japan.
  • 24. Coping with the Bullwhip Effect 5. Lack of supply and supply allocation• Allocate the lacking demand due to sales volume and/or market share instead of order volume. ( General Motors , Saturn, Hewlett-Packard )• Share the inventory and production information of makers with retailers and wholesalers. ( Hewlett- Packard , Motorola )

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