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A brief explanation on Bullwhip effect. Presentation

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  • 1. Bullwhip Effect and Risk Pooling Tokyo University ofMarine Science and Technology Mikio Kubo

2. Bullwhip effect Key concept for understanding the SCM Procter & Gamble noticed an interestingphenomenon that retail sales of theproduct were fairly uniform, butdistributors orders placed to the factoryfluctuated much more than retail sales. 3. Why the bullwhip effect occurs? Demand Forecasting One day, the manager of a retailer observed alarger demand (sales) than expected. He increased the inventory level because heexpected more demand in the future (forecasting). The manager of his wholesaler observed moredemand (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 bullwhip effect. 4. Why the bullwhip effect occurs? Lead time With longer lead times, a small changein the estimate of demand variabilityimplies a significant change in safetystock, reorder level, and thus in orderquantities. Thus a longer lead time leads to anincrease in variability and the bull whipeffect. 5. Why the bullwhip effect occurs? Batch Ordering When using a min-max inventory policy, thenthe 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 highlyvariable pattern of orders. Thus, batch ordering increases the bull whipeffect. 6. Why the bullwhip effect occurs? Variability of Price Retailers (or wholesalers or makers)offer promotions and discounts atcertain times or for certain quantities. Retailers (or customers) often attemptto stock up when prices are lower. It increases the variability of demands andthe bull whip effect. 7. Why the bullwhip effect occurs? Lack of supply and supplyallocation When retailers suspect that a productwill be in short supply, and thereforeanticipate receiving supply proportionalto the amount ordered (supplyallocation). When the period of shortage is over,the retailer goes back to its standardorders, leading to all kinds of distortions 8. Quantifying the BullwhipEffectOne stage modelFor each period t=1,2, let RetailerCustomerOrderingquantity 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)DemandD[t] occurstt+1t+2t+3t+4 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 : a parameter that represents the correlationbetween two consecutive periods 1 < < 1) ( t = 1,2, ) : An error parameter in period t; it(thas an independent distribution with mean 0 andstandard deviation Dt: the demand in period tDt = d + Dt 1 + t 11. An example of demand processd=80,=0.5,[t]=[-10,10] =80+0.5*B2+(RAND()*(-20)+10) 250 D(t )=d + t * D(t - 1 )+ 2001 8021 46.43491 0731 66.249025315041 81 .9468235200.6561 255100621 0.03596447202.0940006 508200.3971 69791 93.98555510 1 94.6002961 035791 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 pDj =1 t j dt =pWe 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 ArrivalVolumeI[0]=A Safety Stock LevelI[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 D(t )=d+ q(t )=y(t )- y(t - I(t )=I(t - 1 )- t * D(t - 1 )+ F(t ):p=4 F(t ) * :L, L=2 y(t )= F[t ]* L+ z * 1 )+D(t - 1 )D(t )+q(t - 3)1 808002 127.81847 8003144.87703168004152.9420471803005157.4258033 126.4093872252.8187744254.8187744 196.138705 222.57419676151.3785902145.765838291.5316761293.5316761 163.1586503151.19560647161.1899679 151.6558681303.3117361305.3117361 169.346436170.005638518158.4760476 155.7341022311.4682043313.4682043 161.2430479107.66829599164.937867157.1176023314.2352046316.2352046 168.6938988105.889079210 156.4019926 158.9956182317.9912364319.9912364 158.9136938118.8335227 15. Demand, ordering quantity, anddemand processes 350 300 250 200 D(t )=d+e * D(t - 1 )+e ps ilo n 1 50 q(t )=y(t )- y(t - 1 001 )+D(t - 1 ) I )=I - 1 )- (t (t50 D(t )+q(t - 3)0 5 9 1317 292533 37 1 2141 - 50- 1 00 16. Asymptotic analysis:expectation,variance, and Covariance)dE ( D[t ]) = By solving E[D]=d+E[D] 1 2 Var ( D[t ]) =By solving1 2Var[D]=2 Var[D]+2 p 2Cov ( D[t ], D[t p ]) =1 2 17. Expansion of ordering quantityq[t ] = D[t ] + LF [t + 1] LF [t ] ppL 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 quantityL 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 ) Var ( D[t ]) 1 + 2 Var ( q[t ]) 2 L 2 L2 =1+ p+ 2 (1 ) 2 Var ( D[t ]) p 19. Observations Var (q[t ]) 2 L 2 L2 = 1+ + 2 (1 ) 2 Var ( D[t ]) pp When p is large, and L is small, the bullwhipeffect due to forecasting error is negligible. The bullwhip effect is magnified as we increasethe lead time and decrease p. A positive correlation DECRESES the bullwhip effect. 20. Coping with the Bullwhip Effect Demand uncertainty Adjust the forecasting parameters, e.g.,larger p for the moving average method. Centralizing demand information; byproviding each stage of the supplychain with complete information onactual customer demand (POS: Point-Of-Sales data Continuous replenishment VMI Vender Managed Inventory:VMI 21. Coping with the Bullwhip Effect Lead time Lead time reduction Information lead time can be reduced ujsingEDI Electric Data Interchange orCAO Computer Assisted Ordering . QR Quick Response in apparelindustry 22. Coping with the Bullwhip Effect Batch ordering Reduction of fixed ordering cost using EDIand CAO 3PL Third Party Logistics VMI 23. Coping with the Bullwhip Effect Variability of Price EDLP: Every Day Low Price P&G Remark that the same strategy does notwork well in Japan. 24. Coping with the Bullwhip Effect Lack of supply and supplyallocation Allocate the lacking demand due to salesvolume and/or market share instead of ordervolume. General Motors Saturn,Hewlett-Packard Share the inventory and productioninformation of makers with retailers andwholesalers. Hewlett-Packard Motorola