Bullwhip effectKey concept for understanding the SCMProcter & 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.
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.
Why the bullwhip effect occurs?２． Lead timeWith 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.
Why the bullwhip effect occurs?３． Batch OrderingWhen 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.
Why the bullwhip effect occurs?４． Variability of PriceRetailers (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.
Why the bullwhip effect occurs?５． Lack of supply and supplyallocation 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 and variations
Quantifying the BullwhipEffectOne stage modelFor each period t=1,2…, let Retailer CustomerOrderingquantity q[t] Inventory I[t] Demand D[t]
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)
Demand process d: a constant term of the demand process ρ: a parameter that represents the correlation between two consecutive periods : An error parameter in period t; it has an independent distribution with mean 0 and standard deviation σ Dt: the demand in period t ρ 1 < ρ < 1) (− ε t = 1,2,) (t Dt = d + ρDt −1 + ε t
Ordering quantity q[t] Forecasting （ p period moving average ） p ∑D j =1 t− j ˆ dt = p denote ˆWe 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,…
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
Expansion of ordering quantity q[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
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
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.
Coping with the Bullwhip Effect１． 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 ）
Coping with the Bullwhip Effect２． Lead timeLead time reductionInformation lead time can be reduced ujsing EDI （ Electric Data Interchange ） or CAO （ Computer Assisted Ordering ） .QR （ Quick Response ） in apparel industry
Coping with the Bullwhip Effect３． Batch orderingReduction of fixed ordering cost using EDI and CAO3PL （ Third Party Logistics ）VMI
Coping with the Bullwhip Effect４． Variability of PriceEDLP: Every Day Low Price （ P&G ）Remark that the same strategy does not work well in Japan.
Coping with the Bullwhip Effect５． 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 ）