SCperf (version 1.0)

bullwhip: bullwhip effect

Description

bullwhip computes the increase of the demand variability (the bullwhip effect) for a simple two-stage supply chains consisting of a single retailer and a single manufacturer using three forcasting methods: Minimum Mean Square Error (MMSE), Simple Moving Average (SMA) and Exponential Smoothing (ES) when the demand follows a known stationary AR(1) stochastic process.

Usage

bullwhip(method = c("MMSE", "SMA", "ES"), phi, L, p, alpha)

Arguments

method

character string specifing which method to use,

phi

a vector of autoregressive parameters,

L

a positive lead-time,

p

the order to be used in the SMA method,

alpha

smoothing factor to be used in the ES method (0 < alpha < 1).

Value

Details

The bullwhip effect is commonly defined as the ratio between the unconditional variance of the order process to that of the demand process, $Var(O_t)/Var(d_t)$. If this ratio is equal to one there is no variance amplification, while a ratio greater than one means that the bullwhip effect is present. On the other hand, a ratio less than one means that the orders are smoothed if compared with the demand.

References

Chen, F.; Drezner, Z.; Ryan, J. ; Simchi-Levi, D. (2000a) Quantifying the bullwhip effect in a simple supply chain: the impact of forecasting, lead times and information. Management Science, v.46, n.3, p. 436-443.

Silva Marchena, M. (2010) Measuring and implementing the bullwhip effect under a generalized demand process. http://arxiv.org/abs/1009.397 Zhang, X. (2004a) The impact of forecasting methods on the bullwhip effect, International Journal of Production Economics.l, v.88, n.1, p. 15-27.

See Also

SCperf

Examples

bullwhip("SMA",0.9,2,4)

bullwhip("ES",0.9,2,0,0.6)

bullwhip("MMSE",0.9,2)