SCperf (version 1.0)

SCperf: Supply Chain Perform

Description

SCperf computes the bullwhip effect for an stationary ARMA(p,q) demand process and other supply chain performance variables.

Usage

SCperf(phi, theta, L = L, SL = 0.95)

Arguments

phi

a vector of autoregressive parameters,

theta

a vector of moving-average parameters,

L

positive lead-time,

SL

service level, (default:0.95).

Value

returns a list containing:

M

measure for the bullwhip effect,

VarD

variance of the demand,

VarDL

variance of forecasting error for lead-time demand,

SS

safety stock calculated using the standard deviation of the demand,

SSL

safety stock calculated using the standard deviation of L periods forecast error,

z

safety factor.

Details

The bullwhip effect for a stationary ARMA(p,q) demand process is defined as: $$M=\frac{1+2\sum_{i=0}^L\sum_{j=i+1}^L\psi_i\psi_j}{\sum_{j=0}^\infty\psi_j^2}$$ where the $\psi$-weights solve the equations $\psi(z)\theta(z)=\phi(z)$. If $M=1$ there is no variance amplification, while $M>1$ means that the bullwhip effect is present. On the other hand, $M

References

Zhang, X. (2004b). Evolution of ARMA demand in supply chains. Manufacturing and Services Operations Management, 6 (2), 195-198.

Silva Marchena, M. (2010) Measuring and implementing the bullwhip effect under a generalized demand process. http://arxiv.org/abs/1009.3977

See Also

bullwhip

Examples

#ARMA(1,1) case,

SCperf(phi=0.95,theta=0.1,L=2,SL=0.99)

#AR(2) case,

SCperf(phi=c(0.8,-0.2),theta=0,L=1)