Supply Chain Perform

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Description

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

Usage

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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).

Details

The bullwhip effect for a stationary ARMA(p,q) demand process is defined as:

M

where the ψ-weights solve the equations ψ(z)θ(z)=φ(z). If M=1 there is no variance amplification, while M>1 means that the bullwhip effect is present. On the other hand, M<1 means that the orders are smoothed if compared with the demand.

Two safety stock measures are presented as well: SS and SSL=z√{VarDL}. SSL is calculated using an estimate of the standard deviation of L periods forecast error √{VarDL} where \hat{D}_t^L is an estimate of the mean demand over L periods after period t.

Value

SCperf() 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.

Author(s)

Marlene Silva Marchena marchenamarlene@gmail.com

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

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#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)