SCperf: Supply Chain Perform

Description Usage Arguments Details Value Author(s) References See Also Examples

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)


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