# 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

 1 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

bullwhip

### Examples

 1 2 3 4 5 6 7 #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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