# 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

### See Also

`bullwhip`

### Examples

1 2 3 4 5 6 7 |