# POM Prof. Tempelmeier GmbH

## Production and Operations Management Consulting.

# Inventory management: (s,q) inventory policy with normally-distributed period demand

A (s,q) inventory policy for a product with normal-distributed demand per period and a fixed lead time is computed. In the standard version, continuous review is assumed. In this case, an iterative algorithm for finding the optimal values of s and q is applied. Alternatively, reviewing the inventory position at the end of each period (e.g. a day) while maintaining a fixed-quantity q [opposite to the (s,S) policy] is assumed. In this case the expectation and variance of the undershoot variable is computed and integrated into the computation of s.

Symbols:

E{D} | expected demand per period |

E{L} | lead time |

E{Y} | expected demand during lead time |

V{Y} | variance of the demand during lead time |

E{Y*} | expected value of the sum of the demand during lead time and the undershoot |

V{Y*} | variance of the sum of the demand during lead time and the undershoot |

E{U} | expected undershoot |

V{U} | variance of the undershoot |

P{.} | probability |

s | reorder point |

q | order size |

Assumptions:

- normal-distributed demand
- ß-service level
- backorders, no lost sales

After computation of the optimal values of s and q these values are transfered to the simulation module.

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- Tempelmeier (2011)