# POM Prof. Tempelmeier GmbH

## Production and Operations Management Consulting.

# Lot sizing with random demand: Static-Dynamic Uncertainty Strategy

We consider a product with dynamic period demands, which are normally-distributed with period-specific means and standard deviations.
As a means to handle the randomness and the dynamics of the demand over time,
there are several alternative response strategies available, which define rules with
respect to the timing and sizing of production. One option is to **fix the production periods and order-up-to levels advance**. Then, in a production period, the actual production quantity is calculated as the difference of the order-up-to level S(t) and the available inventory. This leads to variable (random) production quantities. This approach is known as the Static-Dynamic Uncertainty Strategy. For this strategy, the optimum dynamic lot sizes which are required to met a target cycle fillrate are calculated.

Symbols:

t | index of periods |

E{D} | expected demand |

Std.-Dev | standard deviation |

D(t) | demand in period t |

Y(t) | cumulated demand from period 0 to period t |

S(t) | order-up-to level in period t |

Ip | physical inventory at the end of period t (stock on hand) |

F | cumulated backorders in th current production cycle (starting with the latest production period) |

ß(cyc) | cycle fill rate = 1 - (backorders in current cycle)/(demand in current cycle) |

Assumptions:

- planning horizon with t periods
- normally-distributed demands
- cycle fill rate

- Tempelmeier, Horst, Inventory Management in Supply Networks - Problems, Models, Solution, Norderstedt(Books on Demand) 2011, ISBN 978-3-8423-4677-2