# POM Prof. Tempelmeier GmbH

## Production and Operations Management Consulting.

# Lot sizing with random demand: Static 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 both the production periods and the lot sizes in advance**
and execute the complete production plan independently from the realization of
the demands. This approach is known as the Static 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 |

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

The "Optimise" menu item starts the calculation of the optimum production plan.

You can also define a production plan by entering "1" in the column "Production". In this case the "Compute" button starts the calculation of the optimum lot sizes given the production periods set in column "Production".

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