# UP

Uncertain Programming (UP) denotes optimization where some of the data are not exactly known at the time of computation. This data can be given as random variables or uncertainty sets. In the first case, specializes to Stochastic Programming (SP), in the second case to Robust Programming (RP).

# Uncertain Programming

**Coordination:**Prof. Dr. Jörg Rambau

**Contact:**Prof. Dr. Jörg Rambau

**Represented in MODUS since**2009/01

**Members with experience in this area:**

**The method "Uncertain Programming":**

## What is this?

Uncertain Programming (UP) denotes optimization problems where some of the data are not exactly known at the time of computation. This data can be given as random variables or uncertainty sets. In the first case, specializes to Stochastic Programming (SP), in the second case to Robust Programming (RP).

## What is it good for?

Models of UP are the right approach whenever the data for the optimization are volatile. Optimization based on point estimates of uncertain input data bears the risk that model-optimal feasible solutions may be more expensive in reality or even infeasible. Consider, for example, the problem of distributing apparel over a thousand branches. Whether or not a distribution is profitabble depends on the demand in the respective branches. Ignoring the demand variablility can result in very risky decisions. Moreover, for certain numerical decisions (like the application of heat, a chemical concentration, a velocity) it may be problematic to actually implement this decision without error. In order to better foresee the effects of uncertainty, the methods of Robust Programming (RP) and Stochastic Programming (SP) have been developed. SP handles uncertain data as random variables, RP specifies all possible values of uncertain data by uncertainty sets. While in the model-optimum SP and RP usually provide more expensive solutions (they tend to be conservative) than deterministic optimization models, the real-world performance of them is very often much better and closer to the model prediction.

## Where have we applied it?

The members of MODUS have applied this method for the following challenges:

- Optimal dispatching of pallet elevators in factories
- Optimal distribution of apparel among branches assorted by sizes
- Optimal inventory management in multi-echelon warehouse networks