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Duration: | August 2012 - May 2015 |
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Project heads: | Yann Disser Britta Peis Sebastian Stiller Rolf H. Möhring Martin Skutella |

Researchers: | Wiebke Höhn, Alexander Richter |

Cooperation partner: | 4flow AG |

Official website: | www.robunet.de |

Support: | Europäischer Fonds für Regionale Entwicklung (EFRE) Investitionsbank Berlin (IBB) |

## Background and motivation

Facility location decisions belong to the most important cost drivers in the design of modern logistics networks. Moreover these longterm investments determine the framework for finding cost efficient solutions in tactical and operational planning. This close interrelation between operational cost and longterm investments makes an integrated planning of both aspects desirable.

This integrated approach is even more complex due to the disparate time horizons of both planning aspects. From mathematical point of view, this belongs to the realm of optimizing over scenarios, since the scenario of demands is unknown at the time of investments and the investments have to be convenient for many scenarios. E.g., fluctuations of fuel prices or differing developments of labor costs in different regions constitute relevant uncertainties in designing logistic networks.

In practice it is common to firstly ignore uncertainties in input data and to react a-postiori to changes. It has been shown that with this practice already small fluctuations can lead to much worse results as opposed to a robust optimization, a modelling technique that considers the possible range of fluctuations in input data a priori. A large gap between the actual state of research and the logistic practice has to be closed here. On the other hand, it is essential to the research of robust optimization to understand which kinds of uncertainties appear in practice.

The goal of RobuNet is to develop solutions techniques that are tailored for the use in large scale logistics networks, which requires to link actual mathematical research with practical expertise.

## Research program

The main research focus is on facility location decisions in logistics networks which lie at the intersection of the classical research fields of network flow, covering and packing problems. Moreover they are affected by planning uncertainties and have to be considered in very large networks which requires efficient algorithms in the mathematical sense. To address the whole range of the problem we chose a stepwise approach, that is in each step we disregard a single aspect of the problem. Especially when dealing with uncertainties a profound understanding of the deterministic version is required as a starting point. A more detailed outline of the research program is listed below.

**Modelling**

- Analysis of uncertainties, network structures, and the decision and information model
- Identification of relevant optimization potential
- Development of mathematical models

**Deterministic facility location in logistics networks**

- Mathematical problem structure
- Development and analysis of efficient algorithms for facility location decisions with consolidated routing
- Development of methods for problem specific network separation

**Optimizing over scenarios**

- Mathematical foundation for logistics networks with uncertainties
- Stochastic optimization models
- Robust optimization models

**Non-standard decision-and-information models**

- Increase of network robustness against strong singular fluctuations
- Development and analysis of reoptimization techniques
- Development and analysis of methods for incremental location decisions

**Evaluation on real-world instances and implementation of a demonstrator**

- Case studies for the evaluation of the different approaches for robust optimization
- Implementation of functionalities for analysis and visualization
- Evaluation of practicability
- Compilation of a toolbox for robust planning in logistics

### References

**Liebchen, Christian and Lübbecke, Marco E and Möhring, Rolf H and Stiller, Sebastian**.

**The Concept of Recoverable Robustness, Linear Programming Recovery, and Railway Applications**.

In **Ravindra K. Ahuja and Rolf H. Möhring and Christos D. Zaroliagis (ed.)**, *Robust and Online Large-Scale Optimization: Models and Techniques for Transportation Systems*, pp. 1-27, Springer, 2009.

**Köhler, Ekkehard and Möhring, Rolf H. and Skutella, Martin**.

**Traffic networks and flows over time**.

In **Lerner, Jürgen and Wagner, Dorothea and Zweig, Katharina A. (ed.)**, *Algorithmics of Large and Complex Networks: Design, Analysis, and Simulation*, pp. 166–196, Springer, 2009.

**Hall, Alex and Hippler, Steffen and Skutella, Martin**.

**Multicommodity Flows Over Time: Efficient Algorithms and Complexity**.

*Theoretical Computer Science*, Vol. 379, pp. 387–404, 2007.

**Althaus, Ernst and Funke, Stefan and Har-Peled, Sariel and Könemann, Jochen and Ramos, Edgar A. and Skutella, Martin**.

**Approximating k-Hop Minimum-Spanning Trees**.

*Operations Research Letters*, Vol. 33, pp. 115–120, 2005.