Exact reoptimisation under gradual look-ahead for operational control in production and logistics

Abstract

In decision making, information about the future typically comes in different uncertainty degrees. For the near-future, information is often assumed as deterministic; online optimisation with look-ahead deals with such situations. The more distant future, contrarily, is usually afflicted with uncertainty. The farther in the future, the more pronounced the degree of uncertainty; online optimisation with gradual look-ahead considers such forecasting information. Operational tasks in production and logistics are often coined by mixtures of these information types. We propose a methodology based on mathematical programming (MP) which combines information horizons for the near and more distant future to solve online optimisation problems with gradual look-ahead by exact reoptimisation. To this end, we investigate how MP formulations for offline problems are transferred to the online case by adapting them to gradual look-ahead information. Further, we employ a sampling-based robustification to account for long-term uncertainty. In numerical experiments on online versions of combinatorial problems which lie at the heart of many operational problems from production and logistics (packing, routing, lot sizing, scheduling), we illustrate how the methodology can be applied in practice. Moreover, the analysis allows to establish a sample-based look-ahead and forecasting value indicating the benefit of improving forecasting capabilities.

Keywords:

• Online optimisation
• gradual look-ahead
• mathematical programming
• production and logistics

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data supporting the findings of this study can be generated and reproduced programmatically through executing the source code of the Java program. The source code can be downloaded from our website: https://dol.ior.kit.edu/english/Downloads.php.

Additional information

Funding

This work was partly supported by grant DU 1755/1-1 (project no. 354864080) of the German Research Foundation (DFG). This support is gratefully acknowledged.

Notes on contributors

Fabian Dunke

Fabian Dunke is a researcher at the Institute of Operations Research of Karlsruhe Institute of Technology (Germany). His main research interest lies in the combination of optimization methods (e.g., mathematical programming, meta-heuristics) with specialized analytical tools (e.g., discrete event simulation, artificial neural networks) to support decision making in time-dynamic applications coined by a high degree of uncertainty such as online settings with look-ahead information.

Stefan Nickel

Stefan Nickel is a full professor at the Karlsruhe Institute of Technology (Germany) and one of the directors of the Institute of Operations Research. He additionally holds the positions of one of the directors of the Karlsruhe Service Research Institute (KSRI) and of the Research Center for Computer Science (FZI). His research interests are in the fields of supply chain analytics, intralogistics and production, health care, transportation, mobility and next generation logistics.