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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.

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