Integrating uncertainties into the optimization process is crucial to obtain solutions suitable for practical needs. In particular, the considered uncertainty set has a huge impact on the quality of the computed solutions. In this paper, we consider a storage loading problem in which a set of items must be loaded into a partly filled storage area, regarding stacking constraints and taking into account stochastic data of items arriving later. We propose a robust optimization approach dealing with the stochastic uncertainty. With a focus on constructing the uncertainty set, we offer a rule-based scenario generation approach to derive such a set from the stochastic data. To evaluate the robustness of stacking solutions, we introduce the concept of a security level, which is the probability that a stacking solution is feasible when the data of the uncertain items are realized. Computational results for randomly generated problem instances are presented showing the impact of various factors on the trade-off between robustness and cost of the stacking solutions.
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The authors would like to thank two anonymous referees for their constructive comments. This work was partially supported by the Deutsche Forschungsgemeinschaft (DFG, Germany) under Grant Number GRK 1916/1, and the National Foundation for Science and Technology Development (NAFOSTED, Vietnam) under Grant Number 101.01-2017.315.
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