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In many businesses, firms are selling different types of products, which share mutual substitution effects in demand. To compute effective pricing strategies is challenging as the sales probabilities of each of a firm's products can also be affected by the prices of potential substitutes. In this paper, we analyze stochastic dynamic multi-product pricing models for the sale of perishable goods. To circumvent the limitations of time-consuming optimal solutions for highly complex models, we propose different relaxation techniques, which allow to reduce the size of critical model components, such as the state space, the action space, or the set of potential sales events. Our heuristics are able to decrease the size of those components by forming corresponding clusters and using subsets of representative elements. Using numerical examples, we verify that our heuristics make it possible to dramatically reduce the computation time while still obtaining close-to-optimal expected profits. Further, we show that our heuristics are (i) flexible, (ii) scalable, and (iii) can be arbitrarily combined in a mutually supportive way.
Bidirectional order dependencies (bODs) capture order relationships between lists of attributes in a relational table. They can express that, for example, sorting books by publication date in ascending order also sorts them by age in descending order. The knowledge about order relationships is useful for many data management tasks, such as query optimization, data cleaning, or consistency checking. Because the bODs of a specific dataset are usually not explicitly given, they need to be discovered. The discovery of all minimal bODs (in set-based canonical form) is a task with exponential complexity in the number of attributes, though, which is why existing bOD discovery algorithms cannot process datasets of practically relevant size in a reasonable time. In this paper, we propose the distributed bOD discovery algorithm DISTOD, whose execution time scales with the available hardware. DISTOD is a scalable, robust, and elastic bOD discovery approach that combines efficient pruning techniques for bOD candidates in set-based canonical form with a novel, reactive, and distributed search strategy. Our evaluation on various datasets shows that DISTOD outperforms both single-threaded and distributed state-of-the-art bOD discovery algorithms by up to orders of magnitude; it can, in particular, process much larger datasets.