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In this paper, we analyze stochastic dynamic pricing and advertising differential games in special oligopoly markets with constant price and advertising elasticity. We consider the sale of perishable as well as durable goods and include adoption effects in the demand. Based on a unique stochastic feedback Nash equilibrium, we derive closed-form solution formulas of the value functions and the optimal feedback policies of all competing firms. Efficient simulation techniques are used to evaluate optimally controlled sales processes over time. This way, the evolution of optimal controls as well as the firms’ profit distributions are analyzed. Moreover, we are able to compare feedback solutions of the stochastic model with its deterministic counterpart. We show that the market power of the competing firms is exactly the same as in the deterministic version of the model. Further, we discover two fundamental effects that determine the relation between both models. First, the volatility in demand results in a decline of expected profits compared to the deterministic model. Second, we find that saturation effects in demand have an opposite character. We show that the second effect can be strong enough to either exactly balance or even overcompensate the first one. As a result we are able to identify cases in which feedback solutions of the deterministic model provide useful approximations of solutions of the stochastic model.
In discrete manufacturing, the knowledge about causal relationships makes it possible to avoid unforeseen production downtimes by identifying their root causes. Learning causal structures from real-world settings remains challenging due to high-dimensional data, a mix of discrete and continuous variables, and requirements for preprocessing log data under the causal perspective. In our work, we address these challenges proposing a process for causal reasoning based on raw machine log data from production monitoring. Within this process, we define a set of transformation rules to extract independent and identically distributed observations. Further, we incorporate a variable selection step to handle high-dimensionality and a discretization step to include continuous variables. We enrich a commonly used causal structure learning algorithm with domain-related orientation rules, which provides a basis for causal reasoning. We demonstrate the process on a real-world dataset from a globally operating precision mechanical engineering company. The dataset contains over 40 million log data entries from production monitoring of a single machine. In this context, we determine the causal structures embedded in operational processes. Further, we examine causal effects to support machine operators in avoiding unforeseen production stops, i.e., by detaining machine operators from drawing false conclusions on impacting factors of unforeseen production stops based on experience.
Workload-Driven Fragment Allocation for Partially Replicated Databases Using Linear Programming
(2019)
In replication schemes, replica nodes can process read-only queries on snapshots of the master node without violating transactional consistency. By analyzing the workload, we can identify query access patterns and replicate data depending to its access frequency. In this paper, we define a linear programming (LP) model to calculate the set of partial replicas with the lowest overall memory capacity while evenly balancing the query load. Furthermore, we propose a scalable decomposition heuristic to calculate solutions for larger problem sizes. While guaranteeing the same performance as state-of-the-art heuristics, our decomposition approach calculates allocations with up to 23% lower memory footprint for the TPC-H benchmark.