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Currently available wearables are usually based on a single sensor node with integrated capabilities for classifying different activities. The next generation of cooperative wearables could be able to identify not only activities, but also to evaluate them qualitatively using the data of several sensor nodes attached to the body, to provide detailed feedback for the improvement of the execution. Especially within the application domains of sports and health-care, such immediate feedback to the execution of body movements is crucial for (re-) learning and improving motor skills. To enable such systems for a broad range of activities, generalized approaches for human motion assessment within sensor networks are required. In this paper, we present a generalized trainable activity assessment chain (AAC) for the online assessment of periodic human activity within a wireless body area network. AAC evaluates the execution of separate movements of a prior trained activity on a fine-grained quality scale. We connect qualitative assessment with human knowledge by projecting the AAC on the hierarchical decomposition of motion performed by the human body as well as establishing the assessment on a kinematic evaluation of biomechanically distinct motion fragments. We evaluate AAC in a real-world setting and show that AAC successfully delimits the movements of correctly performed activity from faulty executions and provides detailed reasons for the activity assessment.
Merchants on modern e-commerce platforms face a highly competitive environment. They compete against each other using automated dynamic pricing and ordering strategies. Successfully managing both inventory levels as well as offer prices is a challenging task as (i) demand is uncertain, (ii) competitors strategically interact, and (iii) optimized pricing and ordering decisions are mutually dependent. We show how to derive optimized data-driven pricing and ordering strategies which are based on demand learning techniques and efficient dynamic optimization models. We verify the superior performance of our self-adaptive strategies by comparing them to different rule-based as well as data-driven strategies in duopoly and oligopoly settings. Further, to study and to optimize joint dynamic ordering and pricing strategies on online marketplaces, we built an interactive simulation platform. To be both flexible and scalable, the platform has a microservice-based architecture and allows handling dozens of competing merchants and streams of consumers with configurable characteristics.
Online markets have become highly dynamic and competitive. Many sellers use automated data-driven strategies to estimate demand and to update prices frequently. Further, notification services offered by marketplaces allow to continuously track markets and to react to competitors’ price adjustments instantaneously. To derive successful automated repricing strategies is challenging as competitors’ strategies are typically not known. In this paper, we analyze automated repricing strategies with data-driven price anticipations under duopoly competition. In addition, we account for reference price effects in demand, which are affected by the price adjustments of both competitors. We show how to derive optimized self-adaptive pricing strategies that anticipate price reactions of the competitor and take the evolution of the reference price into account. We verify that the results of our adaptive learning strategy tend to optimal solutions, which can be derived for scenarios with full information. Finally, we analyze the case in which our learning strategy is played against itself. We find that our self-adaptive strategies can be used to approximate equilibria in mixed strategies.
Circular economy
(2021)
In a circular economy, the use of recycled resources in production is a key performance indicator for management. Yet, academic studies are still unable to inform managers on appropriate recycling and pricing policies. We develop an optimal control model integrating a firm's recycling rate, which can use both virgin and recycled resources in the production process. Our model accounts for recycling influence both at the supply- and demandsides. The positive effect of a firm's use of recycled resources diminishes over time but may increase through investments. Using general formulations for demand and cost, we analytically examine joint dynamic pricing and recycling investment policies in order to determine their optimal interplay over time. We provide numerical experiments to assess the existence of a steady-state and to calculate sensitivity analyses with respect to various model parameters. The analysis shows how to dynamically adapt jointly optimized controls to reach sustainability in the production process. Our results pave the way to sounder sustainable practices for firms operating within a circular economy.
Most sales applications are characterized by competition and limited demand information. For successful pricing strategies, frequent price adjustments as well as anticipation of market dynamics are crucial. Both effects are challenging as competitive markets are complex and computations of optimized pricing adjustments can be time-consuming. We analyze stochastic dynamic pricing models under oligopoly competition for the sale of perishable goods. To circumvent the curse of dimensionality, we propose a heuristic approach to efficiently compute price adjustments. To demonstrate our strategy’s applicability even if the number of competitors is large and their strategies are unknown, we consider different competitive settings in which competitors frequently and strategically adjust their prices. For all settings, we verify that our heuristic strategy yields promising results. We compare the performance of our heuristic against upper bounds, which are obtained by optimal strategies that take advantage of perfect price anticipations. We find that price adjustment frequencies can have a larger impact on expected profits than price anticipations. Finally, our approach has been applied on Amazon for the sale of used books. We have used a seller’s historical market data to calibrate our model. Sales results show that our data-driven strategy outperforms the rule-based strategy of an experienced seller by a profit increase of more than 20%.
In many revenue management applications risk-averse decision-making is crucial. In dynamic settings, however, it is challenging to find the right balance between maximizing expected rewards and minimizing various kinds of risk. In existing approaches utility functions, chance constraints, or (conditional) value at risk considerations are used to influence the distribution of rewards in a preferred way. Nevertheless, common techniques are not flexible enough and typically numerically complex. In our model, we exploit the fact that a distribution is characterized by its mean and higher moments. We present a multi-valued dynamic programming heuristic to compute risk-sensitive feedback policies that are able to directly control the moments of future rewards. Our approach is based on recursive formulations of higher moments and does not require an extension of the state space. Finally, we propose a self-tuning algorithm, which allows to identify feedback policies that approximate predetermined (risk-sensitive) target distributions. We illustrate the effectiveness and the flexibility of our approach for different dynamic pricing scenarios. (C) 2020 Elsevier Ltd. All rights reserved.
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 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.
In dynamic decision problems, it is challenging to find the right balance between maximizing expected rewards and minimizing risks. In this paper, we consider NP-hard mean-variance (MV) optimization problems in Markov decision processes with a finite time horizon. We present a heuristic approach to solve MV problems, which is based on state-dependent risk aversion and efficient dynamic programming techniques. Our approach can also be applied to mean-semivariance (MSV) problems, which particularly focus on the downside risk. We demonstrate the applicability and the effectiveness of our heuristic for dynamic pricing applications. Using reproducible examples, we show that our approach outperforms existing state-of-the-art benchmark models for MV and MSV problems while also providing competitive runtimes. Further, compared to models based on constant risk levels, we find that state-dependent risk aversion allows to more effectively intervene in case sales processes deviate from their planned paths. Our concepts are domain independent, easy to implement and of low computational complexity.
We examine a special class of dynamic pricing and advertising models for the sale of perishable goods, including marginal unit costs and inventory holding costs. The time horizon is assumed to be finite and we allow several model parameters to be dependent on time. For the stochastic version of the model, we derive closed-form expressions of the value function as well as of the optimal pricing and advertising policy in feedback form. Moreover, we show that for small unit shares, the model converges to a deterministic version of the problem, whose explicit solution is characterized by an overage and an underage case. We quantify the close relationship between the open-loop solution of the deterministic model and the expected evolution of optimally controlled stochastic sales processes. For both models, we derive sensitivity results. We find that in the case of positive holding costs, on average, optimal prices increase in time and advertising rates decrease. Furthermore, we analytically verify the excellent quality of optimal feedback policies of deterministic models applied in stochastic models. (C) 2015 Elsevier B.V. All rights reserved.