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Linwei Xin (linwei.xinchicagobooth.edu) Abstract: Demand forecasting plays an important role in many inventory control problems. To mitigate the potential harms of model misspecification in this context, various forms of distributionally robust optimization have been applied. Although many of these methodologies suffer from the problem of timeinconsistency, the work of Klabjan, SimchiLevi and Song [85] established a general timeconsistent framework for such problems by connecting to the literature on robust Markov decision processes. Motivated by the fact that many forecasting models exhibit very special structure, as well as a desire to understand the impact of positing different dependency structures, in this paper we formulate and solve a timeconsistent distributionally robust multistage newsvendor model which naturally unifies and robustifies several inventory models with demand forecasting. In particular, many simple models of demand forecasting have the feature that demand evolves as a martingale (i.e. expected demand tomorrow equals realized demand today). We consider a robust variant of such models, in which the sequence of future demands may be any martingale with given mean and support. Under such a model, past realizations of demand are naturally incorporated into the structure of the uncertainty set going forwards. We explicitly compute the minimax optimal policy (and worstcase distribution) in closed form, by combining ideas from convex analysis, probability, and dynamic programming. We prove that at optimality the worstcase demand distribution corresponds to the setting in which inventory may become obsolete at a random time, a scenario of practical interest. To gain further insight, we prove weak convergence (as the time horizon grows large) to a simple and intuitive process. We also compare to the analogous setting in which demand is independent across periods (analyzed previously in Shapiro [119]), and identify interesting differences between these models, in the spirit of the price of correlations studied in Agrawal et al. [2]. Finally, we complement our theoretical results by providing a targeted and concise numerical experiment further demonstrating the benefits of our model. Keywords: inventory control, distributionally robust optimization, martingale, dynamic programming, robust Markov decision process, demand forecasting Category 1: Robust Optimization Category 2: Applications  OR and Management Sciences Category 3: Stochastic Programming Citation: Submitted for publication Download: [PDF] Entry Submitted: 11/30/2015 Modify/Update this entry  
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