  


Distributionally Robust Newsvendor Problems with Variation Distance
Hamed Rahimian(rahimian.1osu.edu) Abstract: We use distributionally robust stochastic programs (DRSPs) to model a general class of newsvendor problems where the underlying demand distribution is unknown, and so the goal is to find an order quantity that minimizes the worstcase expected cost among an ambiguity set of distributions. The ambiguity set consists of those distributions that are not farin the sense of the socalled variation distancefrom a nominal distribution. The maximum distance allowed in the ambiguity set (called level of robustness) places the DRSP between the ``classical" stochastic programming and robust optimization models, which correspond to setting the level of robustness to zero and infinity, respectively. The structure of the newsvendor problem allows us to analyze the problem from multiple perspectives: First, we derive explicit formulas and properties of the optimal solution as a function of the level of robustness. Moreover, we determine the regions of demand that are critical (in a precise sense) to optimal cost from the viewpoint of a riskaverse decision maker. Finally, we establish quantitative relationships between the distributionally robust model and the corresponding riskneutral and classical robust optimization models, which include the price of optimism/pessimism, and the nominal/worst case regrets, among others. Our analyses can help the decision maker better understand the role of demand uncertainty in the problem and can guide him/her to choose an appropriate level of robustness. We illustrate our results with numerical experiments on a variety of newsvendor problems with different characteristics. Keywords: stochastic programs; distributionally robust optimization; newsvendor problems Category 1: Stochastic Programming Citation: Manuscript, submitted for publication. Download: [PDF] Entry Submitted: 03/31/2017 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  