Consider the newsvendor model, but under the assumption that the underlying demand distribution is not known as part of the input. Instead, the only information available is a random, independent sample drawn from the demand distribution. This paper analyzes the sample average approximation (SAA) approach for the data-driven newsvendor problem. We obtain a new analytical bound on the probability that the relative regret of the SAA solution exceeds a threshold. This bound is significantly tighter than existing bounds, and it matches the empirical accuracy of the SAA solution observed in extensive computational experiments.This bound reveals that the demand distribution's weighted mean spread (WMS) affects the accuracy of the SAA heuristic.

Expected utility models in portfolio optimization is based on the assumption of complete knowledge of the distribution of random returns. In this paper, we relax this assumption to the knowledge of only the mean, covariance and support information. No additional assumption on the type of distribution such as normality is made. The investor's utility is modeled as a piecewise-linear concave function. We derive exact and approximate optimal trading strategies for a robust or maximin expected utility model, where the investor maximizes his worst case expected utility over a set of ambiguous distributions. The optimal portfolios are identified using a tractable conic programming approach. Using the optimized certainty equivalent (OCE) framework of Ben-Tal and Teboulle [6], we provide connections of our results with robust or ambiguous convex risk measures, in which the investor minimizes his worst case risk under distributional ambiguity. New closed form expressions for the OCE risk measures and optimal portfolios are provided for two and three piece utility functions. Computational experiments indicate that such robust approaches can provide good trading strategies in financial markets.

The traditional decision-making framework for newsvendor models is to assume a distribution of the underlying demand. However, the resulting optimal policy is typically sensitive to the choice of the distribution. A more conservative approach is to assume that the distribution belongs to a set parameterized by a few known moments. An ambiguity-averse newsvendor would choose to maximize the worst-case profit. Most models of this type assume that only the mean and the variance are known, but do not attempt to include asymmetry properties of the distribution. Other recent models address asymmetry by including skewness and kurtosis. However, closed-form expressions on the optimal bounds are difficult to find for such models. In this paper, we propose a framework under which the expectation of a piecewise linear objective function is optimized over a set of distributions with known asymmetry properties. This asymmetry is represented by the first two moments of multiple random variables that result from partitioning the original distribution. In the simplest case, this reduces to semivariance. The optimal bounds can be solved through a second-order cone programming (SOCP) problem. This framework can be applied to the risk-averse and risk-neutral newsvendor problems and option pricing. We provide a closed-form expression for the worst-case newsvendor profit with only mean, variance and semivariance information.

Omnichannel retail refers to a seamless integration of the e-commerce channel and the network of brickand-mortar stores. New cross-channel interactions emerge from the integration: (i) cross-channel fulfillment allows inventory to be shared between channels, and (ii) accessible price information induces price-based channel substitution. However, existing price optimization systems have not been able to keep pace with these new interactions. In this paper, we propose a novel multistage stochastic program for the dynamic pricing of a product offered in an omnichannel network incorporating the new interactions. We propose a deterministic and a robust heuristic where, in each period, omnichannel prices and cross-channel fulfillment inventories are jointly optimized via computationally tractable mixed integer programs. In extensive simulations, the heuristics incur an average revenue loss of less than 4% and 8%, respectively. The key benefits of these approaches arise from inventory rebalancing using omnichannel prices (more cross-channel fulfillment inventories from stores with low sell-through rates) and through better management of channel demands. In experiments with historical consumer electronics data of a major U.S. retailer, the proposed analytics shows a 6-12% increase in markdown revenue over the retailer's actual revenue across different categories. A proprietary implementation of the analytics is now commercially available as part of the IBM Commerce Markdown Price Solution and has been piloted for clearance pricing at the retailer. A causal model analysis on the live pilot data shows a 12% increase in clearance period revenue.

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An omnichannel retailer with a network of physical stores and online fulfillment centers facing two demands (online and in‐store) has to make important, interlinked decisions—how much inventory to keep at each location and where to fulfill each online order from, as online demand can be fulfilled from any location with available inventory. We consider inventory decisions at the start of the selling horizon for a seasonal product, with online fulfillment decisions made multiple times over the horizon. To address the intractability in considering inventory and fulfillment decisions together, we relax the problem using a hindsight‐optimal bound, for which the inventory decision can be made independent of the optimal fulfillment decisions, while still incorporating virtual pooling of online demands across locations. We develop a computationally fast and scalable inventory heuristic for the multilocation problem based on the two‐store analysis. The inventory heuristic directly informs dynamic fulfillment decisions that guide online demand fulfillment from stores. Using a numerical study based on a fictitious network embedded in the United States, we show that our heuristic significantly outperforms traditional strategies. The value of centralized inventory planning is highest when there is a moderate mix of online and in‐store demands leading to synergies between pooling within and across locations, and this value increases with the size of the network. The inventory‐aware fulfillment heuristic considerably outperforms myopic policies seen in practice, and is found to be near‐optimal under a wide range of problem parameters.

Problem definition: We study the problem faced by the Philippine Department of Social Welfare (DSWD) in prepositioning relief items before landfall of an oncoming typhoon whose future outcome (trajectory and wind speed) is uncertain. Academic/practical relevance: The importance of prepositioning was a hard lesson learned from Super Typhoon Haiyan that devastated the Philippines in 2013, when many affected by the typhoon did not have immediate access to food and water. In a typhoon-prone country, it is important to build resilience through an effective prepositioning model. Methodology: By engaging with DSWD, we developed a practically relevant stochastic prepositioning model. The probability models of municipality-level demand and of supply damage are both dependent on the typhoon outcome. A linear mixed effects model is used to estimate the dependence of demand on the typhoon outcome using a large data set that includes the municipality-level impact of West Pacific typhoons during 2008–2019. The model has two objectives motivated from the practical realities of the Philippine network: prioritizing regions with high demand and prepositioning in all affected regions proportional to their total demand. Results: We find that the choice of the demand model significantly impacts the distributed relief items in the Philippine setting where it is challenging to adjust region-level supply after a typhoon. By using the historical data on past typhoons, we show that in this setting, our stochastic demand model provides the best distribution to date of any existing demand models. Managerial implications: There currently exists a gap between theory and practice in the management of relief inventories. We contribute toward bridging this gap by engaging with DSWD to develop a practically relevant relief distribution model. Our work is an effective example of collaboration with government and nongovernment agencies in developing a relief distribution model.

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