Joline Uichanco

When underlying demand follows a complex stochastic process, pricing problems are difficult to solve. In such cases, certainty equivalent (CE) policies, based on the solution to the deterministic relaxation of the stochastic pricing problem, can be used as practical alternatives. CE policies have lighter computational and informational requirements compared with solving the problem to optimality. Although the effectiveness of CE pricing policies has been theoretically studied when demands are independent, performance is not well known when demands are state-dependent and price-changing opportunities are limited. This paper analyzes the performance of CE policies in a pricing problem where future demand depends on sales and inventory, and the firm has limited opportunities to change prices. We show that CE policies are asymptotically optimal; as the problem scale (denoted by m) becomes large, the percentage revenue loss decreases at the rate of ⁢Θ(\sqrtm). We also extend the result to the joint pricing and (initial) inventory problem.

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. 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. 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. 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. 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.

Omnichannel retail refers to a seamless integration of an e-commerce channel and a network of brick-and-mortar stores. An example is cross-channel fulfillment, which allows a store to fulfill online orders in any location. Another is price transparency, which allows customers to compare the online price with store prices. This paper studies a new and widespread problem resulting from omnichannel retail: price optimization in the presence of cross-channel interactions in demand and supply, where cross-channel fulfillment is exogenous. We propose two pricing policies that are based on the idea of “partitions” to the store inventory that approximate how this shared resource will be utilized. These policies are practical because they rely on solving computationally tractable mixed integer programs that can accept various business and pricing rules. In extensive simulation experiments, they achieve a small optimality gap relative to theoretical upper bounds on the optimal expected profit. The good observed performance of our pricing policies results from managing substitutive channel demands in accordance with partitions that rebalance inventory in the network. A proprietary implementation of the analytics is commercially available as part of the IBM Commerce markdown price solution. The system results in an estimated 13.7% increase in clearance-period revenue based on causal model analysis of the data from a pilot implementation for clearance pricing at a large U.S. retailer.

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 affects the accuracy of the SAA heuristic.