Search for: All records

The main focus of this article is radius-based (supplier) clustering in the two-stage stochastic setting with recourse, where the inherent stochasticity of the model comes in the form of a budget constraint. In addition to the standard (homogeneous) setting where all clients must be within a distance\(R\)of the nearest facility, we provide results for the more general problem where the radius demands may beinhomogeneous(i.e., different for each client). We also explore a number of variants where additional constraints are imposed on the first-stage decisions, specifically matroid and multi-knapsack constraints, and provide results for these settings. We derive results for the most general distributional setting, where there is only black-box access to the underlying distribution. To accomplish this, we first develop algorithms for thepolynomial scenariossetting; we then employ a novelscenario-discardingvariant of the standardSample Average Approximationmethod, which crucially exploits properties of the restricted-case algorithms. We note that the scenario-discarding modification to the SAA method is necessary to optimize over the radius. 

In e-commerce, customers have an unknown patience in terms of how far down the page they are willing to scroll. In light of this, how should products be ranked? The e-commerce retailer’s problem is further complicated by the fact that the supply of each product may be limited, and that multiple customers who are interested in these products will arrive over time. In “Online Matching Frameworks Under Stochastic Rewards, Product Ranking, and Unknown Patience,” Brubach, Grammel, Ma, and Srinivasan provide a general framework for studying this complicated problem that decouples the product ranking problem for a single customer from the online matching of products to multiple customers over time. They also develop a better algorithm for the single-customer product ranking problem under well-studied cascade-click models. Finally, they introduce a model where the products are also arriving over time and cannot be included in the search rankings until they arrive.