Stochastic Optimization and Learning for Two-Stage Supplier Problems

7 Aug 2020  ·  Brian Brubach, Nathaniel Grammel, David G. Harris, Aravind Srinivasan, Leonidas Tsepenekas, Anil Vullikanti ·

The main focus of this paper 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 be inhomogeneous (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 the polynomial scenarios setting; we then employ a novel scenario-discarding variant of the standard Sample Average Approximation (SAA) method, which crucially exploits properties of the restricted-case algorithms. We note that the scenario-discarding modification to the SAA method is necessary in order to optimize over the radius.

PDF Abstract
No code implementations yet. Submit your code now

Categories


Data Structures and Algorithms

Datasets


  Add Datasets introduced or used in this paper