Minimization Fractional Prophet Inequalities for Sequential Procurement

• 成果类型: Article
• 署名作者: Qin, Junjie; Vardi, Shai; Wierman, Adam
• 署名单位: Purdue University System; Purdue University; California Institute of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.173
• 发表日期: 2024
• 页码: 928-947
• 关键词: marginal optimal transport; traffic-control; multicommodity; cost; formulation; FLOWS

摘要

We consider a minimization variant on the classical prophet inequality with monomial cost functions. A firm would like to procure some fixed amount of a divisible commodity from sellers that arrive sequentially. Whenever a seller arrives, the seller's cost function is revealed, and the firm chooses how much of the commodity to buy. We first show that if one restricts the set of distributions for the coefficients to a family of natural distributions that include, for example, the uniform and truncated normal distributions, then there is a thresholding policy that is asymptotically optimal in the number of sellers. We then compare two scenarios based on whether the firm has in-house production capabilities or not. We precisely compute the optimal algorithm's competitive ratio when in-house production capabilities exist and for a special case when they do not. We show that the main advantage of the ability to produce the commodity in house is that it shields the firm from price spikes in worst-case scenarios.