Function Design for Improved Competitive Ratio in Online Resource Allocation with Procurement Costs

We study the problem of online resource allocation, where customers arrive sequentially, and the seller must irrevocably allocate resources to each incoming customer while also facing a prespecified procurement cost function over the total allocation. The objective is to maximize the reward obtained from fulfilling the customers’ requests sans the cumulative procurement cost. We analyze the competitive ratio of a primal-dual algorithm in this setting and develop an optimization framework for designing a surrogate function for the procurement cost to be used by the algorithm to improve the competitive ratio of the primal-dual algorithm. We use the optimal surrogate function for polynomial procurement cost functions to improve on previous bounds. For general procurement cost functions, our design method uses quasiconvex optimization to find optimal design parameters. We then implement the design techniques and show the improved performance of the algorithm in numerical examples. Finally, we extend the analysis by devising a posted pricing mechanism in which the algorithm does not require the customers’ preferences to be revealed. Funding: M. Fazel’s work was supported in part by the National Science Foundation [Awards 2023166, 2007036, and 1740551]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoo.2021.0012 .