A Dynamic Near-Optimal Algorithm for Online Linear Programming

Understand

A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding objective coefficient.

• In such a model, a decision variable has to be set each time a column is revealed without observing the future inputs and the goal is to maximize the overall objective function.
• In this paper, we provide a near-optimal algorithm for this general class of online problems under the assumption of random order of arrival and some mild conditions on the size of the LP right-hand-side input.
• Specifically, our learning-based algorithm works by dynamically updating a threshold price vector at geometric time intervals, where the dual prices learned from the revealed columns in the previous period are used to determine the sequential decisions in the current period.