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Linear programming (LP) is a widely used tool in the decision-making processes. In practice, the associated parameters are often unknown and the key issue becomes how to interpret these parameters with the real-world data. There are two commonly used approaches. When the unknown parameters only appear in the objective, the point estimation approach is often adopted. This approach estimates the parameters by using statistical methods and then plugs the estimated parameters into the original problem. Consequently, the estimated LP is solved as a surrogate. When the unknown parameters appear in the constraints, the robust optimization approach is often adopted. This approach constructs an uncertainty set for the parameters and then optimizes the objective over the uncertainty set. However, both approaches may yield a large discrepancy from the nominal optimal objective and we call this discrepancy the regret. It is easy to see that both the regret mainly hinges on the data set used to estimate the parameters or construct the uncertainty set. To study the impact of data set, we propose a novel framework that is able to construct the con?dence intervals for both types of regrets as a function of data set, respectively. We ?nd that the regrets (or the widths of con?dence interval) shrink to zero at an order of n-1/2, where n refers to the volume of data set. Furthermore, we design a two-stage procedure to determine the minimal volume of data set required for a prescribed level of regrets.

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