Information collection in a linear program

Consider a linear program where the cost coefficients are uncertain, for which we have a Bayesian prior. We can collect information to improve our understanding of these coefficients, but this may be expensive, giving us a separate problem of optimizing the collection of information to improve the quality of the solution relative to the true cost coefficients. We formulate this information collection problem for linear programs for the first time, and derive a knowledge gradient policy which maximizes the marginal value of each measurement. We prove that this policy is asymptotically optimal, and demonstrate the performance of our algorithm on a network flow problem.