A Sequential Sampling Procedure for Stochastic Programming

Authors:
Güzin Bayraksan;David P. Morton
Affiliations:
Department of Systems and Industrial Engineering, University of Arizona, Tucson, Arizona 85721;Graduate Program in Operations Research and Industrial Engineering, The University of Texas at Austin, Austin, Texas 78712
Venue:
Operations Research
Year:
2011

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Abstract

We develop a sequential sampling procedure for a class of stochastic programs. We assume that a sequence of feasible solutions with an optimal limit point is given as input to our procedure. Such a sequence can be generated by solving a series of sampling problems with increasing sample size, or it can be found by any other viable method. Our procedure estimates the optimality gap of a candidate solution from this sequence. If the point estimate of the optimality gap is sufficiently small according to our termination criterion, then we stop. Otherwise, we repeat with the next candidate solution from the sequence under an increased sample size. We provide conditions under which this procedure (i) terminates with probability one and (ii) terminates with a solution that has a small optimality gap with a prespecified probability.