Optimal solutions for stochastic inventory models when the lead-time demand distribution is partially specified

Stochastic optimization models used in operations management require that the underlying distributions be completely specified. When this requirement cannot be met, a common approach is to fit a member of some flexibly shaped four-parameter family of distributions (via four-moment matching), and thence use the fitted distribution to derive the optimal solution. However, sample estimates of third and fourth moments tend to have large mean-squared errors, which may result in unacceptable departure of the approximate solution from the true optimal solution. In this paper we develop an alternative approach that requires only first- and second-degree moments in the solution procedure. Assuming that only the first two moments, partial and complete, are known, we employ a new four-parameter family of distributions to derive solutions for two commonly used models in inventory analysis. When moments are unknown and have to be estimated from sample data, the new approach incurs mean-squared errors that are appreciably smaller relative to solution procedures based on three- or four-moment fitting.