Consider a newsboy problem with known demand and random replenishment. The distribution of the replenishment quantity is determined by a location-scale parameter, (μ, σ), which can be controlled. The usual expected cost function includes a separate term associated with the choice of σ. The asymptotic behavior of the optimal parameter values, as functions of the holding and shortage costs, is examined.
Rose, John S. 1990. "The Newsboy with Known Demand and Uncertain Replenishment: Applications to Quality Control and Container Fill." E.C.R.S.B. 90-1. Robins School of Business White Paper Series. University of Richmond, Richmond, Virginia.