AbstractThis paper presents a basic loss minimization model which has been applied in varying contexts for Polaris logistics problems. Definitive results are obtained in a general framework which extends the classic newsboy problem in two principal directions. First, probability distributions for demand are unrestricted. Second, a general framework for “penalties” or “premiums” is introduced to permit formulation of possibly non‐convex loss functions. The main result is a constructive existence theorem for minimum values of these general expected loss