All-or-nothing ordering under a capacity constraint

We consider a special case of the single-item, periodic-review inventory control problem with fixed plus linear ordering costs and an upper bound on production capacity. We assume that the fixed cost is large relative to the variable cost and restrict our analysis to full-capacity orders. We show that the optimal policy is a threshold policy, with respect to the inventory position, for a class of cost-to-go functions that include the class of convex functions.