This paper considers two popular inventory models: the continuous review and periodic review reorder-point, order-quantity, control systems. Specifically we present two procedures which determine optimal values for the two control parameters (i.e., reorder-point and order-quantity) when the holding-and-shortage costs are non-quasi-convex. This cost structure may arise when non-linear cost rate is considered, for instance when the shortage cost is the shadow cost of a service-level constraint. The algorithms based on a fractional programming method are intuitive and efficient, and as the holding-and-shortage cost functions become quasi-convex, they are compatible to existing algorithms. © 2003 Elsevier B.V. All rights reserved.