Bounded Production and Inventory Models with Piecewise Concave Costs

An n period single-product single-facility model with known requirements and separable piecewise concave production and storage costs is considered. It is shown using network flow concepts that for arbitrary bounds on production and inventory in each period there is an optimal schedule such that if, for any two periods, production does not equal zero or its upper or lower bound, then the inventory level in some intermediate period equals zero or its upper or lower bound. An algorithm for searching such schedules for an optimal one is given where the bounds on production are −∞, 0 or ∞. A more efficient algorithm assumes further that inventory bounds satisfy “exact requirements.”