A planning horizon algorithm for deterministic inventory management with piecewise linear concave costs

The authors consider a single-product, discrete-time production/inventory-control problem with nonstationary concave nondecreasing costs. Given a forecast horizon K, the problem is to find a decision horizon. The authors specialize to piecewise linear costs a general approach whereby a problem with horizon K+1 and arbitrary final demand is parametrically solved. The resulting algorithm is polynomial in the input size.