Summary: We consider an \(N\) period production planning problem in which a sequence of known demands \(d_1, d_2,\ldots, d_N\) must be satisfied. The cost of production in period \(t\) consists of a setup cost \(K_t\) plus a marginal cost per unit \(c_t\). The cost of carrying a unit of inventory into period t is \(h_{t-1}\). An optimal policy is a production plan that satisfies demand at minimum cost.
The main results of the paper are a theorem that decreases the computational effort required to find optimal policies and a theorem that establishes the existence of planning horizons. The results of these two theorems are combined in a forward algorithm for the efficient solution of the problem.