Optimal policies for inventory models with some specified markets and finite time horizon

The paper presents the deterministic finite time horizon inventory lot size model, without backlogs and with no lead time, for a single commodity, with some specified markets. The specified markets are represented by the family b(t)=ktr of demand functions where k>0, r>-2 are known parameters and t stands for time, 0<t0≤t≤T. The strict positivity of t0. compared to the restrictive condition t0=0 which has been already solved, is crucial and implies entirely different analytical techniques. An important special case is the affine function (r = 1) partly treated already by Donaldson [3]. The problem is to find the optimal schedule of replenishments, i.e., the number and timings of orders. The problem is completely resolved (compared to a recent heuristic by Silver [8]) and the solution is given in a closed form and is proven to be unique. Numerical examples are provided. © 1981.