Optimization of Batch Ordering under Deterministic Variable Demand

We consider the problem of the optimal ordering schedule to satisfy a given demand pattern over a finite planning horizon when ordering must be in batches of size Q > 1, with and without "setup" cost. A dynamic programming model is constructed. The number of stages are minimized through the characterization of a "complete" set of periods in which ordering must take place and through consideration of the role of initial inventory. The state space and the decision space at each stage are also minimized through considerations of dominance, bounding and feasibility relative to established properties of the optimal schedule. All this results in a most computational efficient algorithm.