Scarf's State Reduction Method, Flexibility, and a Dependent Demand Inventory Model

摘要

The author considers a finite horizon inventory model where the holding, shortage and ordering costs are linear. The demand random variables are dependent and average demand is described by an exponential smoothing formula. This model can be formulated as a two state variable (inventory level, weighted past demands) dynamic program. By using a procedure first developed by Scarf for a Bayesian inventory model, the author is able to reformulate the model as a one state variable dynamic program. This, of course, results in a considerable computational saving over the two state variable formulation. The author also shows that this dependent demand model orders less than or equal the amount that a comparable independent demand model orders. This result is established under the assumption that all demand is returned by the beginning of the next period. (Author)