The diffusion process and residual stock in periodic review, coordinated control of families of items

Inventory control models which provide coordinated control ( or joint replenish ment) of families of items are very useful in practice. These models require expressions for the residual stock levels for each item in the family when a replenishment is placed. In this paper expressions are developed for the periodic review residual stock probability density function, when inventory position is modelled as a diffusion process, and heuristics are presented for quick calculation of these expressions. The importance of residual stock in setting inventory control model parameters is illustrated by showing how residual stock is taken into account in establishing item reorder points. The relationship of these residual stock pdf expressions to other components in a new class of coordinated control models is also discussed. This class of models has been shown to outperform existing models (IBM's IMPACT Inventory Control package).