Accounting for residual stock in continuous review coordinated control of a family of items

Inventory models which permit coordinated control (or joint replenishment) of families of items are of considerable interest in practice. A major complexity in coordinated control is that, typically, one item triggers the family order and the other items have stock remaining above their reorder points. Account should be taken of this so-called residual stock when establishing the reorder points. In this paper, modelling the inventory position as a diffusion process permits us to develop expressions for the components of the residual stock probability density functions. Heuristics are presented for quick calculation of these expressions. Then we show how residual stock is taken into account in determining the reorder points of the individual items. 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(.