On a Basic Class of Multi-Item Inventory Problems

The paper evaluates and compares classes of multi-item inventory problems, where joint order of several items may save a part of the setup cost. A cost ratio and simple decision rule are determined for joint versus individual orders in specified cases. The comparisons call for the necessity of a new policy for reorder point-triggered random output multi-item systems. This policy, the “random joint order policy,” operates through the determination of a reorder range within which several items can be ordered. The existence of an optimum reorder range is proved, and a computational technique is demonstrated with the help of a machine-interference type queueing model. Under favorable conditions the results exhibited on the diagram of optimum reorder ranges are generally applicable. The random joint order policy model is especially suitable for computer controlled inventory systems.