Multi-item inventory grouping with dependent set-up cost and group overhead cost

Abstract

The inventory control problem can be greatly simplified if the replenishments of inventory items are coordinated with one another. That is, whenever an item is replenished, n other items, where n is a decision variable, are also replenished. One way to ensure this would be to classify the inventory items into several groups with a common order interval for each group. In this paper we establish that the optimal groups will be consecutive by hD/A where h, D and A are the holding cost, demand rate and setup cost of an item, respectively. Using this consecutiveness property and incorporating a group overhead cost we develop a shortest-path model which creates the optimal groups. We compare our results with the policy of inventory coordination using integer multiplier constraints for order cycles.