Direct and indirect grouping strategies for a multi-item probabilistic inventory model

In this paper we develop joint replenishment strategies, namely direct and indirect grouping to find the optimal solution for a multi-item probabilistic inventory problem. Basically, direct grouping is a strategy to group items according to a predetermined ratio of holding cost and minor ordering cost. On the other hand, in indirect grouping strategy, items are ordered every predetermined basic cycle time with a possibility that not all items are ordered. We assume that demands are normally distributed and all shortages are backordered. In developing our model, we also develop an algorithm for direct and indirect grouping. In the numerical experiments, we consider six items with their own parameters, ordered from one supplier, and compare the total inventory cost between direct and indirect grouping strategies. We found that in our examples that indirect grouping strategies gives lower total inventory cost than direct grouping strategy.