Periodic Review Probabilistic Multi-Item Inventory System with Zero Lead Time under Constraints and Varying Order Cost

This study treats the probabilistic safety stock n-items inventory system having varying order cost and zero lead-time subject to two linear constraints. The expected total cost is composed of three components: the average purchase cost; the expected order cost and the expected holding cost. The policy variables in this model are the number of periods N_r^* and the optimal maximum inventory level Q_mr^* and the minimum expected total cost. We can obtain the optimal values of these policy variables by using the geometric programming approach. A special case is deduced and an illustrative numerical example is added.