Inventory positioning and optimal cycle service level in a supply chain under stochastic demand and lead time

In this research, the inventory positioning problem under stochastic demand and lead time is solved by a mixed-integer programming model. The inventory placements involve a decision that determines where to keep safety stocks within a supply chain network such that the total holding inventory cost is minimized while maintaining an acceptable customer service level (CSL). In this study, the decision variables are theposition, amount of safety stock at each location, and service level while the objective function is the total holding inventory cost. The total holding inventory cost includes the holding cost of raw materials, the holding cost of finished goods, the shortage costof raw materials, and the shortage cost of finished goods. The commercial methodology is used to find the optimal solution for each model. In addition, this study concerns three mathematical models including the basic inventory positioning model, the singleservice level model, and the multiple service levels model. Selected numerical experiments and a case study are presented to examine the applicability of the proposed mathematical model. The findings indicate that the optimal results are easily obtained via a commercial solver and the proposed approach is suitable for various types of supply chain networks.