A South German mechanical engineering company needs 20 complex gearboxes per week (1 year = 50 weeks) from its key supplier from the Lake Constance. The order costs amount to 450 Euro, the inventory holding costs 950 Euro per year per unit. The lead time is 6 weeks.

Last year, the company found out that demand fluctuated considerably during lead time. Hence, they often had to delay delivery, which resulted in additional costs of 750 Euro per unit. The purchasing department has measured the demand during delivery time and found the following discrete distribution: in 6% of the cases demand during lead time was 100 units, in 29% 110 units, in 31% 120 units, in 26% 130 units and in 8% 140 units of gearboxes.

On this basis, determine the optimal reorder point including safety stock, the corresponding costs and the level of safety stock. Eventually, calculate the cost advantage of safety stock.

Cost advantage (difference expected additional cost) of optimal reorder point with safety stock over optimal reorder point without safety stock: