Final answer:
The expected inventory levels before and after receiving an order in a (Q, R) policy are calculated using the safety factor, standard deviation of demand, lead time, and order quantity. The formulas consider demand variability and ensure sufficient stock is available both before and after an order is received.
Step-by-step explanation:
The question refers to inventory management strategies within the context of a (Q, R) policy, typically applied in supply chain management and operations. This policy involves determining when to reorder stock (the reorder point R) and how much to reorder (the order quantity Q).
The expected level of inventory before receiving the order is calculated as (z)(STD) + √L, where 'z' is the safety factor based on service level, 'STD' is the standard deviation of demand during the lead time, and '√L' represents the square root of the average lead time. This formula is used to buffer against variability in demand during lead time.
When an order arrives, the inventory level immediately increases by the order quantity Q. Hence, the expected level of inventory immediately after receiving the order is Q + z(STD) √L, reflecting the addition of the new stock (Q) to the existing safety stock level calculated before.