Complete the Problems

Problem 4: What is the impact of lead time, and lead time variability, on inventory levels?

Problem 5: What factors should management consider when determining a target service level?

Problem 6: Consider the (Q, R) policy analyzed in Section 2.2.6. Explain why the expected level of inventory before receiving the order is while the expected level of inventory immediately after receiving the order is.

Section 2.2.6

(2.2.6 Continuous Review Policy We first consider a system in which inventory is continuously reviewed. Such a review system typically provides a more responsive inventory management strategy than the one associated with a periodic review system (why?). Page 42We make the following additional assumptions. • Daily demand is random and follows a normal distribution. In other words, we assume that the probabilistic forecast of daily demand follows the famous bell-shaped curve. Note that we can completely describe normal demand by its average and standard deviation. • Every time the distributor places an order from the manufacturer, the distributor pays a fixed cost, K, plus an amount proportional to the quantity ordered. • Inventory holding cost is charged per item per unit time. • Inventory level is continuously reviewed, and if an order is placed, the order arrives after the appropriate lead time. • If a customer order arrives when there is no inventory on hand to fill the order (i.e., when the distributor is stocked out), the order is lost. • The distributor specifies a required service level. The service level is the probability of not stocking out during lead time. For example, the distributor might want to ensure that the proportion of lead times in which demand is met out of stock is 95 percent. Thus, the required service level is 95 percent in this case. To characterize the inventory policy that the distributor should use, we need the following information: AVG = Average daily demand faced by the distributor STD = Standard deviation of daily demand faced by the distributor L = Replenishment lead time from the supplier to the distributor in days h = Cost of holding one unit of the product for one day at the distributor α = service level. This implies that the probability of stocking out is 1 − α In addition, we need to define the concept of inventory position. The inventory position at any point in time is the actual inventory at the warehouse plus items ordered by the distributor that have not yet arrived minus items that are backordered. To describe the policy that the distributor should use, we recall the intuition developed when we considered a single period inventory model with initial inventory. In that model, when inventory was below a certain level, we ordered enough to raise the inventory up to another, higher level. For the continuous review model, we employ a similar approach, known as a (Q, R) policy—whenever inventory level falls to a reorder level R, place an order for Q units. The reorder level, R, consists of two components. The first is the average inventory during lead time, which is the product of average daily demand and the lead time. This ensures that when the distributor places an order, the system has enough inventory to cover expected demand during lead time. The average demand during lead time is exactly L × AVG The second component represents the safety stock, which is the amount of inventory that the distributor needs to keep at the warehouse and in the pipeline to protect against deviations from average demand during lead time. This quantity is calculated as follows: where z is a constant, referred to as the safety factor. This constant is associated with the service level. Thus, the reorder level is equal to Page 43 The safety factor z is chosen from statistical tables to ensure that the probability of stockouts during lead time is exactly 1 − α. This implies that the reorder level must satisfy:)