# Reorder Point

In our description of the EOQ models in the previous sections, we addressed how much should be ordered. Now we will discuss the other aspect of inventory management, when to order. The determinant of when to order in a continuous inventory system is the reorder point, the inventory level at which a new order is placed.

The reorder point for our basic EOQ model with constant demand and a constant lead time to receive an order is equal to the amount demanded during the lead time,

 EXAMPLE12.5 Reorder Point for the Basic EOQ Model

The I-75 Discount Carpet Store in Example 12.2 is open 311 days per year. If annual demand is 10,000 yards of Super Shag carpet and the lead time to receive an order is 10 days, determine the reorder point for carpet.

SOLUTION:

When the inventory level falls to approximately three hundred twenty one yards of carpet, a new order is placed. Notice that the reorder point is not related to the optimal order quantity or any of the inventory costs.

## Safety Stocks

In Example 12.5, an order is made when the inventory level reaches the reorder point. During the lead time, the remaining inventory in stock will be depleted at a constant demand rate, such that the new order quantity will arrive at exactly the same moment as the inventory level reaches zero. Realistically, demand--and, to a lesser extent lead time--are uncertain. The inventory level might be depleted at a slower or faster rate during lead time. This is depicted in Figure 12.5 for uncertain demand and a constant lead time.

Notice in the second order cycle that a stockout occurs when demand exceeds the available inventory in stock. As a hedge against stockouts when demand is uncertain, a safety (or buffer) stock of inventory is frequently added to the expected demand during lead time. The addition of a safety stock to the stockout occurrence shown in Figure 12.5 is displayed in Figure 12.6.

## Service Level

There are several ways to determine the amount of the safety stock. One popular method is to establish a safety stock that will meet a specified service level. The service level is the probability that the amount of inventory on hand during the lead time is sufficient to meet expected demand--that is, the probability that a stockout will not occur. The term service is used, since the higher the probability that inventory will be on hand, the more likely that customer demand will be met; that is, that the customer can be served. A service level of 90 percent means that there is a 0.90 probability that demand will be met during the lead time, and the probability that a stockout will occur is 10 percent. The service level is typically a policy decision based on a number of factors, including carrying costs for the extra safety stock and lost sales if customer demand cannot be met.

## Reorder Point with Variable Demand

To compute the reorder point with a safety stock that will meet a specific service level, we will assume the demand during each day of lead time is uncertain, independent, and can be described by a normal distribution. The average demand for the lead time is the sum of the average daily demands for the days of the lead time, which is also the product of the average daily demands multiplied by the lead time. Likewise, the variance of the distribution is the sum of the daily variances for the number of days in the lead time. Using these parameters the reorder point to meet a specific service level can be computed as

The term in this formula for the reorder point is the square root of the sum of the daily variances during lead time:

The reorder point relative to the service level is shown in Figure 12.7. The service level is the shaded area, or probability, to the left of the reorder point, R.

 EXAMPLE12.6 Reorder Point for Variable Demand

For the I-75 Discount Carpet Store in Example 12.2, we will assume that daily demand for Super Shag carpet stocked by the store is normally distributed with an average daily demand of 30 yards and a standard deviation of 5 yards of carpet per day. The lead time for receiving a new order of carpet is 10 days. Determine the reorder point and safety stock if the store wants a service level of 95 percent with the probability of a stockout equal to 5 percent.

SOLUTION:

For a 95 percent service level, the value of z (from the Normal Table in Appendix A) is 1.65. The reorder point is computed as follows:

The safety stock is the second term in the reorder point formula:

## Determining the Reorder Point with Excel

Excel can be used to determine the reorder point for variable demand. Exhibit 12.6 shows the Excel screen for Example 12.6. Notice that the reorder point is computed using the formula in cell E7, which is shown on the formula bar at the top of the screen.

12-15. Explain in general terms how a safety stock level is determined using customer service level.